## Matrix in ABAQUS

Matrices: Stiffness, Mass, Viscous Damping, Structural Damping, Load

Formats:

- FORMAT=MATRIX INPUT (default) to specify that the output use the matrix input text format that is consistent with the format used by the matrix definition technique in Abaqus/Standard.
- FORMAT=LABELS to specify that the output use the standard labeling format.
- FORMAT=COORDINATE to specify that the output use the common mathematical coordinate format.

## Extract Element matrices

It is simple and just edit the keywords in input file. As the ***STEP** in input file, adding the keywords in the last two lines after the definition of step.

** STEP: Step-1 ** *Step, name=Step-1, nlgeom=NO, perturbation *Frequency, eigensolver=Lanczos, acoustic coupling=on, normalization=displacement , , 10., , , *Element Matrix Output,Elset=SET-2, File Name=filename,Frequency=1,Output File=User Defined,Stiffness=Yes,Mass=Yes

**Explanation**: Elset, means the element set that you want to extract matrix from. File Name, you can name it as what you want and a *.mxt* file with this name will be generated in your file folder. In a nonlinear analysis, Dload=Yes can be used to extract the load vector from distributed loads on the element. The exact meanings are detailed in keyword *ELEMENT MATRIX OUTPUT in Abaqus Keywords Reference Guide.

## Extract Global Matrices

It is also easy to extract global matrix. You need to add the following codes at the end of the input file or adding these lines before or between step definitions. The difference of the positions in input file between the three lies on the matrices after which step.

** *STEP *MATRIX GENERATE, STIFFNESS, MASS *MATRIX OUTPUT, STIFFNESS, MASS, FORMAT=MATRIX INPUT *END STEP

After completing the analysis, two *.mtx* files with the name *jobname_STIF2* and *jobname_MASS2 *(2 is the location number of the this step, i.e. the second step) will be generated in your file folder. Open the *jobname_STIF2* file and you will find texts as follows.

1,1, 1,1, 1.000000000000000e+36 1,5, 1,1, 9.283850055777577e-12 1,6, 1,1, -4.181074365176346e+04

The meaning of the five numbers in a line are respectively:

- Row node label
- Degree of freedom for row node
- Column node label
- Degree of freedom for column node
- Matrix entry

**Note 1**: It is noted that a step containing the mass matrix must be used to extract mass matrix. For example, the under a *Static step, the equation of structure is **K****x**=**F** and is not related to mass, and as such the mass matrix can not be extracted. In this example, a *Frequency step is defined.

All structural analyses apart from static will involve calculation and manipulation of the mass matrix.

Static case: **Kx = f**

Eigenvalue (modal or free vibration): **Ma +Kx = 0**

Dynamic (transient): **Ma + Cv + Kx = f(t)**

**Note 2**: This keyword is not available in Abaqus/Explicit and the analysis will be terminated.

Codes I often use in abaqus to extract matrices in dynamic implicit analysis

** *STEP *MATRIX GENERATE, STIFFNESS, MASS, STRUCTURAL DAMPING, VISCOUS DAMPING *MATRIX OUTPUT, STIFFNESS, MASS, STRUCTURAL DAMPING, VISCOUS DAMPING, FORMAT=COORDINATE *END STEP

## 103 comments On Extract Matrix from ABAQUS

Tan NguyenCould you help me to add to my inp. file for extracting stiffness and mass matrix?

*Heading

** Job name: TAN Model name: Model-1

** Generated by: Abaqus/CAE 2018

*Preprint, echo=NO, model=NO, history=NO, contact=NO

**

** PARTS

**

*Part, name=Part-1

*End Part

**

**

** ASSEMBLY

**

*Assembly, name=Assembly

**

*Instance, name=Part-1-1, part=Part-1

0., 2900., 0.

*Node

1, 0., -2900.

2, 0., 1100.

3, 4000., 1100.

4, 4000., -2900.

5, 0., -2500.

6, 0., -2100.

7, 0., -1700.

8, 0., -1300.

9, 0., -900.

10, 0., -500.

11, 0., -100.

12, 0., 300.

13, 0., 700.

14, 400., 1100.

15, 800., 1100.

16, 1200., 1100.

17, 1600., 1100.

18, 2000., 1100.

19, 2400., 1100.

20, 2800., 1100.

21, 3200., 1100.

22, 3600., 1100.

23, 4000., 700.

24, 4000., 300.

25, 4000., -100.

26, 4000., -500.

27, 4000., -900.

28, 4000., -1300.

29, 4000., -1700.

30, 4000., -2100.

31, 4000., -2500.

*Element, type=B21

1, 1, 5

2, 5, 6

3, 6, 7

4, 7, 8

5, 8, 9

6, 9, 10

7, 10, 11

8, 11, 12

9, 12, 13

10, 13, 2

11, 2, 14

12, 14, 15

13, 15, 16

14, 16, 17

15, 17, 18

16, 18, 19

17, 19, 20

18, 20, 21

19, 21, 22

20, 22, 3

21, 3, 23

22, 23, 24

23, 24, 25

24, 25, 26

25, 26, 27

26, 27, 28

27, 28, 29

28, 29, 30

29, 30, 31

30, 31, 4

*Nset, nset=_PickedSet2, internal, generate

1, 31, 1

*Elset, elset=_PickedSet2, internal, generate

1, 30, 1

** Section: Section-1 Profile: Profile-1

*Beam Section, elset=_PickedSet2, material=Material-1, temperature=GRADIENTS, section=RECT

100., 100.

0.,0.,-1.

*End Instance

**

*Nset, nset=_PickedSet4, internal, instance=Part-1-1

1, 4

*End Assembly

**

** MATERIALS

**

*Material, name=Material-1

*Density

7.85e-09,

*Elastic

200000., 0.3

**

** BOUNDARY CONDITIONS

**

** Name: BC-1 Type: Symmetry/Antisymmetry/Encastre

*Boundary

_PickedSet4, ENCASTRE

** —————————————————————-

**

** STEP: Step-1

**

*Step, name=Step-1, nlgeom=NO, perturbation

*Frequency, eigensolver=Lanczos, sim, acoustic coupling=on, normalization=mass

5, , , , ,

**

** OUTPUT REQUESTS

**

*Restart, write, frequency=0

**

** FIELD OUTPUT: F-Output-1

**

*Output, field, variable=PRESELECT

*End Step

DorothyIf you want element matrices, just add the codes as I did. And If you want global matrices, just add the codes as another step which you can find in this article. If you have further questions, please feel free to email me.

Qinbo ZhouHello,

Thank you so much for this nice-presented work! It’s quite useful. I used the command to generate global mass and stiffnes matrix. But it seems that the mass matrix is only global LUMPED MASS MATRICES. What if I want to generate global CONSISTENT MASS MATRICES using abaqus?

Looking forward to your reply!

DorothyHi Qinbo, if you use consistent mass for the model, you can then get consistent mass matrix. What you mean seems to be related to the matrix, actually the mass will be distributed to nodes and what you get from abaqus is just the right answer. You can calculate the mass matrix of a simple model with consistent mass and compare with what you get from abaqus. If you have further questions, please feel free to reply or email me.

Zeyu LinHello Dorothy,

Thank you so much for your article! I have the same question with Qinbo, and I want to generate global consistent mass matrices too. How can I use or define consistent mass for my model ? Looking forward to your reply and thanks in advance!

DorothyHi Zeyu,

If you defined the material density for your model and did not use point mass, then what you get by generating the global mass matrix will be the consistent mass matrix. The default mass matrix in Abaqus is the consistent one. If there is non-zero non-diagonal element in the generated matrix, then you can be sure you got the consistent mass matrix.

JIM ZHANHas your problem been solved? I also use ABAQUS to extract the LUMPED mass matrix.

JIM ZHANHello Zeyu,

Have you solved this problem? The mass matrix extracted by ABAQUS now is also a lumped mass matrix, and a consistent mass matrix cannot be obtained.

Nikhil KHello Dorothy,

Thanks for this article. I have some doubt in further usage of these mass and stiffness matrices. I would like to find natural frequencies using Matlab (e = eig(K,M);) by finding eigenvalues and taking their square roots.

First of all, my matrices’ size is thrice the number of nodes (actually it is a 3D problem, but DOFs isn’t 6 per node, I need a bit clarification on this too). So, I’m getting the same number of eigenvalues from Matlab as that of the size of mass and stiffness matrices and the results are not the same as that obtained from Abaqus (1st 10 natural frequencies are not matching).

Please clarify

DorothyHi Nikhil,

Did you compare the mass matrix and stiffness matrix from abaqus and the ones you used in matlab? I suggest you make a comparison.

Another thing is that the mass calculated in abaqus is distributed mass if you did not add the mass on nodes, while we tend to use lumped mass for convenience.

Since the dofs per node in your problem is not 6, abaqus magnifies the elements in stiffness matrix for fixed dofs while we prefer to delete the corresponding rows and columns in K matrix.

The different methods in dealing with mass matrix and stiffness matrix may lead to different eigenvalues. If the relative errors of eigenvalues are within 5%, the results are acceptable.

DHEERAJ KULKARNIHello Dorothy,

Nice article. Thank you.

I used the 2nd method to generate global mass and stiffness matrices. But what I found is, the total mass calculated in Abaqus and the sum of all the entries from .mtx files are not matching. Analytical way mass calculation (density*volume) is agreeing with Abaqus result, but not with extracted matrix. So, the Abaqus answer is right.

Can you please help?

Thank you in advance

DorothyHi Dheeraj,

Do you mean the sum of mass matrix is not consistent with the total mass you calculated with density*volume? It is the right case because you have two/three directions (for 2D/3D problem) in the model and the load applied to it may induce deformation(velocity, acceleration) in two/three directions. So, the different directions have the same mass for distributed mass condition. If mass only exists in gravity, there will be no deformation(velocity, acceleration) in other directions. The sum of mass matrix from abaqus should be two/three times of the total mass you calculated for distributed mass condition.

AKBjkHello Dorothy,

Thanks for this article. I followed your instruction and then get the element stiffness matrix successfully. But yet I don’t know the meaning of the stiffness matrix element. For example, when I deal with a beam section from your article “Beam elements in ABAQUS”, it outputs the matrix as：

1062000.0000000 ,

0.0000000000000 , 43264.656088429

0.0000000000000 , 0.0000000000000 , 43264.656088429

0.0000000000000 , 0.0000000000000 , 0.0000000000000 , 4553.8475200000

0.0000000000000 , 0.0000000000000 , 21632.328044215 , 0.0000000000000 16736.164022107 ,

0.0000000000000 , -21632.328044215 , 0.0000000000000 , 0.0000000000000 0.0000000000000 , 6736.164022107

Can you explain to me how can I associate this matrix with the section property?(EI、EA、etc)

Looking forward to your reply!

DorothyHi Akbjiang,

The elements in stiffness matrix is associated with node number and the degree of freedoms of each node. You can check the meaning from https://zxding.me/archives/d702tw.html or http://abaqus.software.polimi.it/v6.14/books/usb/default.htm?startat=pt04ch10s03at32.html#usb-anl-amtxgenerationperturbation. You cannot get section properties from stiffness matrix because stiffness matrix is related to both section properties and the length of elements. If you were doing nonlinear analysis, the stiffness matrix will change during the analysis. It seems you were using beam element. You can check E from material property and I and A from the sections you defined in Property Module.

AKBjkHello Dorothy,

Thanks for your kindly reply, actually I wonder how abaqus calculate the element stiffness matrix and is there any relation of the element stiffness matrix we derived from abaqus and the section properties we input(for example, we input EA、EI、GJ as section properties when use MESHED), how can I get the stiffness matrix manually if node number and the degree of freedoms is determined?

Looking forward to your reply!

DorothySorry for the late reply. Something was wrong about the WordPress email. The stiffness matrix is definitely related to the section properties and also the meshing size. You can find the derivation of the stiffness matrix in any finite element book. This is one recommendation for you and you can download the PDF file from this link, http://web.mit.edu/kjb/www/Books/FEP_2nd_Edition_4th_Printing.pdf . You can also watch the lecture videos given by Prof. Bathe from MIT https://ocw.mit.edu/resources/res-2-002-finite-element-procedures-for-solids-and-structures-spring-2010/linear/. There is also course on nonlinear finite element analysis in MIT open course. If you just want to derive the initial stiffness matrix, you can just focus on the linear part which is much easier. There are also many lecture ppts online and you can find the derived matrix and just use it directly. The stiffness matrix of beam element is easier and there are at least three different stiffness matrix because of different consideration such as shear effects and integration method. The stiffness matrix you got from abaqus is also related to your settings about shear stiffness of beam section in Property module. For the setting, you can check the abaqus analysis user’s guide from http://130.149.89.49:2080/v2016/books/usb/default.htm .

NehaHi Dorothy!

I am also extracting the element stiffness matrix in the analysis. The .mtx file that is given out by Abaqus has the same format as mentioned in the above comment as:

“1062000.0000000 ,

0.0000000000000 , 43264.656088429

0.0000000000000 , 0.0000000000000 , 43264.656088429

0.0000000000000 , 0.0000000000000 , 0.0000000000000 , 4553.8475200000

0.0000000000000 , 0.0000000000000 , 21632.328044215 , 0.0000000000000 16736.164022107 ,

0.0000000000000 , -21632.328044215 , 0.0000000000000 , 0.0000000000000 0.0000000000000 , 6736.164022107”

I am struggling to understand the pattern in which the matrix element are written. Can you help me understand this matrix? It is for sure the lower or upper triangular format. But what id pattern?

ddanielDear All,

thank you for your very interested post.

I am aware of how to get out these matrices from Abaqus.

However I have not found yet any way to get out the MODAL mass/stiffness/damping matrices.

I am running a frequency analysis (my model has also some damping properties) and I would like to get the modal matrices.

This means if [M], [K], [C] are the mass,stiffness and damping matrices and [Φ] the eigevectors matrix I would like to get out

[Φ]'[M][Φ], [Φ]'[K][Φ], [Φ]'[C][Φ].

Does anyone know the way?

Thank you in Advanced,

ddaniel

DorothyHi Ddaniel,

You can try to use the following codes to get the M, K, C matrices, it should work.

`*MATRIX GENERATE, STIFFNESS, MASS, STRUCTURAL DAMPING, VISCOUS DAMPING`

*MATRIX OUTPUT, STIFFNESS, MASS, STRUCTURAL DAMPING, VISCOUS DAMPING, FORMAT=COORDINATE

To get the eigenvectors, you should first request eigenvectors at all nodes. Here is the link related to this, https://abaqus-docs.mit.edu/2017/English/SIMACAEANLRefMap/simaanl-c-freqextraction.htm. Since I never extracted eigenvector before and abaqus is now not available to me, I am not sure how to do. You can have a try after requesting the eigenvectors.

Please feel free to contact me if any questions.

ddanielDear Doothy,

thank you very much for your prompt reply.

