FEM EquationElasticity

Description
This equation describes the mechanical properties of rigid bodies.

Usage

 * 1) After adding an Elmer solver as described here, select it in the tree view.
 * 2) Now either use the toolbar button [[Image:FEM_EquationElasticity.svg|24px]] or the menu.
 * 3) Change the equation's solver settings or the general solver settings if necessary.

Solver Settings
For the general solver settings, see the Elmer solver settings.

The elasticity equation provides these special settings:


 * : If the principal angles should be calculated.
 * : If all stresses should be calculated.
 * : If strains will be calculated. This will also calculate the stresses, even if or  is false.
 * : If stresses should be calculated. Compared to the Tresca and the pincipal stress will not be calculated.
 * : If a frequency analysis should be performed (calculation of eigenmodes and eigenfrequencies).
 * : The number of the highest eigenmode that should be calculated.

Eigenmode Analysis
To perform an eigenmode analysis (calculation if the eigenmodes and eigenfrequencies), you need to
 * 1) Set : to true
 * 2) Set : to the highest number of eigenmodes you are interested in. The smaller this number the shorter the solver runtime since higher modes can be omitted to be determined.
 * 3) Add a constraint fixed and set at least one face of the body as fixed.
 * 4) Accordingto the Elmer manual the best results for eigenmode analysis are obtained with direct solving. Therefore
 * 5) Set  to Direct.
 * 6) Set  to Umfpack.
 * 7) Eventually run the solver.

Note: If you use more than one CPU core for the solver, you cannot use Umfpack, the only direct method for parallel solving is MUMPS. Also note that iterative solving is not recommended for eigenmode analysis.

Results
The available results depend on the solver settings. If none of them was set to true, only the displacement is calculated. Otherwise also the corresponding results will be available. If was set to true all results will be available for every calculated eigenmode.

If was set to true, the eigenvalues are output at the end of the document SolverElmerOutput that will be created in the tree view after the solver has finished. A typical output would for example be EigenSolve: Computed 5 Eigen Values EigenSolve: 1:   9.584853E+04   0.000000E+00 EigenSolve: 2:   3.080755E+06   0.000000E+00 EigenSolve: 3:   3.725429E+06   0.000000E+00 EigenSolve: 4:   2.909430E+07   0.000000E+00 EigenSolve: 5:   3.525298E+07   0.000000E+00

The second column is hereby the real part of the eigenvalue $$\omega^2$$, the third column the imaginary part.

To calculate the eigenfrequency $$f_e$$ out of it, this has to be done (because of the root the imaginary part cannot just be omitted):

$$\quad f_{e} =\cfrac{\sqrt{\omega^{2}}}{2\pi} $$