Base class for all Fem Element (1D, 2D, 3D) It handles the node ids to which it is connected and requires all derived classes to compute the element mass matrix and the force vector along with the derivatives (the stiffness and damping matrices). More...

#include <FemElement.h>

Inheritance diagram for SurgSim::Physics::FemElement:

Public Types
typedef SurgSim::Framework::ObjectFactory1< FemElement, std::shared_ptr< FemElementStructs::FemElementParameter > >	FactoryType

Public Member Functions
	FemElement ()
	Constructor.

virtual	~FemElement ()
	Virtual destructor.

virtual void	initialize (const SurgSim::Math::OdeState &state)
	Initialize the FemElement once everything has been set. More...

size_t	getNumDofPerNode () const
	Gets the number of degree of freedom per node. More...

size_t	getNumNodes () const
	Gets the number of nodes connected by this element. More...

size_t	getNodeId (size_t elementNodeId) const
	Gets the elementNodeId-th node id. More...

const std::vector< size_t > &	getNodeIds () const
	Gets the node ids for this element. More...

void	setYoungModulus (double E)
	Sets the Young modulus (in N.m-2) More...

double	getYoungModulus () const
	Gets the Young modulus (in N.m-2) More...

void	setPoissonRatio (double nu)
	Sets the Poisson ratio (unitless) More...

double	getPoissonRatio () const
	Gets the Poisson ratio (unitless) More...

void	setMassDensity (double rho)
	Sets the mass density (in Kg.m-3) More...

double	getMassDensity () const
	Gets the mass density (in Kg.m-3) More...

double	getMass (const SurgSim::Math::OdeState &state) const
	Gets the element mass based on the input state (in Kg) More...

virtual double	getVolume (const SurgSim::Math::OdeState &state) const =0
	Gets the element volume based on the input state (in m-3) More...

virtual void	addForce (SurgSim::Math::Vector *F, double scale) const
	Adds the element force (computed for a given state) to a complete system force vector F (assembly) More...

virtual void	addForce (SurgSim::Math::Vector *F) const

virtual void	addMass (SurgSim::Math::SparseMatrix *M, double scale) const
	Adds the element mass matrix M (computed for a given state) to a complete system mass matrix M (assembly) More...

virtual void	addMass (SurgSim::Math::SparseMatrix *M) const

virtual void	addDamping (SurgSim::Math::SparseMatrix *D, double scale) const
	Adds the element damping matrix D (= -df/dv) (comuted for a given state) to a complete system damping matrix D (assembly) More...

virtual void	addDamping (SurgSim::Math::SparseMatrix *D) const

virtual void	addStiffness (SurgSim::Math::SparseMatrix *K, double scale) const
	Adds the element stiffness matrix K (= -df/dx) (computed for a given state) to a complete system stiffness matrix K (assembly) More...

virtual void	addStiffness (SurgSim::Math::SparseMatrix *K) const

virtual void	addFMDK (SurgSim::Math::Vector F, SurgSim::Math::SparseMatrix M, SurgSim::Math::SparseMatrix D, SurgSim::Math::SparseMatrix K) const
	Adds the element force vector, mass, stiffness and damping matrices (computed for a given state) into a complete system data structure F, M, D, K (assembly) More...

virtual void	addMatVec (double alphaM, double alphaD, double alphaK, const SurgSim::Math::Vector &x, SurgSim::Math::Vector F, SurgSim::Math::Vector extractedX, SurgSim::Math::Vector *acumulator) const
	Adds the element matrix-vector contribution F += (alphaM.M + alphaD.D + alphaK.K).x (computed for a given state) into a complete system data structure F (assembly) More...

bool	isValidCoordinate (const SurgSim::Math::Vector &naturalCoordinate) const
	Determines whether a given natural coordinate is valid. More...

virtual SurgSim::Math::Vector	computeCartesianCoordinate (const SurgSim::Math::OdeState &state, const SurgSim::Math::Vector &naturalCoordinate) const =0
	Computes a given natural coordinate in cartesian coordinates. More...