What you describe is exactly what I am currently doing.

However I was hoping for a way to get the modal M,K,C matrices directly from Abaqus (this is something posible to be done for example with Nastran) without the need to multiply them with the eigenvectors matrix my self.

Best Regards,

ddaniel

DorothyHi Ddaniel,

Now I clearly understand what you want from abaqus. I think the ‘OUTPUT’ part in this link may be helpful. The generalized mass is written automatically to the output database as history data.

DianaHi Dorothy,

I would like to extract the stiffness matrix at the initial step of the analysis and then after cracking occurs. I would like to view how the stiffness changed with the cracks.

Is this possible. Thank you

DorothyHi Diana,

You can add a step to extract the initial stiffness matrix and also a step after your cracking analysis for the final stiffness matrix. As far as I known, it’s not possible to extract stiffness matrix during the analysis for each substep. You can check the abaqus documents.

KatyHi Dorothy,

I tried using the code for the extraction of element mass and stiffness matrix. The stiffness matrix works fine but not for the mass matrix in which I find a diagonal matrix. The problem is that I cannot calculate the eigenvalues with such a mass matrix. I tried to do the same for a cantilever beam and it works well but not for my 2D model. Can you help me with that? Thank you in advance

DorothyHi Katy,

To my best knowledge, the eigenvalues could be calculated with a lumped mass matrix which is a diagonal matrix. If you want consistent mass matrix, it should work if you avoid using point mass.

KatyHi Dororthy,

I didn’t find a way to find the eigenvalues with a lumped mass can you share it if you know. And for the second option I would like to know how to do that in Abaqus.

DorothyHi Katy,

I am a little confused with your question, so I will explain what may be useful to you.

For the eigenvalues given by abaqus, you can go to the location where your abaqus job files are saved, then you search the

jobname.datfile and you can find the eigenvalue output with eigenvalues and frequencies.For the manual calculation of eigenvalues, you can use the matlab code

`[eigen_vec, w_square] = eig(K, M)`

, in which the K and M are the stiffness matrix and mass matrix you have, and the w_square is the eigenvalue (which is the eigenvalue in abaqus). You can get the frequency w in rad/s (which is the frequency in rad/time in abaqus) by taking square root of w_square and w/(2*pi) in Hz.If you use the material with density and do nothing else in abaqus, you will get consistent mass matrix, which will have non-diagonal elements because of the shape function of the element. If you want to use lumped mass matrix which only have diagonal elements, do not define density in material and go to the ‘

Property‘ module and then go to the ‘Special->Inertia‘ to create the point mass/inertia. After successfully defined the point mass at the nodes you want, there will be a green square at the node with point mass.Hope these could help you and feel free to contact me if you have further questions.

Remya NairI have extracted the stiffness and mass matrix of an assembly, two beams bolted together. I created one beam as part and the other beam is a copy of this beam. I have to apply boundary conditions on certain nodes in the stiffness matrix. But when I created node-set, both my instances have the same node numbers. How to relate this to the stiffness matrix.

DorothyHi Remya,

I did not deal with this before, but I think one way to get the stiffness matrix related to the node numbers is renumbering the nodes. Here is the link about how to renumber the nodes.

Alirezahi Dorothy

i have modeled a 2D-plate using Q4 element in matlab. i have used consistent formulation of mass matrix to form the elemental mass matrix of the plate and then assembled them to creat the Global mass matrix of the plate. to extract the eigenvalues, i used eig(K,M) in matlab. i did the same in abaqus to model a 2D plate using CPS4 element in plane stress condition. the stiffness matrix calculated by abaqus is as same as the matlab. but the mass matrix extarcted from abaqus seems to be lumped mass matrix, because it’s numebr of values are as equal as the number of DOFs. so the first 3 eigenvalues calculated by matlab are 100 times greater than those of calculated by abaqus.

do you know the reason of this diffrence? is it possible to model a 2D-plate in abaqus whose mass matrix is consistent?

thank you.

DorothyHi Alireza,

From my understanding, abaqus uses consistent mass matrix by default. One can obtain lumped mass matrix only by create the point mass/inertia. If you only define the material density for your plate, the mass matrix should be the consistent one. You can double check the mass matrix you obtained from abaqus and also the one you have in matlab. I once compared the eigenvalues for a beam element from consistent and lumped mass matrix. The first eigenvalue is the same corresponding to rigid body motion, and the second one is about two times with consistent mass matrix.

AlirezaThanks for your response.

I have compared both mass matrices extracted from Matlab and Abaqus. As I mentioned it in my first comment, the number of mass matirx entries calculated by Abaqus are equal to the number of DOFs, which means it is a diagonal mass matrix.

I have used Abaqus’ mass matrix values to form a diagonal mass matrix in Matlab. I have employed eig(K,M) again to extract the eigenvalues. The extracted eigenvalues didn’t differ from the previous ones (using consistent mass matrix). I was wondered because I used diagonal mass matrix instead of consistent mass matrix. so I have another question. Do you know how Abaqus calculates the eigenvalues? because Abaqus and Matlab gave the same stiffness matrix and the only diffrence between them was in the mass matrix. Actually I couldn’t understand where the problem was.

Thank you again.

DorothyHi Alireza,

The method for eigenvalue calculation in abaqus depends on which eigensolver you choose in ‘STEP’. It could be Lanczos, subspace or AMS. I used Lanczos method before for a simply supported rectangular plate and the differences of the eigenvalues are within 35% and 10% for the first 10 modes with a coarse and fine mesh respectively. I extracted the mass matrix of this model, and the first ten rows in .mxt file are shown as:

`1,1, 1,1, 1.838929123451831e-03`

2,1, 1,1, 1.837295790156881e-03

12,1, 1,1, 1.837295790156881e-03

13,1, 1,1, 1.836479123509406e-03

1,2, 1,2, 1.838929123451831e-03

2,2, 1,2, 1.837295790156881e-03

12,2, 1,2, 1.837295790156881e-03

13,2, 1,2, 1.836479123509406e-03

1,3, 1,3, 3.266666589899999e-03

2,3, 1,3, 1.633333294950000e-03

You can see the matrix does have off-diagonal elements. Maybe somewhere in your model is not correct.

Aloys DushHello Dorothy,

I am very thankful for the help I am getting from you. However, I want to use the mass, stiffness, and damping matrices from Abaqus to define a state space system: Xdot= Ax+Bu and Y=Cx+Du

In this system, the matrices A and B requires the knowledge of Mass, Stiffness and Damping matrices (Which I can get from Abaqus as you described in the previous texts). My problem is how the matrices from Abaqus are arranged? for example, you mentioned that the last column indicates the matrix entry, does this means we ignore other columns you explained as 1st row: Row node label, 2nd row: degree of freedom for row node, 3rd row: Column node label, and 4th row: Degree of freedom for column node? I mean do we only consider the last row i.e. Matrix entry? if yes how does it mean that the matrices are row vectors?

Kind Regards

DorothyHi Dush,

Sorry for replaying late, I was focusing on my qualifying exams and thankfully it will ends tomorrow. In your case, you need global matrices which you need to form yourself according to the outputs. I would suggest the matrix input format (I used in this post). Let assume you have 10 nodes (indexing from node 1 to node 10) each with 3 dofs for better explanation. Then you will have a 30*30 global matrix. Let’s say in each line we get “n1, d1, n2, d2, v” from the output, then you will have your matrix element with value of v at the [(n1 -1)*3 + d1] th row and [(n2 – 1)*3 + d2] th column.

Hope this helps. Please feel free to let a comment if you have further questions.

AlirezaHi Dorothy,

Thanks a lot for your attention and fast response. Could you please give me your Email? I have some more questions about mesh numbers you used and the first 10 natural frequencies you extracted from Abaqus. I will be appreciated you.

Best regards.

DorothyHi Alireza,

My email address is zhixiading@outlook.com. Please feel free to email me. Hope that I can help.

Karthikayen RajuHi Dorothy!

why cannot we extract matrices in abaqus explcit?

DorothyHi Karthikayen,

I am not sure what the reason is. I tried but the codes could not work. If you know the reason, please let me know. I am also confused.

One way to extract matrices in abaqus/explicit is to add keywords for one more step.

`**`

*STEP

*MATRIX GENERATE, STIFFNESS, MASS, STRUCTURAL DAMPING, VISCOUS DAMPING

*MATRIX OUTPUT, STIFFNESS, MASS, STRUCTURAL DAMPING, VISCOUS DAMPING, FORMAT=COORDINATE

*END STEP

LarsHi Dorothy,

I managed to extract the mass and stiffness matrix from my Abaqus model, however, the mass matrix is a lumped (diagonal) matrix. How can I extract the consistent mass matrix instead? I use 3D solid elements.

Thanks in advance!

Kind regards.

Lars

DorothyHi Lars,

I only tried beam element before. To my best knowledge, consistent mass matrix is the default setting in abaqus. To get consistent mass matrix, one needs to avoid defining point mass and use material density only. Hope this helps.

PanidaHi Dorothy,

This is a good article!!! Because I am new in this field. I am confused that how I add the code in .inp file as an input file. Because we will get the .inp file after completing the run of model. Please tell me how to do this.

Thank you

DorothyHi Panida,

You can right click your model in the model tree, then click ‘Edit Keywords’. Hope this helps.

PanidaThank you so much for your kind reply. I read all your comments that replied to everybody. It is very useful. Now I got the mass matrix and stiffness matrix as your article. I modeled a 2D plate in Abaqus to get mass matrix and stiffness matrix, Then these matrices are input to MATLAB. And I have some questions below;

1. How to extract mass matrix and stiffness matrix that contain only Row node label, Column node label, Matrix entry (like 443 509 6.040995098525574e-04)?

2. Can the mass matrix and stiffness matrix are used for all mode shapes (like my problem considers only the first five mode shapes)?

3. Now I have known that I have to use the synx code ( [Phi,Wn]=eig(K,M)) to plot eigenvector but still confused how to write the MATLAB code. If you have the code for plotting mode shape, could you please share to me as an example?

Look forward to your reply

Thank you in advance

DorothyHi Panida,

Hope you find the following helpful. Please feel free to leave questions in comments.

R1: You can switch the format from ‘matrix input’ to ‘coordinate’, like

`*MATRIX OUTPUT, STIFFNESS, MASS, FORMAT=COORDINATE`

. Then, you will get matrix like this`1 1 1.962500490625005e+00`

. The first and second are the row and column numbers in the matrix.R2: Of course you can use the mass and stiffness matrices for all mode shapes since mass and stiffness are the properties of a structure. As long as you use the same structure and do not consider the damage after analysis, the mass and stiffness matrices are the same.

R3: Mode shape is closely related to your structure, so most codes are specific to particular structure. You might need to write your own. You can start with plotting the original structure, and then add the scaled ‘displacements’ from mode analysis to corresponding nodes.

PanidaHi Dorothy,

Thank you for your prompt reply. I really appreciate your kindness.

I have got mass and stiffness matrices by changing the format to ‘coordinate’. But I wonder that the number of rows and columns is higher than the format ‘matrix input’.

For example, A model has around 6000 elements (check from mesh). The format ‘matrix input’. also has around 6000 elements, BUT the format to ‘coordinate’ has around 40,000 elements. I think I misunderstand on something. Could you please clarify. Thank you.

DorothyHi Panida,

The 40,000 rows/columns are correct since the ‘coordinate’ format expands the matrix from ‘matrix input’ by ignoring the node numbers and degrees of freedoms.

You have around 6,000 elements and each element has 6 degrees of freedoms. Then the matrices should have around 6,000*6=36,000 rows/columns.

If you look at the

.mtxfiles from ‘matrix input’ and ‘coordinate’, you should have the same numbers of lines.Hope this helps.

PanidaHi Dorothy,

Thank you so much for your advice. It helps me a lot. I will try to continue my simulation further.

Stay safe during epidemic 🙂

Best Regards,

SasthaHi Dorothy,

With your good reference i was able to extract mass matrix for my problem, but i didn’t understood the significance of first 4 terms of the .mtx file (Row node label, Degree of freedom for row node, Column node label, Degree of freedom for column node). How can i get a single mass matrix entry for a single node or How to obtain the value which is assigned to a single node. If my problem is not clear to you i will mail you with the attached .mtx file. Hoping to hear good from your side.

DorothyHi Sastha,

From my understanding to your question, you want to have only the mass on one node instead of the mass at all nodes in the mass matrix. If so, you can search for the entry from the mass matrix according to the number and degrees of freedom of that node. For example,

`2,2, 2,2, -4.181074365176346e+04`

, means this is the mass in the second degree of freedom for node 2 and it is in the diagonal element in the mass matrix. Another way is to extract the mass matrix for all elements that containing that node, so that you can find the element more quickly and also save time in outputting a big global matrix. But in this way you need to calculate the mass element manually or with some software such as matlab. I didn’t try this before, but it should work.If this is not what you mean in the question, please feel free to contact me.

SasthaHi Dorothy,

Thank you for your immediate response, actually I need find a single mass value acted on each node, so how to find that singular mass value for that particular node? Here we can get many values of mass attached to a particular node according to different degrees of freedom. So how to obtain the net mass value which is being acted on that particular node.

Hoping to hear good from your side.

Regards,

SASTHA

DorothyHi Sastha,

As far as I know, there is no such a convenient way to just extract one mass value for a node. Feasible way to achieve the mass value on a node would be either the one I mentioned in the previous reply. If you want to extract the mass matrix for all elements that containing that node, you can first define an element set and then generate mass matrix for this set only.

SasthaHi Dorothy,

Thanks for the followup, I will find an alternative way for solving the same. I will definitely update you once i am done. Thank you once again for your support will keep in contact.

Regards,

Sastha

IvanHi Dorothy,

I managed to extract the mass and stiffness matrix from abaqus, please guide me on hw to read the sparse matrix in matlab. I am abit confused on the numbering of the matrices

DorothyHi Ivan,

If you output the matrices with ‘matrix input’ format, the first four numbers are the row node number, degree of freedom of the row node, column node number, degree of freedom of the column node, respectively.

If you output the matrices with ‘coordinate’ format, the first two numbers are the row number and column number.

You can assemble the matrices according to the first four or two numbers in a mathematical way.

Hope this helps.

SREESASTHARAMHi Dorothy,

I was a bit confused with the incorporation of boundary condition for Dynamic Analysis of Cantilever with base excitation. Can you try help me to figure out this. In my analysis there is cantilever with a tip, as we know one end of the cantilever must be fixed but to where we can incorporate displacement boundary condition (base excitation) on to the cantilever. Here i can’t attach my model, if it is possible I can send the model image via email

DorothyHi Sreesastharam,

I am not sure what you are confused about from the description. If you need the stiffness matrix, you can extract the matrix and ABAQUS will assign a large value (1.000000000000000e+36) for fixed nodes. Hope this will help.

