Obsah
Modal superposition
Computation diagram
Computation steps
1. Prepare the computation
The solution of this problem must be preceded by the solution of the Linear elastostatics, 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.
It is recommended to check whether rigid body motion is prevented, meaning no pivots smaller than $\mathtt{PIVOT}$ are reported in the name.o4 file.
| Program | RMD2, RPD2, SRH2, FEFS (2D problem) / RMD3, RPD3, SRH3, FEFS (3D problem) |
|---|---|
| Inputs | name.i1, name.i2, name.i3, name.i4 |
| Report | name.o1, name.o2, name.o3, name.o4 |
| 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. Solve the equation system
The input data is written into the name.iE text file, where the key $\mathtt{KEVP}=0$.
The program uses the subspace iteration method to calculate $\mathtt{NROOT}$ eigenpairs (eigenvectors and eigenvalues) of the generalized eigenvalue problem
$$\sum(\mathbf{K}-\lambda_i\mathbf{M})\mathbf{v}_i=0, \quad i=1,\dots,\mathtt{NROOT},$$
where $\mathbf{v}_i$ and $\lambda_i$ are the $i$-th eigenvector and eigenvalue, and $\sum(\dots)$ denotes global (not element) matrices.
| Program | HEIG (2D / 3D problem) |
|---|---|
| Inputs | name.iE, binary files from the previous steps |
| Report | name.oE |
| Outputs | binary files (the solution is in the name.EIG file) |
| Details | Computation overview / Reference Manual: Inputs |
4. Perform the modal superposition
The input data is written into the name.iD text file.
The solution algorithm is based on the Duhamel integral method.
General means are available for specifying the initial conditions and excitation (harmonic kinematic excitation, seismicity, spectral acceleration).
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. Optional modal damping can also be specified within the name.iD file.
| Program | HMOD (2D / 3D problem) |
|---|---|
| Inputs | name.iD, binary files from the previous steps |
| Report | name.oD |
| Outputs | binary files (the solution is in the name.S file) |
| Details | Computation overview / Reference Manual: Inputs |
Note
If $\mathtt{KDUMP}=0$, thename.Sbinary file with the solution is not created, therefore, it is not possible to continue with the next step (Calculate the strains and stresses).
5. 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 |