virtual SurgSim::Math::Vector	computeNaturalCoordinate (const SurgSim::Math::OdeState &state, const SurgSim::Math::Vector &cartesianCoordinate) const =0
	Computes a natural coordinate given a global coordinate. More...

template<typename T , int Opt, typename StorageIndex >
void	assembleMatrixBlocks (const Eigen::Ref< const Math::Matrix > &subMatrix, const std::vector< size_t > &blockIds, size_t blockSize, Eigen::SparseMatrix< T, Opt, StorageIndex > *matrix) const
	Add a sub-matrix made of squared-blocks into a matrix that could be un-initialized. More...

template<typename T , int Opt, typename StorageIndex >
void	assembleMatrixBlocksNoInitialize (const Eigen::Ref< const Math::Matrix > &subMatrix, const std::vector< size_t > &blockIds, size_t blockSize, Eigen::SparseMatrix< T, Opt, StorageIndex > *matrix) const
	Add a sub-matrix made of squared-blocks into a matrix that is already initialized. More...

void	updateFMDK (const Math::OdeState &state, int options)
	Update the FemElement based on the given state. More...

Static Public Member Functions
static FactoryType &	getFactory ()

Protected Member Functions
void	setNumDofPerNode (size_t numDofPerNode)
	Sets the number of degrees of freedom per node. More...

virtual void	doUpdateFMDK (const Math::OdeState &state, int options)=0
	Update the FemElement based on the given state. More...

void	initializeFMDK ()
	Initialize f, M, D, K variables.

virtual void	doInitializeFMDK ()
	Function to be overridden by the derived classes to initialize the f, M, D, K variables.

Protected Attributes
size_t	m_numDofPerNode
	Number of degree of freedom per node for this element.

std::vector< size_t >	m_nodeIds
	Node ids connected by this element.

SurgSim::Math::Vector	m_f
	The force vector.

SurgSim::Math::Matrix	m_K
	The stiffness matrix.

SurgSim::Math::Matrix	m_M
	The mass matrix.

SurgSim::Math::Matrix	m_D
	The damping matrix.

bool	m_useDamping
	Flag to specify of the damping is used.

double	m_rho
	Mass density (in Kg.m-3)

double	m_E
	Young modulus (in N.m-2)

double	m_nu
	Poisson ratio (unitless)

Detailed Description

Base class for all Fem Element (1D, 2D, 3D) It handles the node ids to which it is connected and requires all derived classes to compute the element mass matrix and the force vector along with the derivatives (the stiffness and damping matrices).

A extra method also exist to compute all of them at once for performance purposes. It holds on to the actual computed values (m_f, m_M, m_D, m_K) as its size is not predefined from outside and would requires intensive (de)allocation or a temporary variable anyway. It contains the linear elasticity parameter (Young modulus and Poisson ratio) as well as mass density

Member Function Documentation

§ addDamping()

void SurgSim::Physics::FemElement::addDamping	(	SurgSim::Math::SparseMatrix *	D,
		double	scale
	)		const

virtual

Adds the element damping matrix D (= -df/dv) (comuted for a given state) to a complete system damping matrix D (assembly)

Parameters

[in,out]	D	The complete system damping matrix to add the element damping matrix into
	scale	A factor to scale the added damping matrix with

Note: The element damping matrix is square of size getNumDofPerNode() x getNumNodes(); This method supposes that the incoming state contains information with the same number of; dof per node as getNumDofPerNode()

§ addFMDK()

void SurgSim::Physics::FemElement::addFMDK	(	SurgSim::Math::Vector *	F,
		SurgSim::Math::SparseMatrix *	M,
		SurgSim::Math::SparseMatrix *	D,
		SurgSim::Math::SparseMatrix *	K
	)		const

virtual

Adds the element force vector, mass, stiffness and damping matrices (computed for a given state) into a complete system data structure F, M, D, K (assembly)

