asl::FDElasticityIncompressibleStatic Class Reference
Physics » Elasticity | Numerics » Numerical Methods

Numerical method which computes homogenious isotropic elasticity equation. More...

`#include <aslFDElasticity.h>`

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## Public Member Functions

| FDElasticityIncompressibleStatic ()
| FDElasticityIncompressibleStatic (Data d, Param bM, Param sM, const VectorTemplate *vT)
| ~FDElasticityIncompressibleStatic ()
virtual void | init ()
| Builds the necesery internal data and kernels. More...
virtual void | execute ()
| Executes the numerical procedure. More...
Data | getPressureData () const
| FDElasticityIncompressibleStatic ()
| FDElasticityIncompressibleStatic (Data d, Param bM, Param sM, const VectorTemplate *vT)
| ~FDElasticityIncompressibleStatic ()
virtual void | init ()
| Builds the necesery internal data and kernels. More...
virtual void | execute ()
| Executes the numerical procedure. More...
Data | getPressureData () const
Public Member Functions inherited from asl::ElasticityCommonA
| ElasticityCommonA ()
| ElasticityCommonA (Data d, Param bM, Param sM, const VectorTemplate *vT)
| ~ElasticityCommonA ()
void | setVectorTemplate (const VectorTemplate *vT)
VectorTemplate | getVectorTemplate ()
void | setForce (Param f)
Data | getDisplacementData () const
Data | getDisplacementInternalData () const
const Param | getBulkModulus () const
const Param | getShearModulus () const
| ElasticityCommonA ()
| ElasticityCommonA (Data d, Param bM, Param sM, const VectorTemplate *vT)
| ~ElasticityCommonA ()
void | setVectorTemplate (const VectorTemplate *vT)
VectorTemplate | getVectorTemplate ()
void | setForce (Param f)
Data | getDisplacementData () const
Data | getDisplacementInternalData () const
const Param | getBulkModulus () const
const Param | getShearModulus () const
Public Member Functions inherited from asl::NumMethod
virtual | ~NumMethod ()
virtual | ~NumMethod ()

## Additional Inherited Members

Public Types inherited from asl::ElasticityCommonA
typedef SPDataWithGhostNodesACLData | Data
typedef acl::VectorOfElements | Param
typedef SPDataWithGhostNodesACLData | Data
typedef acl::VectorOfElements | Param
Public Attributes inherited from asl::ElasticityCommonA
const VectorTemplate * | vectorTemplate
Protected Attributes inherited from asl::ElasticityCommonA
std::unique_ptr< acl::Kernel > | kernel
Data | displacementData
Data | displacementInternalData
Param | bulkModulus
Param | shearModulus
Param | force

## Detailed Description

Numerical method which computes homogenious isotropic elasticity equation.

\[ \rho\ddot u_j =(K+\mu/3)\nabla_j \nabla_k u_k+ \mu \Delta u_j \]

where

- \(K\) is the bulk modulus,
- \(\mu\) is the shear modulus,
- \(\vec u\) is a displacement vector field

This implementation is aided to improve stability for incompressible materials. Let us reformulate the elasticity equation by the following way:

\[ \rho\ddot u_j =\mu (\Delta u_j - \nabla_j p), \]

\[ p = -\frac{K+\mu/3}{\mu} \nabla_k u_k. \]

The second equation leads to an instability for low values of the Poisson ration (for nearly incompressible materials). Therefore the last equation we would like to replace by a relaxation one:

\[ \dot p = - w\left( \frac{K+\mu/3}{\mu} \nabla_k u_k + p\right), \]

where \( w \) is a relaxation parameter.

Definition at line 98 of file aslFDElasticity.h.

## Constructor & Destructor Documentation

## FDElasticityIncompressibleStatic() [1/4]

asl::FDElasticityIncompressibleStatic::FDElasticityIncompressibleStatic | ( |  | ) |

## FDElasticityIncompressibleStatic() [2/4]

asl::FDElasticityIncompressibleStatic::FDElasticityIncompressibleStatic | ( | Data | d,
|  | Param | bM,
|  | Param | sM,
|  | const VectorTemplate * | vT
| ) |  |

Parameters

  d | is a displacement field
  bM | is the bulk modulus
  sM | is the shear modulus
  vT | is a vector template

## ~FDElasticityIncompressibleStatic() [1/2]

asl::FDElasticityIncompressibleStatic::~FDElasticityIncompressibleStatic | ( |  | ) |

## FDElasticityIncompressibleStatic() [3/4]

asl::FDElasticityIncompressibleStatic::FDElasticityIncompressibleStatic | ( |  | ) |

## FDElasticityIncompressibleStatic() [4/4]

asl::FDElasticityIncompressibleStatic::FDElasticityIncompressibleStatic | ( | Data | d,
|  | Param | bM,
|  | Param | sM,
|  | const VectorTemplate * | vT
| ) |  |

Parameters

  d | is a displacement field
  bM | is the bulk modulus
  sM | is the shear modulus
  vT | is a vector template

## ~FDElasticityIncompressibleStatic() [2/2]

asl::FDElasticityIncompressibleStatic::~FDElasticityIncompressibleStatic | ( |  | ) |

## Member Function Documentation

## execute() [1/2]

virtual void asl::FDElasticityIncompressibleStatic::execute | ( |  | ) |

virtual

Executes the numerical procedure.

Implements asl::ElasticityCommonA.

## execute() [2/2]

virtual void asl::FDElasticityIncompressibleStatic::execute | ( |  | ) |

virtual

Executes the numerical procedure.

Implements asl::ElasticityCommonA.

## getPressureData() [1/2]

ElasticityCommonA::Data asl::FDElasticityIncompressibleStatic::getPressureData | ( |  | ) | const

inline

Definition at line 244 of file aslFDElasticity.h.

## getPressureData() [2/2]

Data asl::FDElasticityIncompressibleStatic::getPressureData | ( |  | ) | const

inline

## init() [1/2]

virtual void asl::FDElasticityIncompressibleStatic::init | ( |  | ) |

virtual

Builds the necesery internal data and kernels.

Implements asl::ElasticityCommonA.

## init() [2/2]

virtual void asl::FDElasticityIncompressibleStatic::init | ( |  | ) |

virtual

Builds the necesery internal data and kernels.

Implements asl::ElasticityCommonA.

The documentation for this class was generated from the following file:

- /build/asl-1Fw6fH/asl-0.1.7/debian/tmp/usr/include/ASL/num/aslFDElasticity.h