ASL
0.1.7
Advanced Simulation Library
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Numerical method which computes homogenious isotropic elasticity equation. More...
#include <aslFDElasticity.h>
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 |
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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 |
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virtual | ~NumMethod () |
Additional Inherited Members | |
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typedef SPDataWithGhostNodesACLData | Data |
typedef acl::VectorOfElements | Param |
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const VectorTemplate * | vectorTemplate |
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std::unique_ptr< acl::Kernel > | kernel |
Data | displacementData |
Data | displacementInternalData |
Param | bulkModulus |
Param | shearModulus |
Param | force |
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
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.
asl::FDElasticityIncompressibleStatic::FDElasticityIncompressibleStatic | ( | ) |
asl::FDElasticityIncompressibleStatic::FDElasticityIncompressibleStatic | ( | Data | d, |
Param | bM, | ||
Param | sM, | ||
const VectorTemplate * | vT | ||
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d | is a displacement field |
bM | is the bulk modulus |
sM | is the shear modulus |
vT | is a vector template |
asl::FDElasticityIncompressibleStatic::~FDElasticityIncompressibleStatic | ( | ) |
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virtual |
Executes the numerical procedure.
Implements asl::ElasticityCommonA.
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inline |
Definition at line 244 of file aslFDElasticity.h.
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virtual |
Builds the necesery internal data and kernels.
Implements asl::ElasticityCommonA.