FEM EquationElasticity/ru: Difference between revisions

From FreeCAD Documentation
(Updating to match new version of source page)
(Updating to match new version of source page)
 
(2 intermediate revisions by the same user not shown)
Line 27: Line 27:
==Описание==
==Описание==


This equation describes the mechanical properties of rigid bodies.
This equation describes the mechanical properties of solid bodies.


For info about the math of the equation, see the [http://www.elmerfem.org/blog/documentation/ Elmer models manual], section ''Linear Elasticity''.
For info about the math of the equation, see the [http://www.elmerfem.org/blog/documentation/ Elmer models manual], section ''Linear Elasticity''.
Line 37: Line 37:
# Change the [[#Solver_Settings|equation's solver settings]] or the [[FEM_SolverElmer_SolverSettings|general solver settings]] if necessary.
# Change the [[#Solver_Settings|equation's solver settings]] or the [[FEM_SolverElmer_SolverSettings|general solver settings]] if necessary.


'''Note''': For analyses of nonlinear deformation you must use the [[Image:FEM_EquationDeformation.svg|32px]] [[FEM_EquationDeformation|Deformation equation]] ({{Version|0.21}}). The Elasticity equation is only for linear deformations.
'''Note''': For analyses of nonlinear elasticity you must use the [[Image:FEM_EquationDeformation.svg|32px]] [[FEM_EquationDeformation|Deformation equation]] ({{Version|0.21}}). The Elasticity equation is only for linear elasticity.


'''Note''': If you use more than one CPU core for the solver ({{Version|0.21}}), 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 {{PropertyData|Linear Solver Type}} is set to ''Direct'' (the default, described [[FEM_SolverElmer_SolverSettings#Linear_System|here]]). For multi-CPU solving one can only use the {{PropertyData|Linear Direct Method}} ''MUMPS''. However, MUMPS is not freely available as a direct download.
'''Note''': If you use more than one CPU core for the solver ({{Version|0.21}}), 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 {{PropertyData|Linear Solver Type}} is set to ''Direct'' (the default, described [[FEM_SolverElmer_SolverSettings#Linear_System|here]]). For multi-CPU solving one can only use the {{PropertyData|Linear Direct Method}} ''MUMPS''. However, MUMPS is not freely available as a direct download.
Line 48: Line 48:
* {{PropertyData|Calculate Pangle}}: If the principal angles should be calculated.
* {{PropertyData|Calculate Pangle}}: If the principal angles should be calculated.
* {{PropertyData|Calculate Principal}}: If all stresses 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 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 yield criterion and the principal stress will not be calculated.
* {{PropertyData|Calculate Stresses}}: If stresses should be calculated. Compared to {{PropertyData|Calculate Principal}} the Tresca yield criterion and the principal stress will not be calculated.
* {{PropertyData|Constant Bulk System}}: See the Elmer manual for more info.
* {{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|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|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|Geometric Stiffness}}: Considers the geometric stiffness of the body.
Line 58: Line 58:
* {{PropertyData|Model Lumping}}: Uses [https://en.wikipedia.org/wiki/Lumped-element_model model lumping].
* {{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|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|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|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.
* {{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:
Eigenvalues:
* {{PropertyData|Eigen Analysis}}: If an eigen analysis should be performed (calculation of eigenmodes and eigenfrequencies).
* {{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 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 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 Damped}}: Set a damped eigen analysis. Can only be used if {{PropertyData|[[FEM_SolverElmer_SolverSettings#Linear_System|Linear Solver Type]]}} is ''Iterative''.
Line 74: Line 74:
* {{PropertyData|Plane Stress}}: Computes solution according to the plane stress situation. Applies only for 2D geometry.
* {{PropertyData|Plane Stress}}: Computes solution according to the plane stress situation. Applies only for 2D geometry.