DanHi Dorothy,

Thanks very much for this article. Just wondering whether you can change the format of the element stiffness matrix output file for use in MATLAB afterwards; currently, the output file has lots of text surrounding the matrix data (e.g. Element number or type) for each element, which is making it challenging to extract only the element stiffness matrix values. Is there a way to make the Abaqus output file more MATLAB-friendly, or alternatively do you know of some MATLAB code that could extract only the element stiffness matrix data, without the text between each element?

Many thanks for your help!

DorothyHi Dan,

As far as I know, there is no such a way in abaqus to extract only numbers for element matrices. You can do it in matlab with some commands for reading files like

`fgetl`

.Also, the output matrices from abaqus follow some patterns. You can take advantage of the patterns when read with matlab.

Hope this helps.

Dan`Hi Dorothy,

Thanks very much for this article. Just wondering whether there was a more MATLAB-friendly output format for the Abaqus element stiffness matrix file. The current output has lots of text between each element (describing element number or type for example), making it challenging to extract only the element stiffness matrix data. Do you know of a way to change the format of the output of Abaqus element stiffness matrices, or alternatively a MATLAB code that can extract only the element stiffness matrix data from the Abaqus file?

Many thanks!

DorothyHi Dan,

Please check the response under your first comment. Sorry about the late reply. The emails from wordpress keep going into junk folder in my outlook even though I reported this problem. I have to check every a few days and cannot see the comments in time, very annoying.

S4JJ4DHi,

Abaqus2Matlab package enables you to extract stiffness matrix in various formats suitable for MATLAB manipulation. I am not sure but maybe you can use it for your intended post-processing operations. The link to this free tool:

https://abaqus2matlab.wixsite.com/abaqus2matlab

DorothyHi Sajjad,

Thank you for sharing! This is really an awesome website!

EvaHi Dorothy,

Many thanks for putting this nice resource together!

I am trying to recreate a model from COMSOL in Abaqus. The geometry, material properties and boundary conditions are identical, but there are some discrepancies in the mass and stiffness matrices (and hence the natural frequencies, around 2% difference). Any ideas on why this is the case/how to get them to match? I am using C3D15 elements.

Thanks,

Eva

DorothyHi Eva,

From my perspective, 2% difference is totally acceptable. Even though you have two ‘same’ models in different software, the results could differ a little bit. The tolerance for iterations, the precision of numerical calculations, the default method (if you did not specify) for frequency analysis could differ. All these would lead to discrepancies in final results. I would accept both models if the discrepancy is less than 5%.

EvaI see. Thank you very much Dorothy!

Constance efioHi Dorothy,

Thanks for this great article , I read the comments and questions above. I have another question please

Is there a way in Abaqus to convert the applied load( point load, line load or distributed load) to masses for it to be accounted in the mass matrix?

Thanks for your reply

DorothyHi Efio,

Thank you Efio. From my understanding, there is no such a way to convert load to mass in abaqus (load and mass are very different for analysis in governing equation). But you can output the load vectors and then combine the load with mass matrix in Matlab or with python. Hope this helps.

Hley AshleyedDear Dorothy,

I hope my email finds you well. Thank you for this great article. I tried to modify the input files (that I got from the analysis in Abaqus) using the codes you wrote in this article. However, I still cannot get the mass and stiffness matrices. The .mtx files with the jobname do not generate after the analysis completes. I have tried many times with different input files, but I still do not get the matrices. I will be grateful if you can advise or direct me on how to proceed. Thank you very much in advance for your help.

DorothyHi Ashleyed,

Did you get any warning or error message when you change input file or run the jobs? You can check the data file when analysis finishes. You can find contents ‘The following global matrices will be written to the following text files’, followed by a list of matrices and corresponding file names. If you cannot find contents like these, the input file was not correctly modified.

Hley AshleyedDear Dorothy,

Thank you for your response. The analysis completes perfectly and In the data file, I get one warning message saying

***WARNING: THIS OPTION WILL NOT BE STEP-DEPENDENT.

LINE IMAGE: *matrixgenerate, stiffness, mass

and one note saying

***NOTE: THE MATRIX OUTPUT OPTION IS ONLY VALID IN THE MATRIX GENERATION

PROCEDURE

Could you please direct me on how to fix this?

Here is the .inp file that I added the lines for the matrix generation before End Step. I do not understand what is wrong with it.

*Heading

This is the analysis of a simple beam.

** Job name: Beam Model name: Model-1

** Generated by: Abaqus/CAE 2019

*Preprint, echo=NO, model=NO, history=NO, contact=NO

**

** PARTS

**

*Part, name=Part-1

*Node

1, -1., 0., 0.

2, -0.800000012, 0., 0.

3, -0.600000024, 0., 0.

4, -0.400000006, 0., 0.

5, -0.200000003, 0., 0.

6, 0., 0., 0.

7, 0.200000003, 0., 0.

8, 0.400000006, 0., 0.

9, 0.600000024, 0., 0.

10, 0.800000012, 0., 0.

11, 1., 0., 0.

12, -0.997894764, 0., 0.

13, -0.995789468, 0., 0.

14, -0.993684232, 0., 0.

15, -0.991578937, 0., 0.

16, -0.989473701, 0., 0.

17, -0.987368405, 0., 0.

18, -0.985263169, 0., 0.

19, -0.983157873, 0., 0.

20, -0.981052637, 0., 0.

21, -0.978947341, 0., 0.

22, -0.976842105, 0., 0.

23, -0.974736869, 0., 0.

24, -0.972631574, 0., 0.

25, -0.970526338, 0., 0.

26, -0.968421042, 0., 0.

27, -0.966315806, 0., 0.

28, -0.96421051, 0., 0.

29, -0.962105274, 0., 0.

30, -0.959999979, 0., 0.

31, -0.957894742, 0., 0.

32, -0.955789447, 0., 0.

33, -0.953684211, 0., 0.

34, -0.951578975, 0., 0.

35, -0.949473679, 0., 0.

36, -0.947368443, 0., 0.

37, -0.945263147, 0., 0.

38, -0.943157911, 0., 0.

39, -0.941052616, 0., 0.

40, -0.93894738, 0., 0.

41, -0.936842084, 0., 0.

42, -0.934736848, 0., 0.

43, -0.932631552, 0., 0.

44, -0.930526316, 0., 0.

45, -0.92842108, 0., 0.

46, -0.926315784, 0., 0.

47, -0.924210548, 0., 0.

48, -0.922105253, 0., 0.

49, -0.920000017, 0., 0.

50, -0.917894721, 0., 0.

51, -0.915789485, 0., 0.

52, -0.913684189, 0., 0.

53, -0.911578953, 0., 0.

54, -0.909473658, 0., 0.

55, -0.907368422, 0., 0.

56, -0.905263186, 0., 0.

57, -0.90315789, 0., 0.

58, -0.901052654, 0., 0.

59, -0.898947358, 0., 0.

60, -0.896842122, 0., 0.

61, -0.894736826, 0., 0.

62, -0.89263159, 0., 0.

63, -0.890526295, 0., 0.

64, -0.888421059, 0., 0.

65, -0.886315763, 0., 0.

66, -0.884210527, 0., 0.

67, -0.882105291, 0., 0.

68, -0.879999995, 0., 0.

69, -0.877894759, 0., 0.

70, -0.875789464, 0., 0.

71, -0.873684227, 0., 0.

72, -0.871578932, 0., 0.

73, -0.869473696, 0., 0.

74, -0.8673684, 0., 0.

75, -0.865263164, 0., 0.

76, -0.863157868, 0., 0.

77, -0.861052632, 0., 0.

78, -0.858947396, 0., 0.

79, -0.856842101, 0., 0.

80, -0.854736865, 0., 0.

81, -0.852631569, 0., 0.

82, -0.850526333, 0., 0.

83, -0.848421037, 0., 0.

84, -0.846315801, 0., 0.

85, -0.844210505, 0., 0.

86, -0.842105269, 0., 0.

87, -0.839999974, 0., 0.

88, -0.837894738, 0., 0.

89, -0.835789502, 0., 0.

90, -0.833684206, 0., 0.

91, -0.83157897, 0., 0.

92, -0.829473674, 0., 0.

93, -0.827368438, 0., 0.

94, -0.825263143, 0., 0.

95, -0.823157907, 0., 0.

96, -0.821052611, 0., 0.

97, -0.818947375, 0., 0.

98, -0.816842079, 0., 0.

99, -0.814736843, 0., 0.

100, -0.812631607, 0., 0.

101, -0.810526311, 0., 0.

102, -0.808421075, 0., 0.

103, -0.80631578, 0., 0.

104, -0.804210544, 0., 0.

105, -0.802105248, 0., 0.

106, -0.797894716, 0., 0.

107, -0.79578948, 0., 0.

108, -0.793684185, 0., 0.

109, -0.791578948, 0., 0.

110, -0.789473712, 0., 0.

111, -0.787368417, 0., 0.

112, -0.785263181, 0., 0.

113, -0.783157885, 0., 0.

114, -0.781052649, 0., 0.

115, -0.778947353, 0., 0.

116, -0.776842117, 0., 0.

117, -0.774736822, 0., 0.

118, -0.772631586, 0., 0.

119, -0.77052629, 0., 0.

120, -0.768421054, 0., 0.

121, -0.766315818, 0., 0.

122, -0.764210522, 0., 0.

123, -0.762105286, 0., 0.

124, -0.75999999, 0., 0.

125, -0.757894754, 0., 0.

126, -0.755789459, 0., 0.

127, -0.753684223, 0., 0.

128, -0.751578927, 0., 0.

129, -0.749473691, 0., 0.

130, -0.747368395, 0., 0.

131, -0.745263159, 0., 0.

132, -0.743157923, 0., 0.

133, -0.741052628, 0., 0.

134, -0.738947392, 0., 0.

135, -0.736842096, 0., 0.

136, -0.73473686, 0., 0.

137, -0.732631564, 0., 0.

138, -0.730526328, 0., 0.

139, -0.728421032, 0., 0.

140, -0.726315796, 0., 0.

141, -0.724210501, 0., 0.

142, -0.722105265, 0., 0.

143, -0.720000029, 0., 0.

144, -0.717894733, 0., 0.

145, -0.715789497, 0., 0.

146, -0.713684201, 0., 0.

147, -0.711578965, 0., 0.

148, -0.70947367, 0., 0.

149, -0.707368433, 0., 0.

150, -0.705263138, 0., 0.

151, -0.703157902, 0., 0.

152, -0.701052606, 0., 0.

153, -0.69894737, 0., 0.

154, -0.696842134, 0., 0.

155, -0.694736838, 0., 0.

156, -0.692631602, 0., 0.

157, -0.690526307, 0., 0.

158, -0.688421071, 0., 0.

159, -0.686315775, 0., 0.

160, -0.684210539, 0., 0.

161, -0.682105243, 0., 0.

162, -0.680000007, 0., 0.

163, -0.677894711, 0., 0.

164, -0.675789475, 0., 0.

165, -0.673684239, 0., 0.

166, -0.671578944, 0., 0.

167, -0.669473708, 0., 0.

168, -0.667368412, 0., 0.

169, -0.665263176, 0., 0.

170, -0.66315788, 0., 0.

171, -0.661052644, 0., 0.

172, -0.658947349, 0., 0.

173, -0.656842113, 0., 0.

174, -0.654736817, 0., 0.

175, -0.652631581, 0., 0.

176, -0.650526345, 0., 0.

177, -0.648421049, 0., 0.

178, -0.646315813, 0., 0.

179, -0.644210517, 0., 0.

180, -0.642105281, 0., 0.

181, -0.639999986, 0., 0.

182, -0.63789475, 0., 0.

183, -0.635789454, 0., 0.

184, -0.633684218, 0., 0.

185, -0.631578922, 0., 0.

186, -0.629473686, 0., 0.

187, -0.62736845, 0., 0.

188, -0.625263155, 0., 0.

189, -0.623157918, 0., 0.

190, -0.621052623, 0., 0.

191, -0.618947387, 0., 0.

192, -0.616842091, 0., 0.

193, -0.614736855, 0., 0.

194, -0.612631559, 0., 0.

195, -0.610526323, 0., 0.

196, -0.608421028, 0., 0.

197, -0.606315792, 0., 0.

198, -0.604210556, 0., 0.

199, -0.60210526, 0., 0.

200, -0.597894728, 0., 0.

201, -0.595789492, 0., 0.

202, -0.593684196, 0., 0.

203, -0.59157896, 0., 0.

204, -0.589473665, 0., 0.

205, -0.587368429, 0., 0.

206, -0.585263133, 0., 0.

207, -0.583157897, 0., 0.

208, -0.581052661, 0., 0.

209, -0.578947365, 0., 0.

210, -0.576842129, 0., 0.

211, -0.574736834, 0., 0.

212, -0.572631598, 0., 0.

213, -0.570526302, 0., 0.

214, -0.568421066, 0., 0.

215, -0.56631577, 0., 0.

216, -0.564210534, 0., 0.

217, -0.562105238, 0., 0.

218, -0.560000002, 0., 0.

219, -0.557894766, 0., 0.

220, -0.555789471, 0., 0.

221, -0.553684235, 0., 0.

222, -0.551578939, 0., 0.

223, -0.549473703, 0., 0.

224, -0.547368407, 0., 0.

225, -0.545263171, 0., 0.

226, -0.543157876, 0., 0.

227, -0.541052639, 0., 0.

228, -0.538947344, 0., 0.

229, -0.536842108, 0., 0.

230, -0.534736872, 0., 0.

231, -0.532631576, 0., 0.

232, -0.53052634, 0., 0.

233, -0.528421044, 0., 0.

234, -0.526315808, 0., 0.

235, -0.524210513, 0., 0.

236, -0.522105277, 0., 0.

237, -0.519999981, 0., 0.

238, -0.517894745, 0., 0.

239, -0.515789449, 0., 0.

240, -0.513684213, 0., 0.

241, -0.511578977, 0., 0.

242, -0.509473681, 0., 0.

243, -0.507368445, 0., 0.

244, -0.50526315, 0., 0.

245, -0.503157914, 0., 0.

246, -0.501052618, 0., 0.

247, -0.498947382, 0., 0.

248, -0.496842116, 0., 0.

249, -0.49473685, 0., 0.

250, -0.492631584, 0., 0.

251, -0.490526319, 0., 0.

252, -0.488421053, 0., 0.

253, -0.486315787, 0., 0.

254, -0.484210521, 0., 0.

255, -0.482105255, 0., 0.

256, -0.479999989, 0., 0.

257, -0.477894723, 0., 0.

258, -0.475789487, 0., 0.

259, -0.473684222, 0., 0.

260, -0.471578956, 0., 0.

261, -0.46947369, 0., 0.

262, -0.467368424, 0., 0.

263, -0.465263158, 0., 0.

264, -0.463157892, 0., 0.

265, -0.461052626, 0., 0.

266, -0.458947361, 0., 0.

267, -0.456842095, 0., 0.

