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FEM_EquationElasticity.md

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GuiCommand
Name MenuLocation Workbenches Version SeeAlso
FEM EquationElasticity
Solve , Mechanical equations , Elasticity equation
FEM_Workbench
0.17
FEM_EquationDeformation, FEM_tutorial

FEM EquationElasticity

Description

This equation describes the mechanical properties of rigid bodies.

For info about the math of the equation, see the Elmer models manual, section Linear Elasticity.

Usage

  1. After adding an Elmer solver as described here, select it in the tree view.
  2. Now either use the toolbar button or the menu Solve → Mechanical equations → Elasticity equation.
  3. Change the equation's solver settings or the general solver settings if necessary.

Note: For analyses of nonlinear deformation you must use the Deformation equation ((v0.21) ). The Elasticity equation is only for linear deformations.

Note: If you use more than one CPU core for the solver ((v0.21) ), you cannot use the default solver settings. However, using just one CPU and the default solver settings is in many cases faster than using several CPUs because the elasticity solver is only fast when Linear Solver Type is set to Direct (the default, described here). For multi-CPU solving one can only use the Linear Direct Method MUMPS. However, MUMPS is not freely available as a direct download.

Solver Settings

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

The elasticity equation provides these special settings:

  • Calculate Pangle: If the principal angles should be calculated.

  • Calculate Principal: If all stresses should be calculated.

  • Calculate Strains: If strains will be calculated. This will also calculate the stresses, even if Calculate Principal or Calculate Stresses is false.

  • Calculate Stresses: If stresses should be calculated. Compared to Calculate Principal the Tresca yield criterion and the principal stress will not be calculated.

  • Constant Bulk System: See the Elmer manual for more info.

  • Displace Mesh: If mesh can be deformed. This is by default true and must be set to false for eigenfrequency analyses.

  • Fix Displacement: If displacements or forces are set. thereby Model Lumping is automatically used.

  • Geometric Stiffness: Considers the geometric stiffness of the body.

  • Incompressible: Computation of incompressible material in connection with viscoelastic Maxwell material and a custom Variable.

  • Maxwell Material: Compute the viscoelastic material model.

  • Model Lumping: Uses model lumping.

  • Model Lumping Filename: File to save the results from the model lumping.

  • Stability Analysis: If true Eigen Analysis becomes a stability analysis (buckling analysis). Otherwise a modal analysis is performed.

  • Update Transient System: See the Elmer manual for more info.

  • Variable: The variable for the elasticity equation. Only change this if Incompressible is set to true in accordance to the Elmer manual.

Eigenvalues:

  • Eigen Analysis: If an eigen analysis should be performed (calculation of eigenmodes and eigenfrequencies).

  • Eigen System Complex: Should be true if the eigen system is complex. it must be false for a damped eigen value analyses.

  • Eigen System Compute Residuals: Computes residuals of the eigen value system.

  • Eigen System Damped: Set a damped eigen analysis. Can only be used if Linear Solver Type is Iterative.

  • Eigen System Select: Selection of which eigenvalues are computed. Note that the selection of Largest* cause an infinite run for recent Elmer solver (as of August 2022).

  • Eigen System Tolerance: Convergence tolerance for iterative eigensystem solve. The default is 100 times the Linear Tolerance.

  • Eigen System Values: The number of the highest eigenmode that should be calculated.

Equation:

  • Plane Stress: Computes solution according to the plane stress situation. Applies only for 2D geometry.

Constraint Information

The elasticity equation takes the following constraints into account if they are set:

Note

  • Except for calculations in 2D, for all above constraints it is important that they act on a face. Constraints for 3D set to lines or vertices are not recognized by the Elmer solver.

Eigenmode Analysis

To perform an eigenmode analysis (calculation if the eigenmodes and eigenfrequencies), you need to

  1. Set Eigen Analysis: to true
  2. Set Displace Mesh: to false
  3. Set Eigen System Values: 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 from computation.
  4. Add a constraint fixed and set at least one face of the body as fixed.
  5. Run the solver.

It is highly recommended to use Linear Solver Type set to Direct (the default) because this is much faster and the results are more accurate.

Buckling Analysis

To perform a buckling analysis, you need to do the same as for an Eigenmode Analysis, and additionally:

  • Set Stability Analysis to true

Results

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

If Eigen Analysis was set to true, the eigenfrequencies are output at the end of the solver log in the solver dialog and also in the document SolverElmerOutput that will be created in the tree view after the solver has finished.

Note: The eigenmode displacement $\vec{d}$ vector has an arbitrary value since the result is

$\quad \vec{d} = c\cdot\vec{u}$

whereas $\vec{u}$ is the eigenvector and $c$ is a complex number.

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