Table of Contents
Linear stability
Computation schema
Computation steps
1. Prepare the computation
The solution of this problem must be preceded by the solution of the linear elastostatic problem, and the following restrictions apply:
- Only the following elements can be used: pentahedron, hexahedron, semi-loof, and the corresponding connector elements: edge connection, face connection.
- General symmetry or periodicity cannot be used.
| Program | RMD3, RPD3, SRH3, FEFS |
|---|---|
| Inputs | name.i1, name.i2, name.i3, name.i4 |
| Protocol | name.o1, name.o2, name.o3, name.o4 |
| Outputs | binary files (the solution is in the file name.SOL) |
| Details | Linear elastostatics, Computation overview / Reference Manual: Inputs |
2. Calculate the initial stress matrices
The input data is written to the text file name.iG.
The program generates the initial stress matrices $\mathbf{G}$ of all elements for the selected load case from the file name.SOL. The matrices $\mathbf{G}$ are symmetric; they can be regular, singular (with different nullity), definite or indefinite.
| Program | GEO3 |
|---|---|
| Inputs | name.iG, binary files from previous steps |
| Protokol | name.oG |
| Outputs | binary files |
| Details | Computation overview / Reference Manual: Inputs |
3. Solve the equations
The input data is written to the text file name.iE, where the key $\mathtt{KEVP}=1$.
The program calculates, using the subspace iteration method, $\mathtt{NROOT}$ eigenpairs (eigenvectors and eigenvalues) of the general eigenproblem
$$\sum(\mathbf{K}-\lambda_i\mathbf{G})\mathbf{v}_i=0, \quad i=1,\dots,\mathtt{NROOT},$$
where $\mathbf{v}_i$ and $\lambda_i$ are the $i$-th eigenvector and eigenvalue, and $\sum(\dots)$ indicates that these are global (not element) matrices.
| Program | HEIG |
|---|---|
| Inputs | name.iE, binary files from previous steps |
| Protokol | name.oE |
| Outputs | binary files (the solution is in the file name.EIG) |
| Details | Computation overview / Reference Manual: Inputs |
4. Normalize the eigenvectors
The input data is written into the text file name.iS.
The program stores two records for each of the $\mathtt{NROOT}$ eigenpairs calculated in the previous step in a binary file name.S. Odd records contain the normalized eigenvectors $\mathbf{v}_i$ while even records contain their corresponding eigenvalues $\lambda_i$.
| Program | STAB |
|---|---|
| Inputs | name.iS, binary files from previous steps |
| Protokol | name.oS |
| Outputs | binary files (the solution is in the file name.S) |
| Details | Computation overview / Reference Manual: Inputs |
5. Calculate the strains and stresses
The input data is written into the text file name.i5, where the key of problem type is $\mathtt{KPROB}=1$.
| Program | STR3 |
|---|---|
| Inputs | name.i5, binary files from previous steps |
| Protokol | name.o5 |
| Outputs | name.STR (optionally), name.STB (optionally) |
| Details | Computation overview / Reference Manual: Inputs |