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==Описание==
==Описание==


This equation describes the mechanical properties of rigid bodies.
ToDo


For info about the math of the equation, see the [http://www.elmerfem.org/blog/documentation/ Elmer models manual], section ''Linear Elasticity''.
==Применение==


==Usage==
<br />


# After adding an Elmer solver as described [[FEM_SolverElmer#Equations|here]], select it in the [[Tree_view|tree view]].
# Now either use the toolbar button [[Image:FEM_EquationElasticity.svg|24px]] or the menu {{MenuCommand|Solve → Elasticity equation}}.
# Change the [[#Solver_Settings|equation's solver settings]] or the [[FEM_SolverElmer_SolverSettings|general solver settings]] if necessary.

==Solver Settings==

For the general solver settings, see the [[FEM_SolverElmer_SolverSettings|Elmer solver settings]].

The elasticity equation provides these special settings:
* {{PropertyData|Calculate Pangle}}: If the principal angles should be calculated.
* {{PropertyData|Calculate Principal}}: If all stresses should be calculated.
* {{PropertyData|Calculate Strains}}: If strains will be calculated. This will also calculate the stresses, even if {{PropertyData|Calculate Principal}} or {{PropertyData|Calculate Stresses}} is ''false''.
* {{PropertyData|Calculate Stresses}}: If stresses should be calculated. Compared to {{PropertyData|Calculate Principal}} the Tresca and the pincipal stress will not be calculated.
* {{PropertyData|Constant Bulk System}}: See the Elmer manual for more info.
* {{PropertyData|Displace Mesh}}: If mesh can be deformed. This is by default ''true'' and must be set to ''false'' for eigenfrequency analyses.
* {{PropertyData|Fix Displacement}}: If displacements or forces are set. thereby {{PropertyData|Model Lumping}} is automatically used.
* {{PropertyData|Geometric Stiffness}}: Considers the geometric stiffness of the body.
* {{PropertyData|Incompressible}}: Computation of incompressible material in connection with viscoelastic Maxwell material and a custom {{PropertyData|Variable}}.
* {{PropertyData|Maxwell Material}}: Compute the viscoelastic material model.
* {{PropertyData|Model Lumping}}: Uses [https://en.wikipedia.org/wiki/Lumped-element_model model lumping].
* {{PropertyData|Model Lumping Filename}}: File to save the results from the model lumping.
* {{PropertyData|Stability Analysis}}: If ''true'' {{PropertyData|Eigen Analysis}} becomes a stability analysis (buckling analysis). Otherwise a modal analysis is performed.
* {{PropertyData|Update Transient System}}: See the Elmer manual for more info.
* {{PropertyData|Variable}}: The variable for the elasticity equation. Only change this if {{PropertyData|Incompressible}} is set to ''true'' in accordance to the Elmer manual.

Eigenvalues:
* {{PropertyData|Eigen Analysis}}: If an eigen analysis should be performed (calculation of eigenmodes and eigenfrequencies).
* {{PropertyData|Eigen System Complex}}: Should be ''true'' if the eigen system is complex. it must be ''false'' for a damped eigen value analyses.
* {{PropertyData|Eigen System Compute Residuals}}: Computes residuals of the eigen value system.
* {{PropertyData|Eigen System Damped}}: Set a damped eigen analysis. Can only be used if {{PropertyData|[[FEM_SolverElmer_SolverSettings#Linear_System|Linear Solver Type]]}} is ''Iterative''.
* {{PropertyData|Eigen System Select}}: Selection of which eigenvalues are computed. Note that the selection of ''Largest*'' cause an infinite run for recent Elmer (as of August 2022).
* {{PropertyData|Eigen System Tolerance}}: Convergence tolerance for iterative eigensystem solve. The default is 100 times the {{PropertyData|[[FEM_SolverElmer_SolverSettings#Linear_System|Linear Tolerance]]}}.
* {{PropertyData|Eigen System Values}}: The number of the highest eigenmode that should be calculated.

Equation:
* {{PropertyData|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:

* [[Image:FEM_ConstraintFixed.svg|32px]] [[FEM_ConstraintFixed|Constraint fixed]]
* [[Image:FEM_ConstraintDisplacement.svg|32px]] [[FEM_ConstraintDisplacement|Constraint displacement]]
* [[Image:FEM_ConstraintForce.svg|32px]] [[FEM_ConstraintForce|Constraint force]]
* [[Image:FEM_ConstraintPressure.svg|32px]] [[FEM_ConstraintPressure|Constraint pressure]]
* [[Image:FEM_ConstraintSelfWeight.svg|32px]] [[FEM_ConstraintSelfWeight|Constraint self weight]]
* [[Image:FEM_ConstraintInitialTemperature.svg|32px]] [[FEM_ConstraintInitialTemperature|Constraint initial temperature]]

===Note===

For all above constraints it is important that they act on a face. Constraints 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
# Set {{PropertyData|Eigen Analysis}}: to ''true''
# Set {{PropertyData|Displace Mesh}}: to ''false''
# Set {{PropertyData|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.
# Add a [[FEM_ConstraintFixed|constraint fixed]] and set at least one face of the body as fixed.
# Run the solver.

