Table of Contents
Modal superposition
Computational flowchart
Computational steps
1. Preparing the computation
The solution of this problem must be preceded by the first four steps of the linear elastostatic problem solution, which include the calculation of element stiffness matrices $\mathbf{K}$. The following conditions apply:
- The same elements can be used as in linear elastostatics.
- Analytical prescription of symmetry or periodicity cannot be used.
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.
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 |
| Logs | name.o1, name.o2, name.o3, name.o4 |
| 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. Solving the system of equations
Input data are written to the text file name.iE, where $\mathtt{KEVP}=0$.
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 |
| Log | name.oE |
| Outputs | binary files (the solution is in the name.EIG file) |
| Details | Computation overview / Reference Manual: Inputs |
4. Performing the modal superposition
Input data are written to the text file name.iD.
The solution algorithm is 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 |
| Log | 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 (Calculating the stresses and displacements).
5. 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 |