Parameters

[in,out]	F	The complete system force vector to add the element force into
[in,out]	M	The complete system mass matrix to add the element mass matrix into
[in,out]	D	The complete system damping matrix to add the element damping matrix into
[in,out]	K	The complete system stiffness matrix to add the element stiffness matrix into

Note: This method supposes that the incoming state contains information with the same number of dof; per node as getNumDofPerNode()

§ addForce()

void SurgSim::Physics::FemElement::addForce	(	SurgSim::Math::Vector *	F,
		double	scale
	)		const

virtual

Adds the element force (computed for a given state) to a complete system force vector F (assembly)

Parameters

[in,out]	F	The complete system force vector to add the element force into
	scale	A factor to scale the added force with

Note: The element force is of size (getNumDofPerNode() x getNumNodes()); This method supposes that the incoming state contains information with the same number of dof; per node as getNumDofPerNode()

§ addMass()

void SurgSim::Physics::FemElement::addMass	(	SurgSim::Math::SparseMatrix *	M,
		double	scale
	)		const

virtual

Adds the element mass matrix M (computed for a given state) to a complete system mass matrix M (assembly)

Parameters

[in,out]	M	The complete system mass matrix to add the element mass-matrix into
	scale	A factor to scale the added mass matrix with

Note: The element mass matrix is square of size getNumDofPerNode() x getNumNodes(); This method supposes that the incoming state contains information with the same number of; dof per node as getNumDofPerNode()

§ addMatVec()

void SurgSim::Physics::FemElement::addMatVec	(	double	alphaM,
		double	alphaD,
		double	alphaK,
		const SurgSim::Math::Vector &	x,
		SurgSim::Math::Vector *	F,
		SurgSim::Math::Vector *	extractedX,
		SurgSim::Math::Vector *	acumulator
	)		const

virtual

Adds the element matrix-vector contribution F += (alphaM.M + alphaD.D + alphaK.K).x (computed for a given state) into a complete system data structure F (assembly)

Parameters

	alphaM	The scaling factor for the mass contribution
	alphaD	The scaling factor for the damping contribution
	alphaK	The scaling factor for the stiffness contribution
	x	A complete system vector to be used as the vector in the matrix-vector multiplication
[in,out]	F	The complete system force vector to add the element matrix-vector contribution into
[out]	extractedX,acumulator	temporary memory for the function operation, this is an optimization as addMatVec will get repeatedly called during one physics frame, preallocating these vectors helps

Note: This method supposes that the incoming state contains information with the same number of dof; per node as getNumDofPerNode()

§ addStiffness()

void SurgSim::Physics::FemElement::addStiffness	(	SurgSim::Math::SparseMatrix *	K,
		double	scale
	)		const

virtual

Adds the element stiffness matrix K (= -df/dx) (computed for a given state) to a complete system stiffness matrix K (assembly)

Parameters

[in,out]	K	The complete system stiffness matrix to add the element stiffness matrix into
	scale	A factor to scale the added stiffness matrix with

Note: The element stiffness matrix is square of size getNumDofPerNode() x getNumNodes(); This method supposes that the incoming state contains information with the same number of; dof per node as getNumDofPerNode()

§ assembleMatrixBlocks()

template<typename T , int Opt, typename StorageIndex >

void SurgSim::Physics::FemElement::assembleMatrixBlocks	(	const Eigen::Ref< const Math::Matrix > &	subMatrix,
		const std::vector< size_t > &	blockIds,
		size_t	blockSize,
		Eigen::SparseMatrix< T, Opt, StorageIndex > *	matrix
	)		const

Add a sub-matrix made of squared-blocks into a matrix that could be un-initialized.

