## Basic concepts of engineering analysis

Analysis of discrete systems The essence of a lumped-parameter mathematical model is that the state of the system can be described directly with adequate precision by the magnitudes of a finite (and usually small) number of state variables. The solution requires the following steps: System idealization: the actual system is idealized as an assemblage of elements Element equilibrium: the equilibrium requirements of each element are established in terms of state variables Element assemblage: the element interconnection requirements are invoked to

## Finite Element Procedures – Matrix, Vectors, Tensors

Special Matrix symmetric matrix identity matrix / unite matrix symmetric banded matrix the following matrix is a symmetric banded matrix of order 5 and the half-bandwidth is 2. ${\rm{A}} = \left[ {\begin{array}{*{20}{c}} 3&2&1&0&0\\ 2&3&4&1&0\\ 1&4&5&6&1\\ 0&1&6&7&4\\ 0&0&1&4&3 \end{array}} \right]$ diagonal matrix: nonzero elements only on the diagonal of the matrix upper half of the matrix inverse matrix, the inverse of a matrix partitioning of matrix the trace and determinant of a matrix: only defined if the matrix is square tr(A)

## Examples of extracting matrices from ABAQUS

2D frame This is a plane steel frame with box sections subjected to a point load at one node figured as below. An dynamic implicit analysis step was defined and the following lines were added at the end of input file. ** *STEP *MATRIX GENERATE, STIFFNESS, MASS, LOAD, Structural Damping,Viscous Damping *MATRIX OUTPUT, STIFFNESS, MASS, LOAD, Structural Damping,Viscous Damping, FORMAT=COORDINATE *END STEP

## Time and Amplitude in ABAQUS

I am recently using the dynamic analysis in Abaqus, so I decided to summarize the understanding of time and amplitude in it so that I can refer to this article later if needed. Time Step Time: the time period in *STEP definition. Total Time: the sum of all the Step Time. Natural time: actual time that one thing takes. The time in Abaqus/Standard does not have any actual meaning, it can be understood as the relative time. The time in

## 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.

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