# Extract Matrix from ABAQUS

## 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:

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
For more details, you can refer to Abaqus Analysis User’s Guide .

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 Kx=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

### 96 comments On Extract Matrix from ABAQUS

• Tan Nguyen

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

** 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

• Dorothy

If 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 Zhou

Hello,

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?

• Dorothy

Hi 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 Lin

Hello 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!

• Dorothy

Hi 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 ZHAN

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

• JIM ZHAN

Hello 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 K

Hello 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).

• Dorothy

Hi 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 KULKARNI

Hello 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.

• Dorothy

Hi 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.

• AKBjk

Hello 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)

• Dorothy

Hi 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.

• AKBjk

Hello 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?

• Dorothy

Sorry 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 .

• ddaniel

Dear 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?
ddaniel

• Dorothy

Hi 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.

• ddaniel

Dear Doothy,
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

• Dorothy

Hi 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.

• Diana

Hi 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

• Dorothy

Hi 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.

• Katy

Hi 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

• Dorothy

Hi 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.

• Katy

Hi 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.

• Dorothy

Hi 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.dat file 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 Nair

I 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.

• Dorothy

Hi 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.

• Alireza

hi 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.

• Dorothy

Hi 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.

• Alireza

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.

• Dorothy

Hi 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 Dush

Hello 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

• Dorothy

Hi 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.

• Alireza

Hi 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.

• Dorothy

Hi Alireza,

• Karthikayen Raju

Hi Dorothy!
why cannot we extract matrices in abaqus explcit?

• Dorothy

Hi 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

• Lars

Hi 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.

Kind regards.

Lars

• Dorothy

Hi 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.

• Panida

Hi 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

• Dorothy

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

• Panida

Thank 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?

• Dorothy

Hi Panida,
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.

• Panida

Hi Dorothy,
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.

• Dorothy

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

• Panida

Hi 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,

• Sastha

Hi 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.

• Dorothy

Hi 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.

• Sastha

Hi 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

• Dorothy

Hi 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.

• Sastha

Hi 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

• Ivan

Hi 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

• Dorothy

Hi 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.

• SREESASTHARAM

Hi 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

• Dorothy

Hi 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.

• Dan

Hi 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?

• Dorothy

Hi 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!

• Dorothy

Hi 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.

• S4JJ4D

Hi,
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

• Dorothy

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

• Eva

Hi 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

• Dorothy

Hi 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%.

• Eva

I see. Thank you very much Dorothy!

• Constance efio

Hi 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?

• Dorothy

Hi 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 Ashleyed

Dear 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.

• Dorothy

Hi 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 Ashleyed

Dear 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.

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

• Zemos

Hello 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)

• Dorothy

Hi 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.

• Nina

Dear 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.
Regards,

• Dorothy

Hi 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.

• Seokmin

Hello, 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.

• Dorothy

Hi 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.

• Gokay

Hi 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.

• Dorothy

Hi 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.

• zafer

Hi Dorothy,

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.

• Dorothy

Thank 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 Tools, then Query to 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.
The 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.

• Jack

Hi 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?

• Gokay

Hi 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.

• Dorothy

Hi 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.

• Gokay

Hi 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?

• Dorothy

Hi 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.

• Kundan

Hi,
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.

• Dorothy

Thank 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.

• Keser

I 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?

• Dorothy

Hi 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.

• Keser

Yes, 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”.
*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

• Dorothy

Hi 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.

• Keser

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

• Dorothy

Hi 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.

• Keser

Thanks 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?

• Dorothy

Hi 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.

• Keser

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

### Site Footer

Recording Life, Sharing Knowledge, Be Happy~