268, -0.454736829, 0., 0.

269, -0.452631593, 0., 0.

270, -0.450526327, 0., 0.

271, -0.448421061, 0., 0.

272, -0.446315795, 0., 0.

273, -0.444210529, 0., 0.

274, -0.442105263, 0., 0.

275, -0.439999998, 0., 0.

276, -0.437894732, 0., 0.

277, -0.435789466, 0., 0.

278, -0.4336842, 0., 0.

279, -0.431578934, 0., 0.

280, -0.429473698, 0., 0.

281, -0.427368432, 0., 0.

282, -0.425263166, 0., 0.

283, -0.423157901, 0., 0.

284, -0.421052635, 0., 0.

285, -0.418947369, 0., 0.

286, -0.416842103, 0., 0.

287, -0.414736837, 0., 0.

288, -0.412631571, 0., 0.

289, -0.410526305, 0., 0.

290, -0.40842104, 0., 0.

291, -0.406315804, 0., 0.

292, -0.404210538, 0., 0.

293, -0.402105272, 0., 0.

294, -0.39789474, 0., 0.

295, -0.395789474, 0., 0.

296, -0.393684208, 0., 0.

297, -0.391578943, 0., 0.

298, -0.389473677, 0., 0.

299, -0.387368411, 0., 0.

300, -0.385263145, 0., 0.

301, -0.383157909, 0., 0.

302, -0.381052643, 0., 0.

303, -0.378947377, 0., 0.

304, -0.376842111, 0., 0.

305, -0.374736845, 0., 0.

306, -0.37263158, 0., 0.

307, -0.370526314, 0., 0.

308, -0.368421048, 0., 0.

309, -0.366315782, 0., 0.

310, -0.364210516, 0., 0.

311, -0.36210525, 0., 0.

312, -0.360000014, 0., 0.

313, -0.357894748, 0., 0.

314, -0.355789483, 0., 0.

315, -0.353684217, 0., 0.

316, -0.351578951, 0., 0.

317, -0.349473685, 0., 0.

318, -0.347368419, 0., 0.

319, -0.345263153, 0., 0.

320, -0.343157887, 0., 0.

321, -0.341052622, 0., 0.

322, -0.338947356, 0., 0.

323, -0.33684212, 0., 0.

324, -0.334736854, 0., 0.

325, -0.332631588, 0., 0.

326, -0.330526322, 0., 0.

327, -0.328421056, 0., 0.

328, -0.32631579, 0., 0.

329, -0.324210525, 0., 0.

330, -0.322105259, 0., 0.

331, -0.319999993, 0., 0.

332, -0.317894727, 0., 0.

333, -0.315789461, 0., 0.

334, -0.313684225, 0., 0.

335, -0.311578959, 0., 0.

336, -0.309473693, 0., 0.

337, -0.307368428, 0., 0.

338, -0.305263162, 0., 0.

339, -0.303157896, 0., 0.

340, -0.30105263, 0., 0.

341, -0.298947364, 0., 0.

342, -0.296842098, 0., 0.

343, -0.294736832, 0., 0.

344, -0.292631567, 0., 0.

345, -0.29052633, 0., 0.

346, -0.288421065, 0., 0.

347, -0.286315799, 0., 0.

348, -0.284210533, 0., 0.

349, -0.282105267, 0., 0.

350, -0.280000001, 0., 0.

351, -0.277894735, 0., 0.

352, -0.275789469, 0., 0.

353, -0.273684204, 0., 0.

354, -0.271578938, 0., 0.

355, -0.269473672, 0., 0.

356, -0.267368436, 0., 0.

357, -0.26526317, 0., 0.

358, -0.263157904, 0., 0.

359, -0.261052638, 0., 0.

360, -0.258947372, 0., 0.

361, -0.256842107, 0., 0.

362, -0.254736841, 0., 0.

363, -0.252631575, 0., 0.

364, -0.250526309, 0., 0.

365, -0.248421058, 0., 0.

366, -0.246315792, 0., 0.

367, -0.244210526, 0., 0.

368, -0.24210526, 0., 0.

369, -0.239999995, 0., 0.

370, -0.237894744, 0., 0.

371, -0.235789478, 0., 0.

372, -0.233684212, 0., 0.

373, -0.231578946, 0., 0.

374, -0.22947368, 0., 0.

375, -0.227368414, 0., 0.

376, -0.225263163, 0., 0.

377, -0.223157898, 0., 0.

378, -0.221052632, 0., 0.

379, -0.218947366, 0., 0.

380, -0.2168421, 0., 0.

381, -0.214736849, 0., 0.

382, -0.212631583, 0., 0.

383, -0.210526317, 0., 0.

384, -0.208421052, 0., 0.

385, -0.206315786, 0., 0.

386, -0.20421052, 0., 0.

387, -0.202105269, 0., 0.

388, -0.197894737, 0., 0.

389, -0.195789471, 0., 0.

390, -0.193684205, 0., 0.

391, -0.191578954, 0., 0.

392, -0.189473689, 0., 0.

393, -0.187368423, 0., 0.

394, -0.185263157, 0., 0.

395, -0.183157891, 0., 0.

396, -0.181052625, 0., 0.

397, -0.178947374, 0., 0.

398, -0.176842108, 0., 0.

399, -0.174736843, 0., 0.

400, -0.172631577, 0., 0.

401, -0.170526311, 0., 0.

402, -0.16842106, 0., 0.

403, -0.166315794, 0., 0.

404, -0.164210528, 0., 0.

405, -0.162105262, 0., 0.

406, -0.159999996, 0., 0.

407, -0.157894731, 0., 0.

408, -0.15578948, 0., 0.

409, -0.153684214, 0., 0.

410, -0.151578948, 0., 0.

411, -0.149473682, 0., 0.

412, -0.147368416, 0., 0.

413, -0.145263165, 0., 0.

414, -0.143157899, 0., 0.

415, -0.141052634, 0., 0.

416, -0.138947368, 0., 0.

417, -0.136842102, 0., 0.

418, -0.134736836, 0., 0.

419, -0.132631585, 0., 0.

420, -0.130526319, 0., 0.

421, -0.128421053, 0., 0.

422, -0.126315787, 0., 0.

423, -0.124210529, 0., 0.

424, -0.122105263, 0., 0.

425, -0.119999997, 0., 0.

426, -0.117894739, 0., 0.

427, -0.115789473, 0., 0.

428, -0.113684207, 0., 0.

429, -0.111578949, 0., 0.

430, -0.109473683, 0., 0.

431, -0.107368425, 0., 0.

432, -0.105263159, 0., 0.

433, -0.103157893, 0., 0.

434, -0.101052634, 0., 0.

435, -0.0989473686, 0., 0.

436, -0.0968421027, 0., 0.

437, -0.0947368443, 0., 0.

438, -0.0926315784, 0., 0.

439, -0.0905263126, 0., 0.

440, -0.0884210542, 0., 0.

441, -0.0863157883, 0., 0.

442, -0.0842105299, 0., 0.

443, -0.0821052641, 0., 0.

444, -0.0799999982, 0., 0.

445, -0.0778947398, 0., 0.

446, -0.075789474, 0., 0.

447, -0.0736842081, 0., 0.

448, -0.0715789497, 0., 0.

449, -0.0694736838, 0., 0.

450, -0.067368418, 0., 0.

451, -0.0652631596, 0., 0.

452, -0.0631578937, 0., 0.

453, -0.0610526316, 0., 0.

454, -0.0589473695, 0., 0.

455, -0.0568421036, 0., 0.

456, -0.0547368415, 0., 0.

457, -0.0526315793, 0., 0.

458, -0.0505263172, 0., 0.

459, -0.0484210514, 0., 0.

460, -0.0463157892, 0., 0.

461, -0.0442105271, 0., 0.

462, -0.042105265, 0., 0.

463, -0.0399999991, 0., 0.

464, -0.037894737, 0., 0.

465, -0.0357894748, 0., 0.

466, -0.033684209, 0., 0.

467, -0.0315789469, 0., 0.

468, -0.0294736847, 0., 0.

469, -0.0273684207, 0., 0.

470, -0.0252631586, 0., 0.

471, -0.0231578946, 0., 0.

472, -0.0210526325, 0., 0.

473, -0.0189473685, 0., 0.

474, -0.0168421045, 0., 0.

475, -0.0147368424, 0., 0.

476, -0.0126315793, 0., 0.

477, -0.0105263162, 0., 0.

478, -0.00842105225, 0., 0.

479, -0.00631578965, 0., 0.

480, -0.00421052612, 0., 0.

481, -0.00210526306, 0., 0.

482, 0.00210526306, 0., 0.

483, 0.00421052612, 0., 0.

484, 0.00631578965, 0., 0.

485, 0.00842105225, 0., 0.

486, 0.0105263162, 0., 0.

487, 0.0126315793, 0., 0.

488, 0.0147368424, 0., 0.

489, 0.0168421045, 0., 0.

490, 0.0189473685, 0., 0.

491, 0.0210526325, 0., 0.

492, 0.0231578946, 0., 0.

493, 0.0252631586, 0., 0.

494, 0.0273684207, 0., 0.

495, 0.0294736847, 0., 0.

496, 0.0315789469, 0., 0.

497, 0.033684209, 0., 0.

498, 0.0357894748, 0., 0.

499, 0.037894737, 0., 0.

500, 0.0399999991, 0., 0.

501, 0.042105265, 0., 0.

502, 0.0442105271, 0., 0.

503, 0.0463157892, 0., 0.

504, 0.0484210514, 0., 0.

505, 0.0505263172, 0., 0.

506, 0.0526315793, 0., 0.

507, 0.0547368415, 0., 0.

508, 0.0568421036, 0., 0.

509, 0.0589473695, 0., 0.

510, 0.0610526316, 0., 0.

511, 0.0631578937, 0., 0.

512, 0.0652631596, 0., 0.

513, 0.067368418, 0., 0.

514, 0.0694736838, 0., 0.

515, 0.0715789497, 0., 0.

516, 0.0736842081, 0., 0.

517, 0.075789474, 0., 0.

518, 0.0778947398, 0., 0.

519, 0.0799999982, 0., 0.

520, 0.0821052641, 0., 0.

521, 0.0842105299, 0., 0.

522, 0.0863157883, 0., 0.

523, 0.0884210542, 0., 0.

524, 0.0905263126, 0., 0.

525, 0.0926315784, 0., 0.

526, 0.0947368443, 0., 0.

527, 0.0968421027, 0., 0.

528, 0.0989473686, 0., 0.

529, 0.101052634, 0., 0.

530, 0.103157893, 0., 0.

531, 0.105263159, 0., 0.

532, 0.107368425, 0., 0.

533, 0.109473683, 0., 0.

534, 0.111578949, 0., 0.

535, 0.113684207, 0., 0.

536, 0.115789473, 0., 0.

537, 0.117894739, 0., 0.

538, 0.119999997, 0., 0.

539, 0.122105263, 0., 0.

540, 0.124210529, 0., 0.

541, 0.126315787, 0., 0.

542, 0.128421053, 0., 0.

543, 0.130526319, 0., 0.

544, 0.132631585, 0., 0.

545, 0.134736836, 0., 0.

546, 0.136842102, 0., 0.

547, 0.138947368, 0., 0.

548, 0.141052634, 0., 0.

549, 0.143157899, 0., 0.

550, 0.145263165, 0., 0.

551, 0.147368416, 0., 0.

552, 0.149473682, 0., 0.

553, 0.151578948, 0., 0.

554, 0.153684214, 0., 0.

555, 0.15578948, 0., 0.

556, 0.157894731, 0., 0.

557, 0.159999996, 0., 0.

558, 0.162105262, 0., 0.

559, 0.164210528, 0., 0.

560, 0.166315794, 0., 0.

561, 0.16842106, 0., 0.

562, 0.170526311, 0., 0.

563, 0.172631577, 0., 0.

564, 0.174736843, 0., 0.

565, 0.176842108, 0., 0.

566, 0.178947374, 0., 0.

567, 0.181052625, 0., 0.

568, 0.183157891, 0., 0.

569, 0.185263157, 0., 0.

570, 0.187368423, 0., 0.

571, 0.189473689, 0., 0.

572, 0.191578954, 0., 0.

573, 0.193684205, 0., 0.

574, 0.195789471, 0., 0.

575, 0.197894737, 0., 0.

576, 0.202105269, 0., 0.

577, 0.20421052, 0., 0.

578, 0.206315786, 0., 0.

579, 0.208421052, 0., 0.

580, 0.210526317, 0., 0.

581, 0.212631583, 0., 0.

582, 0.214736849, 0., 0.

583, 0.2168421, 0., 0.

584, 0.218947366, 0., 0.

585, 0.221052632, 0., 0.

586, 0.223157898, 0., 0.

587, 0.225263163, 0., 0.

588, 0.227368414, 0., 0.

589, 0.22947368, 0., 0.

590, 0.231578946, 0., 0.

591, 0.233684212, 0., 0.

592, 0.235789478, 0., 0.

593, 0.237894744, 0., 0.

594, 0.239999995, 0., 0.

595, 0.24210526, 0., 0.

596, 0.244210526, 0., 0.

597, 0.246315792, 0., 0.

598, 0.248421058, 0., 0.

599, 0.250526309, 0., 0.

600, 0.252631575, 0., 0.

601, 0.254736841, 0., 0.

602, 0.256842107, 0., 0.

603, 0.258947372, 0., 0.

604, 0.261052638, 0., 0.

605, 0.263157904, 0., 0.

606, 0.26526317, 0., 0.

607, 0.267368436, 0., 0.

608, 0.269473672, 0., 0.

609, 0.271578938, 0., 0.

610, 0.273684204, 0., 0.

611, 0.275789469, 0., 0.

612, 0.277894735, 0., 0.

613, 0.280000001, 0., 0.

614, 0.282105267, 0., 0.

615, 0.284210533, 0., 0.

616, 0.286315799, 0., 0.

617, 0.288421065, 0., 0.

618, 0.29052633, 0., 0.

619, 0.292631567, 0., 0.

620, 0.294736832, 0., 0.

621, 0.296842098, 0., 0.

622, 0.298947364, 0., 0.

623, 0.30105263, 0., 0.

624, 0.303157896, 0., 0.

625, 0.305263162, 0., 0.

626, 0.307368428, 0., 0.

627, 0.309473693, 0., 0.

628, 0.311578959, 0., 0.

629, 0.313684225, 0., 0.

630, 0.315789461, 0., 0.

631, 0.317894727, 0., 0.

632, 0.319999993, 0., 0.

633, 0.322105259, 0., 0.

634, 0.324210525, 0., 0.

635, 0.32631579, 0., 0.

636, 0.328421056, 0., 0.

637, 0.330526322, 0., 0.

638, 0.332631588, 0., 0.

639, 0.334736854, 0., 0.

640, 0.33684212, 0., 0.

641, 0.338947356, 0., 0.

