Table of Contents
Linear stability
Computational diagram
Computational 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:
- Only the following elements can be used: pentahedron, hexahedron, semi-loof, and the corresponding connector elements.
- General symmetry or periodicity cannot be used.
| 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 initial stress matrices
The input data is written to the name.iG text file.
The program generates the initial stress matrices $\mathbf{G}$ of elements for the selected load case from the name.SOL file. The matrices are symmetric and they can be regular, singular (with different nullity), definite or indefinite.
| Program | GEO2 (2D problem) / GEO3 (3D problem) |
|---|---|
| Inputs | name.iG, binary files from the previous steps |
| Report | name.oG |
| Outputs | binary files |
| Details | Computation overview / Reference Manual: Inputs |
3. Solve the equation system
The input data is written to the name.iE text file, where the key $\mathtt{KEVP}=1$.
The program uses the subspace iteration method to calculate $\mathtt{NROOT}$ eigenpairs (eigenvectors and eigenvalues) of the generalized eigenvalue problem
$$\sum(\mathbf{K}-\lambda_i\mathbf{G})\mathbf{v}_i=0, \quad i=1,\dots,\mathtt{NROOT},$$
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. Normalize the eigenvectors
The input data is written into the name.iS text file.
The program stores two records for each of the $\mathtt{NROOT}$ eigenpairs calculated in the previous step in the name.S binary file. Odd records contain the normalized eigenvectors $\mathbf{v}_i$ while even records contain their corresponding eigenvalues $\lambda_i$.
| Program | STAB (2D / 3D problem) |
|---|---|
| Inputs | name.iS, binary files from the previous steps |
| Report | name.oS |
| Outputs | binary files (the solution is in the name.S file) |
| Details | Computation overview / Reference Manual: Inputs |
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 |