Package for Machine Design

Finite Element Analysis in Structural Mechanics

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Transient response

Computational flowchart

Computational steps

1. Preparing the computation

The solution of this problem must be preceded by the calculation of element stiffness matrices $\mathbf{K}$ (i.e., the first three steps of the linear elastostatic problem solution). The following conditions apply:

The right-hand side does not matter in this case; therefore, only quantities specifying material properties and displacement boundary conditions can be considered in the first load case (AS 1) in the name.i2 file.

Program RMD2, RPD2, SRH2 (2D problem) / RMD3, RPD3, SRH3 (3D problem)
Inputs name.i1, name.i2, name.i3
Logs name.o1, name.o2, name.o3
Outputs binary files
Details Linear elastostatics, Computation overview / Reference Manual: Inputs

2. Calculating the mass matrices

Input data are written to the text file name.iM. The program generates consistent (thus positive-definite) mass matrices $\mathbf{M}$ of elements.

Program HMOT (2D / 3D problem)
Inputs name.iM, binary files from the previous steps
Log name.oM
Outputs binary files
Details Computation overview / Reference Manual: Inputs

3. Calculating the damping matrices

Input data are written to the text file name.iC. The program generates Rayleigh proportional damping matrices $\mathbf{C}$ of elements. Regarding the definiteness of the generated matrices, nothing can be stated in advance.

Program HCRE (2D / 3D problem)
Inputs name.iC, binary files from the previous steps
Log name.oC
Outputs binary files
Details Computation overview / Reference Manual: Inputs
Note
Other types of damping matrices may also be considered; however, in such a case, the user must ensure they are stored in the name.AMP binary file and the HCRE program is not invoked.

4. Performing the factorization of the global matrix

Input data are written to the text file name.iR. The program factorizes the matrix $$\sum(\mathbf{K}+a_0\mathbf{M}+a_1\mathbf{C}),$$ where $\sum(\dots)$ denotes global (not element) matrices. The consistent mass matrix $\sum(\mathbf{M})$ is positive definite, and the matrix $\sum(a_0\mathbf{M}+a_1\mathbf{C})$ usually exhibits the same property. Since quasi-static processes are not considered here, the matrix $\sum(\mathbf{K}+a_0\mathbf{M}+a_1\mathbf{C})$ will then also be positive definite, even if $\sum(\mathbf{K})$ is only positive semidefinite. It is recommended to check that no pivots smaller than $\mathtt{PIVOT}$ are reported in the name.oR file.

Program HFRO (2D / 3D problem)
Inputs name.iR, binary files from the previous steps
Log name.oR
Outputs binary files
Details Computation overview / Reference Manual: Inputs

5. Integrating the equations of motion

Input data are written to the text file name.iW. The solution algorithm is the Newmark direct integration method. General means are available for specifying the initial conditions, as well as force or kinematic excitation. Furthermore, the output control allows keeping the amount of result data within reasonable limits and facilitates subsequent graphical post-processing. The method may be used for both damped and undamped processes.

Program HNEW (2D / 3D problem)
Inputs name.iW, binary files from the previous steps
Log name.oW
Outputs binary files (the solution is in the name.S file)
Details Computation overview / Reference Manual: Inputs

6. Calculating the strains and stresses

Input data are written to the text file name.i5, where the problem type key is $\mathtt{KPROB}=1$.

Program STR2 (2D problem) / STR3 (3D problem)
Inputs name.i5, binary files from the previous steps
Log name.o5
Outputs name.STR (optional), name.STB (optional)
Details Computation overview / Reference Manual: Inputs