642, 0.341052622, 0., 0.

643, 0.343157887, 0., 0.

644, 0.345263153, 0., 0.

645, 0.347368419, 0., 0.

646, 0.349473685, 0., 0.

647, 0.351578951, 0., 0.

648, 0.353684217, 0., 0.

649, 0.355789483, 0., 0.

650, 0.357894748, 0., 0.

651, 0.360000014, 0., 0.

652, 0.36210525, 0., 0.

653, 0.364210516, 0., 0.

654, 0.366315782, 0., 0.

655, 0.368421048, 0., 0.

656, 0.370526314, 0., 0.

657, 0.37263158, 0., 0.

658, 0.374736845, 0., 0.

659, 0.376842111, 0., 0.

660, 0.378947377, 0., 0.

661, 0.381052643, 0., 0.

662, 0.383157909, 0., 0.

663, 0.385263145, 0., 0.

664, 0.387368411, 0., 0.

665, 0.389473677, 0., 0.

666, 0.391578943, 0., 0.

667, 0.393684208, 0., 0.

668, 0.395789474, 0., 0.

669, 0.39789474, 0., 0.

670, 0.402105272, 0., 0.

671, 0.404210538, 0., 0.

672, 0.406315804, 0., 0.

673, 0.40842104, 0., 0.

674, 0.410526305, 0., 0.

675, 0.412631571, 0., 0.

676, 0.414736837, 0., 0.

677, 0.416842103, 0., 0.

678, 0.418947369, 0., 0.

679, 0.421052635, 0., 0.

680, 0.423157901, 0., 0.

681, 0.425263166, 0., 0.

682, 0.427368432, 0., 0.

683, 0.429473698, 0., 0.

684, 0.431578934, 0., 0.

685, 0.4336842, 0., 0.

686, 0.435789466, 0., 0.

687, 0.437894732, 0., 0.

688, 0.439999998, 0., 0.

689, 0.442105263, 0., 0.

690, 0.444210529, 0., 0.

691, 0.446315795, 0., 0.

692, 0.448421061, 0., 0.

693, 0.450526327, 0., 0.

694, 0.452631593, 0., 0.

695, 0.454736829, 0., 0.

696, 0.456842095, 0., 0.

697, 0.458947361, 0., 0.

698, 0.461052626, 0., 0.

699, 0.463157892, 0., 0.

700, 0.465263158, 0., 0.

701, 0.467368424, 0., 0.

702, 0.46947369, 0., 0.

703, 0.471578956, 0., 0.

704, 0.473684222, 0., 0.

705, 0.475789487, 0., 0.

706, 0.477894723, 0., 0.

707, 0.479999989, 0., 0.

708, 0.482105255, 0., 0.

709, 0.484210521, 0., 0.

710, 0.486315787, 0., 0.

711, 0.488421053, 0., 0.

712, 0.490526319, 0., 0.

713, 0.492631584, 0., 0.

714, 0.49473685, 0., 0.

715, 0.496842116, 0., 0.

716, 0.498947382, 0., 0.

717, 0.501052618, 0., 0.

718, 0.503157914, 0., 0.

719, 0.50526315, 0., 0.

720, 0.507368445, 0., 0.

721, 0.509473681, 0., 0.

722, 0.511578977, 0., 0.

723, 0.513684213, 0., 0.

724, 0.515789449, 0., 0.

725, 0.517894745, 0., 0.

726, 0.519999981, 0., 0.

727, 0.522105277, 0., 0.

728, 0.524210513, 0., 0.

729, 0.526315808, 0., 0.

730, 0.528421044, 0., 0.

731, 0.53052634, 0., 0.

732, 0.532631576, 0., 0.

733, 0.534736872, 0., 0.

734, 0.536842108, 0., 0.

735, 0.538947344, 0., 0.

736, 0.541052639, 0., 0.

737, 0.543157876, 0., 0.

738, 0.545263171, 0., 0.

739, 0.547368407, 0., 0.

740, 0.549473703, 0., 0.

741, 0.551578939, 0., 0.

742, 0.553684235, 0., 0.

743, 0.555789471, 0., 0.

744, 0.557894766, 0., 0.

745, 0.560000002, 0., 0.

746, 0.562105238, 0., 0.

747, 0.564210534, 0., 0.

748, 0.56631577, 0., 0.

749, 0.568421066, 0., 0.

750, 0.570526302, 0., 0.

751, 0.572631598, 0., 0.

752, 0.574736834, 0., 0.

753, 0.576842129, 0., 0.

754, 0.578947365, 0., 0.

755, 0.581052661, 0., 0.

756, 0.583157897, 0., 0.

757, 0.585263133, 0., 0.

758, 0.587368429, 0., 0.

759, 0.589473665, 0., 0.

760, 0.59157896, 0., 0.

761, 0.593684196, 0., 0.

762, 0.595789492, 0., 0.

763, 0.597894728, 0., 0.

764, 0.60210526, 0., 0.

765, 0.604210556, 0., 0.

766, 0.606315792, 0., 0.

767, 0.608421028, 0., 0.

768, 0.610526323, 0., 0.

769, 0.612631559, 0., 0.

770, 0.614736855, 0., 0.

771, 0.616842091, 0., 0.

772, 0.618947387, 0., 0.

773, 0.621052623, 0., 0.

774, 0.623157918, 0., 0.

775, 0.625263155, 0., 0.

776, 0.62736845, 0., 0.

777, 0.629473686, 0., 0.

778, 0.631578922, 0., 0.

779, 0.633684218, 0., 0.

780, 0.635789454, 0., 0.

781, 0.63789475, 0., 0.

782, 0.639999986, 0., 0.

783, 0.642105281, 0., 0.

784, 0.644210517, 0., 0.

785, 0.646315813, 0., 0.

786, 0.648421049, 0., 0.

787, 0.650526345, 0., 0.

788, 0.652631581, 0., 0.

789, 0.654736817, 0., 0.

790, 0.656842113, 0., 0.

791, 0.658947349, 0., 0.

792, 0.661052644, 0., 0.

793, 0.66315788, 0., 0.

794, 0.665263176, 0., 0.

795, 0.667368412, 0., 0.

796, 0.669473708, 0., 0.

797, 0.671578944, 0., 0.

798, 0.673684239, 0., 0.

799, 0.675789475, 0., 0.

800, 0.677894711, 0., 0.

801, 0.680000007, 0., 0.

802, 0.682105243, 0., 0.

803, 0.684210539, 0., 0.

804, 0.686315775, 0., 0.

805, 0.688421071, 0., 0.

806, 0.690526307, 0., 0.

807, 0.692631602, 0., 0.

808, 0.694736838, 0., 0.

809, 0.696842134, 0., 0.

810, 0.69894737, 0., 0.

811, 0.701052606, 0., 0.

812, 0.703157902, 0., 0.

813, 0.705263138, 0., 0.

814, 0.707368433, 0., 0.

815, 0.70947367, 0., 0.

816, 0.711578965, 0., 0.

817, 0.713684201, 0., 0.

818, 0.715789497, 0., 0.

819, 0.717894733, 0., 0.

820, 0.720000029, 0., 0.

821, 0.722105265, 0., 0.

822, 0.724210501, 0., 0.

823, 0.726315796, 0., 0.

824, 0.728421032, 0., 0.

825, 0.730526328, 0., 0.

826, 0.732631564, 0., 0.

827, 0.73473686, 0., 0.

828, 0.736842096, 0., 0.

829, 0.738947392, 0., 0.

830, 0.741052628, 0., 0.

831, 0.743157923, 0., 0.

832, 0.745263159, 0., 0.

833, 0.747368395, 0., 0.

834, 0.749473691, 0., 0.

835, 0.751578927, 0., 0.

836, 0.753684223, 0., 0.

837, 0.755789459, 0., 0.

838, 0.757894754, 0., 0.

839, 0.75999999, 0., 0.

840, 0.762105286, 0., 0.

841, 0.764210522, 0., 0.

842, 0.766315818, 0., 0.

843, 0.768421054, 0., 0.

844, 0.77052629, 0., 0.

845, 0.772631586, 0., 0.

846, 0.774736822, 0., 0.

847, 0.776842117, 0., 0.

848, 0.778947353, 0., 0.

849, 0.781052649, 0., 0.

850, 0.783157885, 0., 0.

851, 0.785263181, 0., 0.

852, 0.787368417, 0., 0.

853, 0.789473712, 0., 0.

854, 0.791578948, 0., 0.

855, 0.793684185, 0., 0.

856, 0.79578948, 0., 0.

857, 0.797894716, 0., 0.

858, 0.802105248, 0., 0.

859, 0.804210544, 0., 0.

860, 0.80631578, 0., 0.

861, 0.808421075, 0., 0.

862, 0.810526311, 0., 0.

863, 0.812631607, 0., 0.

864, 0.814736843, 0., 0.

865, 0.816842079, 0., 0.

866, 0.818947375, 0., 0.

867, 0.821052611, 0., 0.

868, 0.823157907, 0., 0.

869, 0.825263143, 0., 0.

870, 0.827368438, 0., 0.

871, 0.829473674, 0., 0.

872, 0.83157897, 0., 0.

873, 0.833684206, 0., 0.

874, 0.835789502, 0., 0.

875, 0.837894738, 0., 0.

876, 0.839999974, 0., 0.

877, 0.842105269, 0., 0.

878, 0.844210505, 0., 0.

879, 0.846315801, 0., 0.

880, 0.848421037, 0., 0.

881, 0.850526333, 0., 0.

882, 0.852631569, 0., 0.

883, 0.854736865, 0., 0.

884, 0.856842101, 0., 0.

885, 0.858947396, 0., 0.

886, 0.861052632, 0., 0.

887, 0.863157868, 0., 0.

888, 0.865263164, 0., 0.

889, 0.8673684, 0., 0.

890, 0.869473696, 0., 0.

891, 0.871578932, 0., 0.

892, 0.873684227, 0., 0.

893, 0.875789464, 0., 0.

894, 0.877894759, 0., 0.

895, 0.879999995, 0., 0.

896, 0.882105291, 0., 0.

897, 0.884210527, 0., 0.

898, 0.886315763, 0., 0.

899, 0.888421059, 0., 0.

900, 0.890526295, 0., 0.

901, 0.89263159, 0., 0.

902, 0.894736826, 0., 0.

903, 0.896842122, 0., 0.

904, 0.898947358, 0., 0.

905, 0.901052654, 0., 0.

906, 0.90315789, 0., 0.

907, 0.905263186, 0., 0.

908, 0.907368422, 0., 0.

909, 0.909473658, 0., 0.

910, 0.911578953, 0., 0.

911, 0.913684189, 0., 0.

912, 0.915789485, 0., 0.

913, 0.917894721, 0., 0.

914, 0.920000017, 0., 0.

915, 0.922105253, 0., 0.

916, 0.924210548, 0., 0.

917, 0.926315784, 0., 0.

918, 0.92842108, 0., 0.

919, 0.930526316, 0., 0.

920, 0.932631552, 0., 0.

921, 0.934736848, 0., 0.

922, 0.936842084, 0., 0.

923, 0.93894738, 0., 0.

924, 0.941052616, 0., 0.

925, 0.943157911, 0., 0.

926, 0.945263147, 0., 0.

927, 0.947368443, 0., 0.

928, 0.949473679, 0., 0.

929, 0.951578975, 0., 0.

930, 0.953684211, 0., 0.

931, 0.955789447, 0., 0.

932, 0.957894742, 0., 0.

933, 0.959999979, 0., 0.

934, 0.962105274, 0., 0.

935, 0.96421051, 0., 0.

936, 0.966315806, 0., 0.

937, 0.968421042, 0., 0.

938, 0.970526338, 0., 0.

939, 0.972631574, 0., 0.

940, 0.974736869, 0., 0.

941, 0.976842105, 0., 0.

942, 0.978947341, 0., 0.

943, 0.981052637, 0., 0.

944, 0.983157873, 0., 0.

945, 0.985263169, 0., 0.

946, 0.987368405, 0., 0.

947, 0.989473701, 0., 0.

948, 0.991578937, 0., 0.

949, 0.993684232, 0., 0.

950, 0.995789468, 0., 0.

951, 0.997894764, 0., 0.

