Table of Contents
Linear stability
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:
- Only the following elements can be used: pentahedron, hexahedron, semi-loof, and the corresponding Connector elements.
- Analytical prescription of 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 |
| Logs | name.o1, name.o2, name.o3, name.o4 |
| Outputs | binary files |
| Details | Linear elastostatics, Computation overview / Reference Manual: Inputs |
2. Calculating the initial stress matrices
Input data are written to the text file name.iG.
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 |
| Log | name.oG |
| 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 $\mathtt{KEVP}=1$.
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 |
| Log | name.oE |
| Outputs | binary files (the solution is in the name.EIG file) |
| Details | Computation overview / Reference Manual: Inputs |
4. Normalizing the eigenvectors
Input data are written to the text file name.iS.
For each of the $\mathtt{NROOT}$ eigenpairs calculated in the previous step the program stores two records in the binary file name.S. 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 |
| Log | name.oS |
| Outputs | binary files (the solution is in the name.S file) |
| Details | Computation overview / Reference Manual: Inputs |
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 |