'''Note''': If you use more than one CPU core for the solver ({{Version|1.0}}), you cannot use ''Umfpack'', the only direct method for parallel solving is ''MUMPS''.</br>Also note that iterative solving is not recommended for eigenmode analysis. Therefore either only use one CPU core or install the ''MUMPS'' module to Elmer.

==Buckling Analysis==

To perform a buckling analysis, you need to do the same as for an [[FEM_EquationElasticity#Eigenmode_Analysis|Eigenmode Analysis]], and additionally:
* Set {{PropertyData|Stability Analysis}}: to ''true''

==Results==

The available results depend on the [[#Solver_Settings|solver settings]]. If none of them was set to ''true'', only the displacement is calculated. Otherwise also the corresponding results will be available. If {{PropertyData|Eigen Analysis}} was set to ''true'' all results will be available for every calculated eigenmode.

If {{PropertyData|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 <math>\vec{d}</math> vector has an arbitrary value since the result is

<math>\quad
\vec{d} = c\cdot\vec{u}
</math>

whereas <math>\vec{u}</math> is the eigenvector and <math>c</math> is a complex number.


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Revision as of 19:04, 5 October 2022

Other languages:

Уравнение гибкости

Системное название
FEM EquationElasticity
Расположение в меню
Solve → Уравнение гибкости
Верстаки
FEM
Быстрые клавиши
Нет
Представлено в версии
-
См. также
FEM tutorial

Описание

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 → Elasticity equation.
  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:

  • ДанныеCalculate Pangle: If the principal angles should be calculated.
  • ДанныеCalculate Principal: If all stresses should be calculated.
  • ДанныеCalculate Strains: If strains will be calculated. This will also calculate the stresses, even if ДанныеCalculate Principal or ДанныеCalculate Stresses is false.
  • ДанныеCalculate Stresses: If stresses should be calculated. Compared to ДанныеCalculate Principal the Tresca and the pincipal stress will not be calculated.
  • ДанныеConstant Bulk System: See the Elmer manual for more info.
  • ДанныеDisplace Mesh: If mesh can be deformed. This is by default true and must be set to false for eigenfrequency analyses.
  • ДанныеFix Displacement: If displacements or forces are set. thereby ДанныеModel Lumping is automatically used.
  • ДанныеGeometric Stiffness: Considers the geometric stiffness of the body.
  • ДанныеIncompressible: Computation of incompressible material in connection with viscoelastic Maxwell material and a custom ДанныеVariable.
  • ДанныеMaxwell Material: Compute the viscoelastic material model.
  • ДанныеModel Lumping: Uses model lumping.
  • ДанныеModel Lumping Filename: File to save the results from the model lumping.
  • ДанныеStability Analysis: If true ДанныеEigen Analysis becomes a stability analysis (buckling analysis). Otherwise a modal analysis is performed.
  • ДанныеUpdate Transient System: See the Elmer manual for more info.
  • ДанныеVariable: The variable for the elasticity equation. Only change this if ДанныеIncompressible is set to true in accordance to the Elmer manual.

Eigenvalues:

  • ДанныеEigen Analysis: If an eigen analysis should be performed (calculation of eigenmodes and eigenfrequencies).
  • ДанныеEigen System Complex: Should be true if the eigen system is complex. it must be false for a damped eigen value analyses.
  • ДанныеEigen System Compute Residuals: Computes residuals of the eigen value system.
  • ДанныеEigen System Damped: Set a damped eigen analysis. Can only be used if ДанныеLinear Solver Type is Iterative.
  • ДанныеEigen System Select: Selection of which eigenvalues are computed. Note that the selection of Largest* cause an infinite run for recent Elmer (as of August 2022).
  • ДанныеEigen System Tolerance: Convergence tolerance for iterative eigensystem solve. The default is 100 times the ДанныеLinear Tolerance.
  • ДанныеEigen System Values: The number of the highest eigenmode that should be calculated.

Equation:

  • ДанныеPlane 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

For all above constraints it is important that they act on a face. Constraints 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 ДанныеEigen Analysis: to true
  2. Set ДанныеDisplace Mesh: to false
  3. Set ДанныеEigen 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.

Note: If you use more than one CPU core for the solver (introduced in version 1.0), you cannot use Umfpack, the only direct method for parallel solving is MUMPS.
Also note that iterative solving is not recommended for eigenmode analysis. Therefore either only use one CPU core or install the MUMPS module to Elmer.

Buckling Analysis

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

  • Set ДанныеStability Analysis: to true

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 ДанныеEigen Analysis was set to true all results will be available for every calculated eigenmode.

If ДанныеEigen 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 vector has an arbitrary value since the result is

whereas is the eigenvector and is a complex number.