*Element, type=B31

1, 1, 12

2, 12, 13

3, 13, 14

4, 14, 15

5, 15, 16

6, 16, 17

7, 17, 18

8, 18, 19

9, 19, 20

10, 20, 21

11, 21, 22

12, 22, 23

13, 23, 24

14, 24, 25

15, 25, 26

16, 26, 27

17, 27, 28

18, 28, 29

19, 29, 30

20, 30, 31

21, 31, 32

22, 32, 33

23, 33, 34

24, 34, 35

25, 35, 36

26, 36, 37

27, 37, 38

28, 38, 39

29, 39, 40

30, 40, 41

31, 41, 42

32, 42, 43

33, 43, 44

34, 44, 45

35, 45, 46

36, 46, 47

37, 47, 48

38, 48, 49

39, 49, 50

40, 50, 51

41, 51, 52

42, 52, 53

43, 53, 54

44, 54, 55

45, 55, 56

46, 56, 57

47, 57, 58

48, 58, 59

49, 59, 60

50, 60, 61

51, 61, 62

52, 62, 63

53, 63, 64

54, 64, 65

55, 65, 66

56, 66, 67

57, 67, 68

58, 68, 69

59, 69, 70

60, 70, 71

61, 71, 72

62, 72, 73

63, 73, 74

64, 74, 75

65, 75, 76

66, 76, 77

67, 77, 78

68, 78, 79

69, 79, 80

70, 80, 81

71, 81, 82

72, 82, 83

73, 83, 84

74, 84, 85

75, 85, 86

76, 86, 87

77, 87, 88

78, 88, 89

79, 89, 90

80, 90, 91

81, 91, 92

82, 92, 93

83, 93, 94

84, 94, 95

85, 95, 96

86, 96, 97

87, 97, 98

88, 98, 99

89, 99, 100

90, 100, 101

91, 101, 102

92, 102, 103

93, 103, 104

94, 104, 105

95, 105, 2

96, 2, 106

97, 106, 107

98, 107, 108

99, 108, 109

100, 109, 110

101, 110, 111

102, 111, 112

103, 112, 113

104, 113, 114

105, 114, 115

106, 115, 116

107, 116, 117

108, 117, 118

109, 118, 119

110, 119, 120

111, 120, 121

112, 121, 122

113, 122, 123

114, 123, 124

115, 124, 125

116, 125, 126

117, 126, 127

118, 127, 128

119, 128, 129

120, 129, 130

121, 130, 131

122, 131, 132

123, 132, 133

124, 133, 134

125, 134, 135

126, 135, 136

127, 136, 137

128, 137, 138

129, 138, 139

130, 139, 140

131, 140, 141

132, 141, 142

133, 142, 143

134, 143, 144

135, 144, 145

136, 145, 146

137, 146, 147

138, 147, 148

139, 148, 149

140, 149, 150

141, 150, 151

142, 151, 152

143, 152, 153

144, 153, 154

145, 154, 155

146, 155, 156

147, 156, 157

148, 157, 158

149, 158, 159

150, 159, 160

151, 160, 161

152, 161, 162

153, 162, 163

154, 163, 164

155, 164, 165

156, 165, 166

157, 166, 167

158, 167, 168

159, 168, 169

160, 169, 170

161, 170, 171

162, 171, 172

163, 172, 173

164, 173, 174

165, 174, 175

166, 175, 176

167, 176, 177

168, 177, 178

169, 178, 179

170, 179, 180

171, 180, 181

172, 181, 182

173, 182, 183

174, 183, 184

175, 184, 185

176, 185, 186

177, 186, 187

178, 187, 188

179, 188, 189

180, 189, 190

181, 190, 191

182, 191, 192

183, 192, 193

184, 193, 194

185, 194, 195

186, 195, 196

187, 196, 197

188, 197, 198

189, 198, 199

190, 199, 3

191, 3, 200

192, 200, 201

193, 201, 202

194, 202, 203

195, 203, 204

196, 204, 205

197, 205, 206

198, 206, 207

199, 207, 208

200, 208, 209

201, 209, 210

202, 210, 211

203, 211, 212

204, 212, 213

205, 213, 214

206, 214, 215

207, 215, 216

208, 216, 217

209, 217, 218

210, 218, 219

211, 219, 220

212, 220, 221

213, 221, 222

214, 222, 223

215, 223, 224

216, 224, 225

217, 225, 226

218, 226, 227

219, 227, 228

220, 228, 229

221, 229, 230

222, 230, 231

223, 231, 232

224, 232, 233

225, 233, 234

226, 234, 235

227, 235, 236

228, 236, 237

229, 237, 238

230, 238, 239

231, 239, 240

232, 240, 241

233, 241, 242

234, 242, 243

235, 243, 244

236, 244, 245

237, 245, 246

238, 246, 247

239, 247, 248

240, 248, 249

241, 249, 250

242, 250, 251

243, 251, 252

244, 252, 253

245, 253, 254

246, 254, 255

247, 255, 256

248, 256, 257

249, 257, 258

250, 258, 259

251, 259, 260

252, 260, 261

253, 261, 262

254, 262, 263

255, 263, 264

256, 264, 265

257, 265, 266

258, 266, 267

259, 267, 268

260, 268, 269

261, 269, 270

262, 270, 271

263, 271, 272

264, 272, 273

265, 273, 274

266, 274, 275

267, 275, 276

268, 276, 277

269, 277, 278

270, 278, 279

271, 279, 280

272, 280, 281

273, 281, 282

274, 282, 283

275, 283, 284

276, 284, 285

277, 285, 286

278, 286, 287

279, 287, 288

280, 288, 289

281, 289, 290

282, 290, 291

283, 291, 292

284, 292, 293

285, 293, 4

286, 4, 294

287, 294, 295

288, 295, 296

289, 296, 297

290, 297, 298

291, 298, 299

292, 299, 300

293, 300, 301

294, 301, 302

295, 302, 303

296, 303, 304

297, 304, 305

298, 305, 306

299, 306, 307

300, 307, 308

301, 308, 309

302, 309, 310

303, 310, 311

304, 311, 312

305, 312, 313

306, 313, 314

307, 314, 315

308, 315, 316

309, 316, 317

310, 317, 318

311, 318, 319

312, 319, 320

313, 320, 321

314, 321, 322

315, 322, 323

316, 323, 324

317, 324, 325

318, 325, 326

319, 326, 327

320, 327, 328

321, 328, 329

322, 329, 330

323, 330, 331

324, 331, 332

325, 332, 333

326, 333, 334

327, 334, 335

328, 335, 336

329, 336, 337

330, 337, 338

331, 338, 339

332, 339, 340

333, 340, 341

334, 341, 342

335, 342, 343

336, 343, 344

337, 344, 345

338, 345, 346

339, 346, 347

340, 347, 348

341, 348, 349

342, 349, 350

343, 350, 351

344, 351, 352

345, 352, 353

346, 353, 354

347, 354, 355

348, 355, 356

349, 356, 357

350, 357, 358

351, 358, 359

352, 359, 360

353, 360, 361

354, 361, 362

355, 362, 363

356, 363, 364

357, 364, 365

358, 365, 366

359, 366, 367

360, 367, 368

361, 368, 369

362, 369, 370

363, 370, 371

364, 371, 372

365, 372, 373

366, 373, 374

367, 374, 375

368, 375, 376

369, 376, 377

370, 377, 378

371, 378, 379

372, 379, 380

373, 380, 381

374, 381, 382

375, 382, 383

376, 383, 384

377, 384, 385

378, 385, 386

379, 386, 387

380, 387, 5

381, 5, 388

382, 388, 389

383, 389, 390

384, 390, 391

385, 391, 392

386, 392, 393

387, 393, 394

388, 394, 395

389, 395, 396

390, 396, 397

391, 397, 398

392, 398, 399

393, 399, 400

394, 400, 401

395, 401, 402

396, 402, 403

397, 403, 404

398, 404, 405

399, 405, 406

400, 406, 407

401, 407, 408

402, 408, 409

403, 409, 410

404, 410, 411

405, 411, 412

406, 412, 413

407, 413, 414

408, 414, 415

409, 415, 416

410, 416, 417

411, 417, 418

412, 418, 419

413, 419, 420

414, 420, 421

415, 421, 422

416, 422, 423

417, 423, 424

418, 424, 425

419, 425, 426

420, 426, 427

421, 427, 428

422, 428, 429

423, 429, 430

424, 430, 431

425, 431, 432

426, 432, 433

427, 433, 434

428, 434, 435

429, 435, 436

430, 436, 437

431, 437, 438

432, 438, 439

433, 439, 440

434, 440, 441

435, 441, 442

436, 442, 443

437, 443, 444

438, 444, 445

439, 445, 446

440, 446, 447

441, 447, 448

442, 448, 449

443, 449, 450

444, 450, 451

445, 451, 452

446, 452, 453

447, 453, 454

448, 454, 455

449, 455, 456

450, 456, 457

451, 457, 458

452, 458, 459

453, 459, 460

454, 460, 461

455, 461, 462

456, 462, 463

457, 463, 464

458, 464, 465

459, 465, 466

460, 466, 467

461, 467, 468

462, 468, 469

463, 469, 470

464, 470, 471

465, 471, 472

466, 472, 473

467, 473, 474

468, 474, 475

469, 475, 476

470, 476, 477

471, 477, 478

472, 478, 479

473, 479, 480

474, 480, 481

475, 481, 6

476, 6, 482

477, 482, 483

478, 483, 484

479, 484, 485

480, 485, 486

481, 486, 487

482, 487, 488

483, 488, 489

484, 489, 490

485, 490, 491

486, 491, 492

487, 492, 493

488, 493, 494

489, 494, 495

490, 495, 496

491, 496, 497

492, 497, 498

493, 498, 499

494, 499, 500

495, 500, 501

496, 501, 502

497, 502, 503

498, 503, 504

499, 504, 505

500, 505, 506

501, 506, 507

502, 507, 508

503, 508, 509

504, 509, 510

505, 510, 511

506, 511, 512

507, 512, 513

508, 513, 514

509, 514, 515

510, 515, 516

511, 516, 517

512, 517, 518

513, 518, 519

514, 519, 520

515, 520, 521

516, 521, 522

517, 522, 523

518, 523, 524

519, 524, 525

520, 525, 526

521, 526, 527

522, 527, 528

523, 528, 529

524, 529, 530

525, 530, 531

526, 531, 532

527, 532, 533

528, 533, 534

529, 534, 535

530, 535, 536

531, 536, 537

532, 537, 538

533, 538, 539

534, 539, 540

535, 540, 541

536, 541, 542

537, 542, 543

538, 543, 544

539, 544, 545

540, 545, 546

541, 546, 547

542, 547, 548

543, 548, 549

544, 549, 550

545, 550, 551

546, 551, 552

547, 552, 553

548, 553, 554

549, 554, 555

550, 555, 556

551, 556, 557

552, 557, 558

553, 558, 559

554, 559, 560

555, 560, 561

556, 561, 562

557, 562, 563

558, 563, 564

559, 564, 565

560, 565, 566

561, 566, 567

562, 567, 568

563, 568, 569

564, 569, 570

565, 570, 571

566, 571, 572

567, 572, 573

568, 573, 574

569, 574, 575

570, 575, 7

571, 7, 576

572, 576, 577

573, 577, 578

574, 578, 579

575, 579, 580

576, 580, 581

577, 581, 582

578, 582, 583

579, 583, 584

580, 584, 585

581, 585, 586

582, 586, 587

583, 587, 588

584, 588, 589

585, 589, 590

586, 590, 591

587, 591, 592

588, 592, 593

589, 593, 594

590, 594, 595

591, 595, 596

592, 596, 597

593, 597, 598

594, 598, 599

595, 599, 600

596, 600, 601

597, 601, 602

598, 602, 603

599, 603, 604

600, 604, 605

601, 605, 606

602, 606, 607

603, 607, 608

604, 608, 609

605, 609, 610

606, 610, 611

607, 611, 612

608, 612, 613

609, 613, 614

610, 614, 615

611, 615, 616

612, 616, 617

613, 617, 618

614, 618, 619

615, 619, 620

616, 620, 621

617, 621, 622

618, 622, 623

619, 623, 624

620, 624, 625

621, 625, 626

622, 626, 627

623, 627, 628

624, 628, 629

625, 629, 630

626, 630, 631

627, 631, 632

628, 632, 633

629, 633, 634

630, 634, 635

631, 635, 636

632, 636, 637

633, 637, 638

634, 638, 639

635, 639, 640

636, 640, 641

637, 641, 642

638, 642, 643

639, 643, 644

640, 644, 645

641, 645, 646

642, 646, 647

643, 647, 648

644, 648, 649

645, 649, 650

646, 650, 651

647, 651, 652

648, 652, 653

649, 653, 654

650, 654, 655

651, 655, 656

652, 656, 657

653, 657, 658

654, 658, 659

655, 659, 660

656, 660, 661

657, 661, 662

658, 662, 663

659, 663, 664

660, 664, 665

661, 665, 666

662, 666, 667

663, 667, 668

664, 668, 669

665, 669, 8

666, 8, 670

667, 670, 671

668, 671, 672

669, 672, 673

670, 673, 674

671, 674, 675

672, 675, 676

673, 676, 677

674, 677, 678

675, 678, 679

676, 679, 680

677, 680, 681

678, 681, 682

679, 682, 683

680, 683, 684

681, 684, 685

682, 685, 686

683, 686, 687

684, 687, 688

685, 688, 689

686, 689, 690

687, 690, 691

688, 691, 692

689, 692, 693

690, 693, 694

691, 694, 695

692, 695, 696

693, 696, 697

694, 697, 698

695, 698, 699

696, 699, 700

697, 700, 701

698, 701, 702

699, 702, 703

700, 703, 704

701, 704, 705

702, 705, 706

703, 706, 707

704, 707, 708

705, 708, 709

706, 709, 710

707, 710, 711

708, 711, 712

709, 712, 713

710, 713, 714

711, 714, 715

712, 715, 716

713, 716, 717

714, 717, 718

715, 718, 719

716, 719, 720

717, 720, 721

718, 721, 722

719, 722, 723

720, 723, 724

721, 724, 725

722, 725, 726

723, 726, 727

724, 727, 728

725, 728, 729

726, 729, 730

727, 730, 731

728, 731, 732

729, 732, 733

730, 733, 734

731, 734, 735

732, 735, 736

733, 736, 737

734, 737, 738

735, 738, 739

736, 739, 740

737, 740, 741

738, 741, 742

739, 742, 743

740, 743, 744

741, 744, 745

742, 745, 746

743, 746, 747

744, 747, 748

745, 748, 749

746, 749, 750

747, 750, 751

748, 751, 752

749, 752, 753

750, 753, 754

751, 754, 755

752, 755, 756

753, 756, 757

754, 757, 758

755, 758, 759

756, 759, 760

757, 760, 761

758, 761, 762

759, 762, 763

760, 763, 9

761, 9, 764

762, 764, 765

763, 765, 766

764, 766, 767

765, 767, 768

766, 768, 769

767, 769, 770

768, 770, 771

769, 771, 772

770, 772, 773

771, 773, 774

772, 774, 775

773, 775, 776

774, 776, 777

775, 777, 778

776, 778, 779

777, 779, 780

778, 780, 781

779, 781, 782

780, 782, 783

781, 783, 784

782, 784, 785

783, 785, 786

784, 786, 787

785, 787, 788

786, 788, 789

787, 789, 790

788, 790, 791

789, 791, 792

790, 792, 793

791, 793, 794

792, 794, 795

793, 795, 796

794, 796, 797

795, 797, 798

796, 798, 799

797, 799, 800

798, 800, 801

799, 801, 802

800, 802, 803

801, 803, 804

802, 804, 805

803, 805, 806

804, 806, 807

805, 807, 808

806, 808, 809

807, 809, 810

808, 810, 811

809, 811, 812

810, 812, 813

811, 813, 814

812, 814, 815

813, 815, 816

814, 816, 817

815, 817, 818

816, 818, 819

817, 819, 820

818, 820, 821

819, 821, 822

820, 822, 823

821, 823, 824

822, 824, 825

823, 825, 826

824, 826, 827

825, 827, 828

826, 828, 829

827, 829, 830

828, 830, 831

829, 831, 832

830, 832, 833

831, 833, 834

832, 834, 835

833, 835, 836

834, 836, 837

835, 837, 838

836, 838, 839

837, 839, 840

838, 840, 841

839, 841, 842

840, 842, 843

841, 843, 844

842, 844, 845

843, 845, 846

844, 846, 847

845, 847, 848

846, 848, 849

847, 849, 850

848, 850, 851

849, 851, 852

850, 852, 853

851, 853, 854

852, 854, 855

853, 855, 856

854, 856, 857

855, 857, 10

856, 10, 858

857, 858, 859

858, 859, 860

859, 860, 861

860, 861, 862

861, 862, 863

862, 863, 864

863, 864, 865

864, 865, 866

865, 866, 867

866, 867, 868

867, 868, 869

868, 869, 870

869, 870, 871

870, 871, 872

871, 872, 873

872, 873, 874

873, 874, 875

874, 875, 876

875, 876, 877

876, 877, 878

877, 878, 879

878, 879, 880

879, 880, 881

880, 881, 882

881, 882, 883

882, 883, 884

883, 884, 885

884, 885, 886

885, 886, 887

886, 887, 888

887, 888, 889

888, 889, 890

889, 890, 891

890, 891, 892

891, 892, 893

892, 893, 894

893, 894, 895

894, 895, 896

895, 896, 897

896, 897, 898

897, 898, 899

898, 899, 900

899, 900, 901

900, 901, 902

901, 902, 903

902, 903, 904

903, 904, 905

904, 905, 906

905, 906, 907

906, 907, 908

907, 908, 909

908, 909, 910

909, 910, 911

910, 911, 912

911, 912, 913

912, 913, 914

913, 914, 915

914, 915, 916

915, 916, 917

916, 917, 918

917, 918, 919

918, 919, 920

919, 920, 921

920, 921, 922

921, 922, 923

922, 923, 924

923, 924, 925

924, 925, 926

925, 926, 927

926, 927, 928

927, 928, 929

928, 929, 930

929, 930, 931

930, 931, 932

931, 932, 933

932, 933, 934

933, 934, 935

934, 935, 936

935, 936, 937

936, 937, 938

937, 938, 939

938, 939, 940

939, 940, 941

940, 941, 942

941, 942, 943

942, 943, 944

943, 944, 945

944, 945, 946

945, 946, 947

946, 947, 948

947, 948, 949

948, 949, 950

949, 950, 951

950, 951, 11

*Nset, nset=_PickedSet2, internal, generate

1, 951, 1

*Elset, elset=_PickedSet2, internal, generate

1, 950, 1

** Section: SteelBeam Profile: Profile-1

*Beam Section, elset=_PickedSet2, material=Steel, temperature=GRADIENTS, section=RECT

0.05, 0.03

0.,0.,-1.

