Table of Contents
Transient response
Computation diagram
Computation steps
1. Prepare the computation
The solution of this problem must be preceded by the calculation of element stiffness matrices, and the following conditions apply:
- The same elements can be used as in a Linear elastostatics.
- General symmetry or periodicity cannot be used.
The right-hand side (the load case) 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 |
| Report | name.o1, name.o2, name.o3 |
| Outputs | binary files |
| Details | Linear elastostatics, Computation overview / Reference Manual: Inputs |
2. Calculate the mass matrices
The input data is written into the name.iM text file.
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 |
| Report | name.oM |
| Outputs | binary files |
| Details | Computation overview / Reference Manual: Inputs |
3. Calculate the damping matrices
The input data is written into the name.iC text file.
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 |
| Report | 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 thename.AMPbinary file and the HCRE program is not invoked.
4. Factorize the global matrix
The input data is written into the name.iR text file.
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 |
| Report | name.oR |
| Outputs | binary files |
| Details | Computation overview / Reference Manual: Inputs |
5. Integrate the equations of motion
The input data is written into the name.iW text file.
The solution algorithm is based on 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 |
| Report | name.oW |
| Outputs | binary files (the solution is in the name.S file) |
| Details | Computation overview / Reference Manual: Inputs |
6. Calculate the strains and stresses
The input data is written into the name.i5 text file, where the problem type key $\mathtt{KPROB}=1$.
| Program | STR2 (2D problem) / STR3 (3D problem) |
|---|---|
| Inputs | name.i5, binary files from the previous steps |
| Report | name.o5 |
| Outputs | name.STR (optionally), name.STB (optionally) |
| Details | Computation overview / Reference Manual: Inputs |