==Constraint Information==
==Analysis Feature Information==


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


* [[Image:FEM_ConstraintFixed.svg|32px]] [[FEM_ConstraintFixed|Constraint fixed]]
* [[Image:FEM_ConstraintFixed.svg|32px]] [[FEM_ConstraintFixed|Fixed boundary condition]]
* [[Image:FEM_ConstraintDisplacement.svg|32px]] [[FEM_ConstraintDisplacement|Constraint displacement]]
* [[Image:FEM_ConstraintDisplacement.svg|32px]] [[FEM_ConstraintDisplacement|Displacement boundary condition]]
* [[Image:FEM_ConstraintForce.svg|32px]] [[FEM_ConstraintForce|Constraint force]]
* [[Image:FEM_ConstraintForce.svg|32px]] [[FEM_ConstraintForce|Force load]]
* [[Image:FEM_ConstraintInitialTemperature.svg|32px]] [[FEM_ConstraintInitialTemperature|Constraint initial temperature]]
* [[Image:FEM_ConstraintInitialTemperature.svg|32px]] [[FEM_ConstraintInitialTemperature|Initial temperature condition]]
* [[Image:FEM_ConstraintPressure.svg|32px]] [[FEM_ConstraintPressure|Constraint pressure]]
* [[Image:FEM_ConstraintPressure.svg|32px]] [[FEM_ConstraintPressure|Pressure load]]
* [[Image:FEM_ConstraintSelfWeight.svg|32px]] [[FEM_ConstraintSelfWeight|Constraint self weight]]
* [[Image:FEM_ConstraintSelfWeight.svg|32px]] [[FEM_ConstraintSelfWeight|Gravity load]]
* [[Image:FEM_ConstraintSpring.svg|32px]] [[FEM_ConstraintSpring|Constraint spring]]
* [[Image:FEM_ConstraintSpring.svg|32px]] [[FEM_ConstraintSpring|Spring]]


===Note===
===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.
* Except for calculations in 2D, for all the above analysis features it is important that they act on a face. Features in 3D set to lines or vertices are not recognized by the Elmer solver.


==Eigenmode Analysis==
==Eigenmode Analysis==


To perform an eigenmode analysis (calculation if the eigenmodes and eigenfrequencies), you need to
To perform an eigenmode analysis (calculation if the eigenmodes and eigenfrequencies), you need to
# Set {{PropertyData|Eigen Analysis}}: to ''true''
# Set {{PropertyData|Eigen Analysis}} to {{TRUE}}
# Set {{PropertyData|Displace Mesh}}: to ''false''
# 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.
# 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.
# Add a [[FEM_ConstraintFixed|fixed boundary condition]] and set at least one face of the body as fixed.
# Run the solver.
# Run the solver.


Line 104: Line 104:


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


==Results==
==Results==


The available results depend on the [[#Solver_Settings|solver settings]]. If none of the {{PropertyData|Calculate *}} settings 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.
The available results depend on the [[#Solver_Settings|solver settings]]. If none of the {{PropertyData|Calculate *}} settings 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.
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
'''Note:''' The eigenmode displacement <math>\vec{d}</math> vector has an arbitrary value since the result is
Line 119: Line 119:


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



<div class="mw-translate-fuzzy">
<div class="mw-translate-fuzzy">
Line 133: Line 134:
{{FEM Tools navi{{#translation:}}}}
{{FEM Tools navi{{#translation:}}}}
{{Userdocnavi{{#translation:}}}}
{{Userdocnavi{{#translation:}}}}
{{clear}}

Latest revision as of 13:26, 24 November 2023

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 solid 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 elasticity you must use the Deformation equation (introduced in version 0.21). The Elasticity equation is only for linear elasticity.

Note: If you use more than one CPU core for the solver (introduced in version 0.21), 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 ДанныеLinear Solver Type is set to Direct (the default, described here). For multi-CPU solving one can only use the ДанныеLinear 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:

  • 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 yield criterion and the principal 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 solver (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.

Analysis Feature Information

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

Note

  • Except for calculations in 2D, for all the above analysis features it is important that they act on a face. Features in 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 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 fixed boundary condition and set at least one face of the body as fixed.
  5. Run the solver.

It is highly recommended to use ДанныеLinear 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 ДанныеStability Analysis to true

Results

The available results depend on the solver settings. If none of the ДанныеCalculate * settings 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.