*End Part

**

**

** ASSEMBLY

**

*Assembly, name=Assembly

**

*Instance, name=Part-1-1, part=Part-1

*End Instance

**

*Nset, nset=_PickedSet6, internal, instance=Part-1-1

1,

*Nset, nset=_PickedSet8, internal, instance=Part-1-1, generate

1, 951, 1

*Elset, elset=_PickedSet8, internal, instance=Part-1-1, generate

1, 950, 1

*Nset, nset=_PickedSet9, internal, instance=Part-1-1

11,

*End Assembly

**

** MATERIALS

**

*Material, name=Steel

*Density

8050.,

*Elastic

2e+11, 0.3

**

** BOUNDARY CONDITIONS

**

** Name: BC-1 Type: Displacement/Rotation

*Boundary

_PickedSet6, 2, 2

** Name: BC-3 Type: Displacement/Rotation

*Boundary

_PickedSet8, 1, 1

_PickedSet8, 3, 3

_PickedSet8, 4, 4

** Name: BC-4 Type: Displacement/Rotation

*Boundary

_PickedSet9, 2, 2

** —————————————————————-

**

** STEP: Frequency Extraction

**

*Step, name=”Frequency Extraction”, nlgeom=NO, perturbation

*Frequency, eigensolver=Lanczos, sim=NO, acoustic coupling=on, normalization=displacement

15, , , , ,

**

** OUTPUT REQUESTS

**

*Restart, write, frequency=0

**

** FIELD OUTPUT: F-Output-1

**

*Output, field, variable=PRESELECT

**

*MATRIX GENERATE, STIFFNESS, MASS

*MATRIX OUTPUT, STIFFNESS, MASS, FORMAT=MATRIX INPUT

*End Step

ZemosHello all,

first of all a big thank you for the explanation about exporting mass and stiffness matrices. I have created a beam with a fixed restraint and deposited steel as material model.Works great.

Works great. For a student research project I need the mass and stiffness matrices for a body that consists of a hyperelastic model. The instructions for exporting the matrices also work for this.

The only problem is that at the beginning a number of entries is zero. As an example: A beam consists of 53 nodes, so I get in the TXT file for the mass matrix in the format(coordinate) 424 entries, of which they are the first 106 entries zero, so

1 1 0

2 2 0

.

.

.

106 106 0

After that, the entries are shifting from zero, so in the end there are 318 entries different from zero (53 nodes a 6 degrees of freedom = 318 entries).

so

107 107 x

.

.

.

424 424 y

My question now is, what do the first 106 entries in which there is a zero mean? The mass and stiffness matrix is to be read into MatLab afterwards. Only zeros on the main diagonal are not advantageous, if the matrix has to be inverted. As element type currently C3D4H is used.

I hope someone has a tip. Thanks a lot !

Greetings

Zemos

Translated with http://www.DeepL.com/Translator (free version)

DorothyHi Zemos,

Sorry about late reply, I was focusing on my qualifying exams. I did not use C3D4H element before and am not sure what are the zeros. I would suggest to output the matrices in matrix input format

`FORMAT=MATRIX INPUT`

, and then you will know where the zeros locate, at which node and which dof. Hope this helps.NinaDear Dorothy’s world

First of all i want to thank you for your blog , you helped me a lot with some problems i found in ABAQUS.

i have a question and i Don’t find the ansewer in the internet , can you tell me how do we extract the modeshapes vector in a frequency analysis in Abaqus ?

I need this vector to do calculation with it.

thank you very much for your answer

Regards,

DorothyHi Nina,

As far as I know, abaqus does not output the mode shape vectors automatically. But you can output filed variables (displacements) at each node, then you need to process the data to get it into the format you want. You can output the displacements in Visualization module – creating XY data, then select unique nodal and all the nodes. Hope this helps.

SeokminHello, Dorothy

Thank you for sharing great tips!

I wonder how to lump mass matrix for shell element.

So that I’m going to try your method in the case of Abaqus/Explicit, but as you mentioned in note 2.

This code does not work in Abaqus/Explicit. Do you have any idea about it?

I need a lumping mass matrix for the shell element. I think that if I could make a lumping mass matrix for modal. or implicit dynamics analysis, your code may work.

Thank you.

Regards.

DorothyHi Seokmin,

I am not sure why the codes do not work in Abaqus/Explicit. I searched the official documents and also online, but got no answer.

I think you are exactly correct about how to get lumping mass matrix for the shell element. Since the mass matrix is a property of structure, you can definitely try from modal analysis.

Hope this helps.

Bests.

GokayHi Dorothy,

I generated mass matrix by Abaqus, but it has nonzero off diagonal values.

I need to get lumped mass matrix with nonzero values only at the diagonal.

In Ansys I can turn Lump on and that produces a lumped diagonal mass matrix, but I do not know how to do that in Abaqus.

DorothyHi Gokay,

The default mass matrix in Abaqus is consistent mass matrix. I used point mass for beam elements in order to get lumped mass matrix. I am not sure if there is a similar convenient way as in Ansys (I did not find in official guides). If you are using beam elements, point mass is a good choice. Hope this helps.

zaferHi Dorothy,

Your blog is very informative, thank you for sharing your experiences.

In my case, I have a complex 3D model in Abaqus. Since there are very thin parts in my model, I modeled the structure using solid and shell sections.

I defined some parts of the structure as solids and some parts as shells. After I got the mass matrix, I saw that mass matrix is not diagonal.

Normally, if I only used 3D solid parts, I would have a 3n*3n diagonal mass matrix because it would have 3 DOFs at each node.

But now that I’m using both solid and shell structures, the mass matrix is a non-diagonal matrix. How do I find out the total number of nodes and DOFs? What order is there? Which node has 3 DOFs, which has more or less DOFs?

P.S. I did not use point mass or inertia etc. I just defined the material properties as usual.

DorothyThank you Zafer.

Consistent mass matrix is default in Abaqus, and you used material properties in your model, so you will have off-diagonal elements in mass matrix.

From my understanding, the 3D solid element will have 6 dofs at each node, including the three rotation dofs, and the number of dofs in shell element depends on the particular element.

For detailed number of dofs, you can check the element description in Abaqus Analysis User’s Guide.

You can use select

, thenToolsto check the nodes and elements. To get the total number of nodes or elements, creating a set and then query the set (also select tools and then query) would be a better option.QueryThe order of node number depends on the order of meshing, but I did not investigate this in detail. I usually use matlab or python to postprocess the node or element data.

JackHi Dorothy,

In Abaqus, we can easily see the node numbers by doing the following: View tab–> Assembly display option–>Mesh–>Show node labels.

However, I would like to see the DOF numbers. When we generate mass and stiffness matrices, what we get is:

1.Row node label

2.Degree of freedom for row node

3.Column node label

4.Degree of freedom for column node

5.Matrix entry

How can I figure out the DOF numbers in the corresponding node numbers?

GokayHi Dorothy,

In Abaqus, we can easily see the node numbers by doing the following: View tab–> Assembly display option–>Mesh–>Show node labels.

However, I would like to see the DOF numbers. When we generate mass and stiffness matrices, what we get is:

1.Row node label

2.Degree of freedom for row node

3.Column node label

4.Degree of freedom for column node

5.Matrix entry

How can I figure out the DOF numbers in the corresponding node numbers?

In my case I have both solid and shell elements. Therefore, there are 3DOF for the solid sections and 6DOF for the shell sections.

Let’s think together. I want to see the DOF number at node 8 in solid element. Since the DOF numbers for the solid elements are 3n-2,3n-1,3n, they become 22 23 24.

Same logic.

I want to see the DOF number at node 4 in the shell element. Since the DOF numbers for the shell elements are 6n-5,6n-4,6n-3,6n-2,6n-1,6n, so they become 19 20 21 22 23 24.

As you can see here, it’s very confusing to me.

How can I understand DOF numbers? Since I am implementing Bloch Theory in Abaqus I need corresponding individual DOF numbers for each node.

DorothyHi Gokay,

The dof number could only be 1 to 6 or 1 to 3 depending on the element type. It won’t become 3n-2, 3n-1 or 3n.

Let’s see one example “1,5, 1,1, 9.283850055777577e-12”. The number 9.283850055777577e-12 is at the matrix row node 1 dof 5 and column node 1 dof 1.

I think you might need to check a finite element analysis book to see what the elements in a stiffness/mass matrix mean and how to assemble the element matrices into global matrix. These would definitely help you understand the stiffness matrix in abaqus.

GokayHi Dorothy,

Thank you for your answer. I think I explained it wrong. Let me get this straight.

The dof number could only be 1 to 6 or 1 to 3 depending on the element type. It is definitely correct and I agree with you.

For example, the dof number for node 1 would be 1 to 3. (Because the dof number 1 to 3 for solid element).

So here we can see that n=1(node number), the number of dof should be 3n-2.3n-1.3n. What I mean here is that when we put n=1 into the 3n-2,3n-1,3n equation, we can get 1,2,3 dof numbers.

This is just a representation. For example, the dof number for node 2 would be 4 to 6. (Because the dof number 1 to 3 for each node). When we put n=2 into the 3n-2,3n-1,3n equation, we can get 4,5,6 dof numbers.

Same logic applies to shell elements.

If we have a shell elemet, the dof number should be 1 to 6. For example, the dof number for node 1 would be 1 to 6. (Because the dof number 1 to 6 for shell element).

So here we can see that n=1(node number), the number of dof should be 6n-5. 6n-4, 6n-3. 6n-2. 6n-1. 6n.

So, the dof number for node 1( assume node 1 is a shell element), would be 1 to 6. What I mean here is that when we put n=1 into the 6n-5. 6n-4, 6n-3. 6n-2. 6n-1. 6n equation, we can get 1,2,3,4,5,6 dof numbers.

I think everything is clear so far.

My previous question was that:

Let’s assume, I want to see the DOF number at node 8 in solid element. The dof number for the solid element could only be 1 to 3. If I want to see the dof number at node 8 in solid element, the dof number should be 22,23,24 (They come from the 3n-2,3n-1,3n equation. I explained it above).

Same logic.

I want to see the dof number at node 4 in shell element. The dof number for the shell element could only be 1 to 6. If I want to see the dof number at node 4 in shell element, the dof number should be 19 20 21 22 23 24. (They come from the 6n-5,6n-4,6n-3,6n-2,6n-1,6n equation. I explained it above).

As you can see here I have some common DOF numbers used for solid and shell elements. How can I understand which is which?

DorothyHi Gokay,

I did not notice your comment until I got notification for a new one. Sorry about that.

I now understand what you mean by the equations, the row/column number in the global matrix. You are right about this.

When there are two or more nodes from different elements, we have the original numbers of dofs (for example you used 6 dofs for one node in shell element). We will then have constraints for the dofs since they have the same displacement or rotation (for example some dofs from the node connecting two elements), which means the displacements or rotations in the u vector are the same (as we all know Ku=F).

Hope this helps.

KundanHi,

Thanks for the nice detailing of all the steps.

I have some queries. I am getting global stiffness matrix but some row and column entries are missing in the matrix. For example

1 1

1 2 are there

but 3 2

2 3 are not there in the matrix.

Then without knowing 3 2 and 2 3, how I can form the square mass and stiffness matrix. Without knowing the square mass and stiffness, we cannot do eigen value analysis. Please help.

DorothyThank you Kundan 🙂

The missing ones have a value of zero, and abaqus only outputs those with non-zero values.

You may safely initialize the matrix with all zeros and then write the elements with values from the output.

Hope this helps.

KeserI have more than one beam model which includes also material damping as alpha and beta coefficient. I used substructure in model. I can obtain reduced mass & stiffness Matrix in .mtx format for substructure. (*Substructure Matrix output, file format= user defined, stiffness=yes, mass=yes)

But I can’t obtain reduced damping Matrix for substructure. How I can obtain?

DorothyHi Keser,

I did not output matrix for substructure before. I checked the keyword

`*Substructure Matrix output`

and it does not contain parameter damping. But since you are using Rayleigh damping, you can postprocess by`[C] = alpha*[M] + beta*[K]`

.Hope this helps.

KeserYes, I am using Rayleigh damping. How can I postprocess by [C] = alpha*[M] + beta*[K] ? The below part is our model which causes “unknown parameter damping error”.