Template Parameters

T,Opt,StorageIndex Types and option defining the output matrix type SparseMatrix<T, Opt, StorageIndex>

Parameters

	subMatrix	The sub-matrix (containing all the squared-blocks)
	blockIds	Vector of block indices (for accessing matrix) corresponding to the blocks in sub-matrix
	blockSize	The blocks size
[out]	matrix	The matrix to add the sub-matrix blocks into

§ assembleMatrixBlocksNoInitialize()

template<typename T , int Opt, typename StorageIndex >

void SurgSim::Physics::FemElement::assembleMatrixBlocksNoInitialize	(	const Eigen::Ref< const Math::Matrix > &	subMatrix,
		const std::vector< size_t > &	blockIds,
		size_t	blockSize,
		Eigen::SparseMatrix< T, Opt, StorageIndex > *	matrix
	)		const

Add a sub-matrix made of squared-blocks into a matrix that is already initialized.

Template Parameters

T,Opt,StorageIndex Types and option defining the output matrix type SparseMatrix<T, Opt, StorageIndex>

Parameters

	subMatrix	The sub-matrix (containing all the squared-blocks)
	blockIds	Vector of block indices (for accessing matrix) corresponding to the blocks in sub-matrix
	blockSize	The blocks size
[out]	matrix	The matrix to add the sub-matrix blocks into

§ computeCartesianCoordinate()

virtual SurgSim::Math::Vector SurgSim::Physics::FemElement::computeCartesianCoordinate	(	const SurgSim::Math::OdeState &	state,
		const SurgSim::Math::Vector &	naturalCoordinate
	)		const

pure virtual

Computes a given natural coordinate in cartesian coordinates.

Parameters

state	The state at which to transform coordinates
naturalCoordinate	The coordinates to transform

Returns: The resultant cartesian coordinates

Implemented in SurgSim::Physics::Fem2DElementTriangle, SurgSim::Physics::Fem3DElementCube, SurgSim::Physics::Fem1DElementBeam, and SurgSim::Physics::Fem3DElementTetrahedron.

§ computeNaturalCoordinate()

virtual SurgSim::Math::Vector SurgSim::Physics::FemElement::computeNaturalCoordinate	(	const SurgSim::Math::OdeState &	state,
		const SurgSim::Math::Vector &	cartesianCoordinate
	)		const

pure virtual

Computes a natural coordinate given a global coordinate.

Parameters

state	The state at which to transform coordinates
cartesianCoordinate	The coordinates to transform

Returns: The resultant natural coordinates

Implemented in SurgSim::Physics::Fem2DElementTriangle, SurgSim::Physics::Fem3DElementCube, SurgSim::Physics::Fem1DElementBeam, and SurgSim::Physics::Fem3DElementTetrahedron.

§ doUpdateFMDK()

virtual void SurgSim::Physics::FemElement::doUpdateFMDK	(	const Math::OdeState &	state,
		int	options
	)

protectedpure virtual

Update the FemElement based on the given state.

Parameters

state	\((x, v)\) the current position and velocity to evaluate the various terms with
options	Flag to specify which of the F, M, D, K needs to be updated

Implemented in SurgSim::Physics::Fem2DElementTriangle, SurgSim::Physics::Fem3DElementCube, SurgSim::Physics::Fem1DElementBeam, SurgSim::Physics::Fem3DElementTetrahedron, and SurgSim::Physics::Fem3DElementCorotationalTetrahedron.

§ getMass()

double SurgSim::Physics::FemElement::getMass ( const SurgSim::Math::OdeState & state ) const

Gets the element mass based on the input state (in Kg)

Parameters

state The state to compute the mass with

Returns: The mass of this element (in Kg)

§ getMassDensity()

double SurgSim::Physics::FemElement::getMassDensity ( ) const

Gets the mass density (in Kg.m-3)

Returns: The mass density

§ getNodeId()

size_t SurgSim::Physics::FemElement::getNodeId ( size_t elementNodeId ) const

Gets the elementNodeId-th node id.

Returns: The requested node id

§ getNodeIds()

const std::vector< size_t > & SurgSim::Physics::FemElement::getNodeIds ( ) const

Gets the node ids for this element.

Returns: A vector containing the node ids on which the element is defined

§ getNumDofPerNode()

size_t SurgSim::Physics::FemElement::getNumDofPerNode ( ) const

Gets the number of degree of freedom per node.

