asl::FDElasticityIncompressibleStatic Class Reference

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

#include <aslFDElasticity.h>

Inheritance diagram for asl::FDElasticityIncompressibleStatic:

Collaboration diagram for asl::FDElasticityIncompressibleStatic:

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.
virtual void	execute ()
	Executes the numerical procedure.
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.
virtual void	execute ()
	Executes the numerical procedure.
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

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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.

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

• /build/asl-FBaFQT/asl-0.1.7/debian/tmp/usr/include/ASL/num/aslFDElasticity.h
• /build/asl-FBaFQT/asl-0.1.7/src/num/aslFDElasticity.h