*Heading

*Preprint, echo=NO, model=NO, history=NO, contact=NO

** —————————————————————-

**

** PART INSTANCE: PART-1-1

**

*Node

1, 4430.37988, 0.452399999, 1533.67004

31682, 2463.63989, -873.503662, 726.17688

170918, 2470.02173, -974.755737, 673.070801

170919, 2470.02173, -1088.12451, 550.050293

170920, 2470.02173, -1151.9021, 406.909515

170921, 2470.02173, -1199.73962, 228.377731

170922, 2468.96899, -1247.5, 50.1334686

170923, 1494.91553, -1247.5, 50.1450768

170924, 4070.02173, -1247.5, 50.1334686

170925, 4386.68311, -1247.5, 50.1334686

170926, 4070.02173, -1213.12708, 178.415192

170927, 4070.02173, -1178.69702, 306.909515

170928, 4070.02173, -1114.69446, 450.396088

170929, 4070.02173, -999.773132, 574.43866

170930, 4070.02173, -852.961121, 652.136353

170931, 4070.02173, -695.734131, 677.5

170932, 4070.02173, -656.299744, 677.5

170933, 2463.63721, 873.432861, 726.134338

170934, 2470.0188, 974.682312, 673.023376

170935, 2470.01831, 1088.04517, 549.997314

170936, 2470.01807, 1151.8158, 406.853455

170937, 2470.01807, 1199.64453, 228.319321

170938, 2468.96509, 1247.39624, 50.0727463

170939, 1494.9115, 1247.39319, 50.0843544

170940, 4070.01782, 1247.40137, 50.0727463

170941, 4386.6792, 1247.40234, 50.0727463

170942, 4070.01807, 1213.03455, 178.35614

170943, 4070.01807, 1178.61084, 306.852142

170944, 4070.01831, 1114.61523, 450.341827

170945, 4070.01855, 999.699951, 574.389954

170946, 4070.01904, 852.891724, 652.094849

170947, 4070.01953, 695.666016, 677.466125

170948, 4070.01978, 656.231567, 677.468079

170949, 4430.37988, 0.452399999, 1533.67004

*Element, type=B31H

146235, 31682, 170918

146236, 170918, 170919

146237, 170919, 170920

146238, 170920, 170921

146239, 170921, 170922

146240, 170922, 170923

146241, 170922, 170924

146242, 170924, 170925

146243, 170924, 170926

146244, 170926, 170927

146245, 170927, 170928

146246, 170928, 170929

146247, 170929, 170930

146248, 170930, 170931

146249, 170931, 170932

146250, 170934, 170933

146251, 170935, 170934

146252, 170936, 170935

146253, 170937, 170936

146254, 170939, 170938

146255, 170938, 170937

146256, 170940, 170938

146257, 170941, 170940

146258, 170942, 170940

146259, 170943, 170942

146260, 170944, 170943

146261, 170945, 170944

146262, 170946, 170945

146263, 170947, 170946

146264, 170948, 170947

146265, 31682, 170933

146266, 170932, 170948

*Elset, elset=PART-1-1_PART-1-1_SET-13

146240, 146241, 146242, 146254, 146256, 146257

*Elset, elset=PART-1-1_PART-1-1_SET-14

146235, 146236, 146237, 146238, 146239, 146243, 146244, 146245, 146246, 146247, 146250, 146251, 146252, 146253, 146255, 146258

146259, 146260, 146261, 146262

*Elset, elset=PART-1-1_PART-1-1_SET-15

146248, 146249, 146263, 146264, 146265, 146266

*Elset, elset=PART-1-1_Set-4

146240, 146241, 146242, 146254, 146256, 146257

*Elset, elset=PART-1-1_Set-5

146235, 146236, 146237, 146238, 146239, 146250, 146251, 146252, 146253, 146255, 146265

*Elset, elset=PART-1-1_Set-6

146243, 146244, 146245, 146246, 146247, 146248, 146249, 146258, 146259, 146260, 146261, 146262, 146263, 146264, 146266

** Region: (Ön-Çapraz:Set-5), (Beam Orientation:PART-1-1_SET-14)

*Elset, elset=PART-1-1__I1

146235, 146236, 146237, 146238, 146239, 146250, 146251, 146252, 146253, 146255

** Section: Ön-Çapraz Profile: Profile-Ön-Çapraz

*Beam Section, elset=PART-1-1__I1, material=MATERIAL-1, temperature=GRADIENTS, section=PIPE

40., 2.5

0.,0.,-1.

** Section: Yatay Profile: Profile-Yatay

*Beam Section, elset=PART-1-1_Set-4, material=MATERIAL-1, temperature=GRADIENTS, section=PIPE

37., 2.

0.,0.,-1.

** Region: (Arka-Çapraz:Set-6), (Beam Orientation:PART-1-1_SET-14)

*Elset, elset=PART-1-1__I3

146243, 146244, 146245, 146246, 146247, 146258, 146259, 146260, 146261, 146262

** Section: Arka-Çapraz Profile: Profile-Arka-Çapraz

*Beam Section, elset=PART-1-1__I3, material=MATERIAL-1, temperature=GRADIENTS, section=PIPE

33., 2.5

0.,0.,-1.

** Region: (Arka-Çapraz:Set-6), (Beam Orientation:PART-1-1_SET-15)

*Elset, elset=PART-1-1__I4

146248, 146249, 146263, 146264, 146266

** Section: Arka-Çapraz Profile: Profile-Arka-Çapraz

*Beam Section, elset=PART-1-1__I4, material=MATERIAL-1, temperature=GRADIENTS, section=PIPE

33., 2.5

0.,0.,-1.

** Region: (Ön-Çapraz:Set-5), (Beam Orientation:PART-1-1_SET-15)

*Elset, elset=PART-1-1__I5

146265,

** Section: Ön-Çapraz Profile: Profile-Ön-Çapraz

*Beam Section, elset=PART-1-1__I5, material=MATERIAL-1, temperature=GRADIENTS, section=PIPE

40., 2.5

0.,0.,-1.

*System

*Elset, elset=LG, generate

146235, 146266, 1

*Nset, nset=MASTER_NODE

170949,

*Elset, elset=PART-1-1_SET-3

146240, 146254

*Elset, elset=PART-1-1_SET-4

146241, 146256

*Elset, elset=PART-1-1_SET-5

146242, 146257

*Elset, elset=PART-1-1_SET-6

146239, 146243, 146255, 146258

*Elset, elset=PART-1-1_SET-7

146238, 146244, 146253, 146259

*Elset, elset=PART-1-1_SET-8

146236, 146237, 146245, 146246, 146251, 146252, 146260, 146261

*Elset, elset=PART-1-1_SET-9

146235, 146247, 146250, 146262

*Elset, elset=PART-1-1_SET-10

146235, 146247, 146248, 146250, 146262, 146263

*Elset, elset=PART-1-1_SET-11, generate

146264, 146266, 1

*Elset, elset=PART-1-1_SET-12

146248, 146249, 146263, 146264, 146265, 146266

*Nset, nset=PART-1-1__PICKEDSET18

170922,

*Nset, nset=PART-1-1__PICKEDSET19

170919,

*Nset, nset=PART-1-1__PICKEDSET20

170919,

*Nset, nset=PART-1-1__PICKEDSET21

31682,

*Nset, nset=PART-1-1__PICKEDSET22

170938,

*Nset, nset=PART-1-1__PICKEDSET23

170935,

*Nset, nset=PART-1-1__PICKEDSET24

170935,

*Nset, nset=PART-1-1__PICKEDSET25

170933,

*Nset, nset=PART-1-1__PICKEDSET26

170924,

*Nset, nset=PART-1-1__PICKEDSET27

170929,

*Nset, nset=PART-1-1__PICKEDSET28

170929,

*Nset, nset=PART-1-1__PICKEDSET29

170930,

*Nset, nset=PART-1-1__PICKEDSET30

170940,

*Nset, nset=PART-1-1__PICKEDSET31

170944,

*Nset, nset=PART-1-1__PICKEDSET32

170944,

*Nset, nset=PART-1-1__PICKEDSET33

170946,

*Nset, nset=SET-4

170922, 170924, 170938, 170940

*Nset, nset=SLAVE_NODES

170918, 170930, 170934, 170946

*Nset, nset=Set-32

170922, 170924, 170938, 170940

*Nset, nset=SLAVE_NODES_CNS_

170918, 170930, 170934, 170946

*Surface, type=NODE, name=SLAVE_NODES_CNS__CNS_

SLAVE_NODES_CNS_, 1.

** Constraint: CONSTRAINT-1

*Coupling, constraint name=CONSTRAINT-1, ref node=MASTER_NODE, surface=SLAVE_NODES_CNS__CNS_

*Distributing, weighting method=LINEAR, coupling=STRUCTURAL

**

** MATERIALS

**

*Material, name=MATERIAL-1

*Damping, alpha=0.1, beta=0.05

*Density

2.78e-09,

*Elastic

71016., 0.33

** —————————————————————-

**

** STEP: Modal

**

*Step, name=Modal, nlgeom=NO, perturbation

*Steady State Dynamics, direct, friction damping=NO

0., 300., 2,

**

** OUTPUT REQUESTS

**

**

** FIELD OUTPUT: F-Output-2

**

*Output, field, variable=PRESELECT

**

** HISTORY OUTPUT: H-Output-1

**

*Output, history, variable=PRESELECT

*End Step

** —————————————————————-

**

** STEP: Substructure

**

*Step, name=Substructure, nlgeom=NO

*Substructure Generate, overwrite, type=Z8789, recovery matrix=YES, nset=MASTER_NODE, mass matrix=YES,

structural damping matrix=YES, viscous damping matrix=YES

*Damping Controls, structural=COMBINED, viscous=COMBINED

**

** BOUNDARY CONDITIONS

**

** Name: Fixed Type: Displacement/Rotation

*Boundary

Set-32, 1, 1

Set-32, 2, 2

Set-32, 3, 3

Set-32, 4, 4

Set-32, 5, 5

Set-32, 6, 6

*Retained Nodal Dofs, SORTED=NO

MASTER_NODE, 1, 6

*SUBSTRUCTURE MATRIX OUTPUT, OUTPUT FILE=USER DEFINED, FILE NAME=Matrix, MASS=YES, STIFFNESS=YES, DAMPING=YES

*End Step

DorothyHi Keser,

The “unknown parameter damping error” appears since the keyword

`*Substructure Matrix output`

does not have parameter`damping`

.You may use matlab or python to postprocess

`[C] = alpha*[M] + beta*[K]`

. Form a matrix and fill the corresponding element location with the value you got from the output. Then you can do the matrix operation to get`[C]`

.In the output matrix, you may need to check the node number and dof number to locate the value. But since you are using the substructure matrix, the output format might be different. This web page and the links in it might help.

KeserThanks for comments. What if I used a dashpot element in our model? How can obtain dashpot element damping parameter instead of Rayleigh damping?

DorothyHi Keser,

Sorry for late replay, I was focusing on my finals. I do not have the experience with dashpot element, but I checked the document here and found dashpots cannot be used within substructures. The document recommends to define Rayleigh damping within the substructure definition or on the usage level to create damping within a substructure. So dashpots are not suitable for your case.

Hope this helps.

KeserThanks for explanation. I tried to use Rayleigh damping also. Mu question is that exporting damping matrix in substructure. How can I extract/export reduced damping Matrix? Which type of word is needed for input file?

DorothyHi Keser,

As I explained before, no

`damping`

parameter is available in the keyword`*Substructure Matrix output`

. So I would recommend to get the damping matrix by postprocessing from the mass matrix and stiffness matrix`[C] = alpha*[M] + beta*[K]`

. Please check the previous replay for more details.Hope this helps.

KeserHi Dorothy,

I also added damping=yes in “.inp” file. But I got error “invalid parameter damping”. So, I don’t understand the error😕

surenhow does one extrat the eigen vectors directly from abaqus?

DorothyHi Suren,

I never extracted eigenvector before and abaqus is now not available to me, so I am not sure how exactly to do.

I believe the link https://abaqus-docs.mit.edu/2017/English/SIMACAEANLRefMap/simaanl-c-freqextraction.htm would be helpful, possibly with a line of code added in the input file

`*FREQUENCY, EIGENSOLVER=AMS`

You may have a try and hope this works.

ChanHi Dorothy,

I need to extract the mass and stiffness matrices for a model with the following problem size:

P R O B L E M S I Z E

NUMBER OF ELEMENTS IS 249191

153326 linear line elements of type T3D2

84141 linear hexahedral elements of type C3D8R

102 linear line elements of type B31

11613 linear quadrilateral elements of type S4R

NUMBER OF NODES IS 267444

NUMBER OF NODES DEFINED BY THE USER 267240

NUMBER OF INTERNAL NODES GENERATED BY THE PROGRAM 204

TOTAL NUMBER OF VARIABLES IN THE MODEL 837207

(DEGREES OF FREEDOM PLUS MAX NO. OF ANY LAGRANGE MULTIPLIER

VARIABLES. INCLUDE *PRINT,SOLVE=YES TO GET THE ACTUAL NUMBER.)

The properties are input as mass density, and I believe they will be used to generate a consistent mass matrix.

Here’s the input file code I used:

** Global Mass and Stiffness matrix

*Step, name=Export matrix

*MATRIX GENERATE, STIFFNESS, MASS, VISCOUS DAMPING, STRUCTURAL DAMPING

*MATRIX OUTPUT, STIFFNESS, MASS, VISCOUS DAMPING, STRUCTURAL DAMPING, FORMAT=coordinate

I have the following questions regarding my problem:

Dimensions of M and K matrices

As indicated above, the number of degrees of freedom is 837,207, but the matrix dimensions are reduced to 354,231*354,231. Shouldn’t the number of degrees of freedom match the matrix dimensions?

Node numbering

The model consists of 8 parts, and the nodes start from 1 for each part. However, when I extract the matrices using the FORMAT=matrix input option, a different node numbering system (1 to 241,751) is applied, making it difficult to match the entries to the actual model locations. How can I find the correspondence between the entries in the M and K matrices and the nodes in the model?

In the coordinate format, I get 5,620,189 rows of data, while in the matrix input format, I get 2,987,210 rows of data. Shouldn’t the number of data entries be the same in both cases?

When using the matrix input format, the entries are extracted in the following format:

241751,3, 241751,3, 9.038200770026704e+00

Can I interpret the corresponding data as follows?

1: X (translational)

2: Y (translational)

3: Z (translational)

4: RX (rotational)

5: RY (rotational)

6: RZ (rotational)

The modes obtained from modal analysis in ABAQUS CAE GUI and the eigenanalysis results obtained from extracting the M and K matrices and performing the Lanczos method in MATLAB do not match. Is there any way to reconcile them?

DorothyHi Chan,

1) Dimensions of M and K matrices: the matrix dimension should be the total number of dofs in the model theoretically (I am not sure how you got 837,207). It is possible to have a matrix dimension less than this since you used a format of coordinate for output and abaqus will eliminate some zero elements. You might use

`MATRIX INPUT`

format instead so that you have the node number and dof in the rows. Then you can easily verify the dimensions.2) Node numbering: Honestly I am not sure how to renumber the nodes, but to my best knowledge it is not possible unless you use a python script. Abaqus is not available to me after my graduation, so I cannot help with this. Post processing might also be an option to find the correspondence between the entries in metrices.

3) Interpreting of element

`241751,3, 241751,3, 9.038200770026704e+00`

in matrix: row node label, dof for row node, column node label, dof for column node, matrix entry. The last number is the actual element in a matrix, and the first four numbers indicate the location of the element in the matrix.4) Reconcile eigen analysis results: when you have the correct matrices from abaqus (you may need to assemble the matrix with a script or compare only the eigenvalues and resemble the eigenvectors), and the results should be very close.

Hope these could help.

RamHi Chan, did you get the answer, I am also facing the same issue with my model. The Abaqus and Matlab frequency do not match and not able to understand the obtained matrix from Abaqus.

aazimHi Dorothy,

have you found a way to extract stiffness matrix, mass matrix for explicit dynamic problem, I am currently stuck on this.

Thanks and Regards

Aazim Shafi