Returns: The number of dof per node

§ getNumNodes()

size_t SurgSim::Physics::FemElement::getNumNodes ( ) const

Gets the number of nodes connected by this element.

Returns: The number of nodes

§ getPoissonRatio()

double SurgSim::Physics::FemElement::getPoissonRatio ( ) const

Gets the Poisson ratio (unitless)

Returns: The Poisson ratio

§ getVolume()

virtual double SurgSim::Physics::FemElement::getVolume ( const SurgSim::Math::OdeState & state ) const

pure virtual

Gets the element volume based on the input state (in m-3)

Parameters

state The state to compute the volume with

Returns: The volume of this element (in m-3)

Implemented in SurgSim::Physics::MockFemElement, SurgSim::Physics::Fem2DElementTriangle, SurgSim::Physics::Fem3DElementCube, SurgSim::Physics::Fem3DElementTetrahedron, and SurgSim::Physics::Fem1DElementBeam.

§ getYoungModulus()

double SurgSim::Physics::FemElement::getYoungModulus ( ) const

Gets the Young modulus (in N.m-2)

Returns: The Young modulus

§ initialize()

void SurgSim::Physics::FemElement::initialize ( const SurgSim::Math::OdeState & state )

virtual

Initialize the FemElement once everything has been set.

Parameters

state The state to initialize the FemElement with

Reimplemented in SurgSim::Physics::MockFemElement, SurgSim::Physics::Fem2DElementTriangle, SurgSim::Physics::Fem3DElementCube, SurgSim::Physics::Fem3DElementTetrahedron, SurgSim::Physics::Fem3DElementCorotationalTetrahedron, and SurgSim::Physics::Fem1DElementBeam.

§ isValidCoordinate()

bool SurgSim::Physics::FemElement::isValidCoordinate ( const SurgSim::Math::Vector & naturalCoordinate ) const

Determines whether a given natural coordinate is valid.

Parameters

naturalCoordinate Coordinate to check

Returns: True if valid

§ setMassDensity()

void SurgSim::Physics::FemElement::setMassDensity ( double rho )

Sets the mass density (in Kg.m-3)

Parameters

rho	The mass density

§ setNumDofPerNode()

void SurgSim::Physics::FemElement::setNumDofPerNode ( size_t numDofPerNode )

protected

Sets the number of degrees of freedom per node.

Parameters

numDofPerNode The number of dof per node

Note: Protected to be accessible only to derived classes which should be the only; ones able to set this parameter

§ setPoissonRatio()

void SurgSim::Physics::FemElement::setPoissonRatio ( double nu )

Sets the Poisson ratio (unitless)

Parameters

nu	The Poisson ratio

§ setYoungModulus()

void SurgSim::Physics::FemElement::setYoungModulus ( double E )

Sets the Young modulus (in N.m-2)

Parameters

E	The Young modulus

§ updateFMDK()

void SurgSim::Physics::FemElement::updateFMDK	(	const Math::OdeState &	state,
		int	options
	)

Update the FemElement based on the given state.

Parameters

state	\((x, v)\) the current position and velocity to evaluate the various terms with
options	Flag to specify which of the F, M, D, K needs to be updated

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

SurgSim/Physics/FemElement.h
SurgSim/Physics/FemElement-inl.h
SurgSim/Physics/FemElement.cpp

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Member Function Documentation

§ addDamping()

§ addFMDK()

§ addForce()

§ addMass()

§ addMatVec()

§ addStiffness()

§ assembleMatrixBlocks()

§ assembleMatrixBlocksNoInitialize()

§ computeCartesianCoordinate()

§ computeNaturalCoordinate()

§ doUpdateFMDK()

§ getMass()

§ getMassDensity()

§ getNodeId()

§ getNodeIds()

§ getNumDofPerNode()

§ getNumNodes()

§ getPoissonRatio()

§ getVolume()

§ getYoungModulus()

§ initialize()

§ isValidCoordinate()

§ setMassDensity()

§ setNumDofPerNode()

§ setPoissonRatio()

§ setYoungModulus()

§ updateFMDK()