Class for Fem Element 3D based on a tetrahedron volume discretization. More...

#include <Fem3DElementTetrahedron.h>

Inheritance diagram for SurgSim::Physics::Fem3DElementTetrahedron:

Public Member Functions
	Fem3DElementTetrahedron ()
	Constructor.

	Fem3DElementTetrahedron (std::array< size_t, 4 > nodeIds)
	Constructor. More...

	Fem3DElementTetrahedron (std::shared_ptr< FemElementStructs::FemElementParameter > elementData)
	Constructor for FemElement object factory. More...

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

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

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

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

Public Member Functions inherited from SurgSim::Physics::FemElement
	FemElement ()
	Constructor.

virtual	~FemElement ()
	Virtual destructor.

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 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...

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...

Protected Member Functions
void	initializeMembers ()
	Initializes variables needed before Initialize() is called.

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

void	computeShapeFunctions (const SurgSim::Math::OdeState &state, double volume, std::array< double, 4 > ai, std::array< double, 4 > bi, std::array< double, 4 > ci, std::array< double, 4 > *di) const
	Computes the tetrahedron shape functions. More...

void	computeStiffness (const SurgSim::Math::OdeState &state, SurgSim::Math::Matrix *k)
	Computes the tetrahedron stiffness matrix. More...

void	computeMass (const SurgSim::Math::OdeState &state, SurgSim::Math::Matrix *m)
	Computes the tetrahedron mass matrix. More...

Protected Member Functions inherited from SurgSim::Physics::FemElement
void	setNumDofPerNode (size_t numDofPerNode)
	Sets the number of degrees of freedom per node. 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
Eigen::Matrix< double, 12, 1 >	m_x0
	The tetrahedon rest state.

Protected Attributes inherited from SurgSim::Physics::FemElement
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)

Additional Inherited Members
Public Types inherited from SurgSim::Physics::FemElement
typedef SurgSim::Framework::ObjectFactory1< FemElement, std::shared_ptr< FemElementStructs::FemElementParameter > >	FactoryType

Static Public Member Functions inherited from SurgSim::Physics::FemElement
static FactoryType &	getFactory ()

Detailed Description

Class for Fem Element 3D based on a tetrahedron volume discretization.

Note: The inertia property (mass) of the tetrahedron is derived from; "Theory of Matrix Structural Analysis" from J.S. Przemieniecki; The force and stiffness matrix of the tetrahedron is derived from; http://www.colorado.edu/engineering/CAS/courses.d/AFEM.d/AFEM.Ch09.d/AFEM.Ch09.pdf; The deformation is based on the linear elasticity theory and not on the visco-elasticity theory.; Therefore the element does not have any damping component.; Fem3DElementTetrahedron uses linear elasticity (not visco-elasticity), so it does not give any damping.

Constructor & Destructor Documentation

§ Fem3DElementTetrahedron() [1/2]

SurgSim::Physics::Fem3DElementTetrahedron::Fem3DElementTetrahedron ( std::array< size_t, 4 > nodeIds )

explicit

Constructor.

Parameters

nodeIds An array of 4 node ids defining this tetrahedron element in a overall mesh

Note: It is required that the triangle ABC is CCW looking from D (i.e. dot(cross(AB, AC), AD) > 0); This is required from the signed volume calculation method getVolume(); A warning will be logged when the initialize function is called if this condition is not met, but the; simulation will keep running. Behavior will be undefined because of possible negative volume terms.

§ Fem3DElementTetrahedron() [2/2]

SurgSim::Physics::Fem3DElementTetrahedron::Fem3DElementTetrahedron ( std::shared_ptr< FemElementStructs::FemElementParameter > elementData )

explicit

Constructor for FemElement object factory.

Parameters

elementData A FemElement3D struct defining this tetrahedron element in a overall mesh

Note: It is required that the triangle ABC is CCW looking from D (i.e. dot(cross(AB, AC), AD) > 0); This is required from the signed volume calculation method getVolume(); A warning will be logged when the initialize function is called if this condition is not met, but the; simulation will keep running. Behavior will be undefined because of possible negative volume terms.

Exceptions

SurgSim::Framework::AssertionFailure if nodeIds has a size different than 4

Member Function Documentation

§ computeCartesianCoordinate()

SurgSim::Math::Vector SurgSim::Physics::Fem3DElementTetrahedron::computeCartesianCoordinate	(	const SurgSim::Math::OdeState &	state,
		const SurgSim::Math::Vector &	naturalCoordinate
	)		const

overridevirtual

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

Implements SurgSim::Physics::FemElement.

§ computeMass()

void SurgSim::Physics::Fem3DElementTetrahedron::computeMass	(	const SurgSim::Math::OdeState &	state,
		SurgSim::Math::Matrix *	m
	)

protected

Computes the tetrahedron mass matrix.

Parameters

	state	The state to compute the mass matrix from
[out]	m	The mass matrix to store the result into

§ computeNaturalCoordinate()

SurgSim::Math::Vector SurgSim::Physics::Fem3DElementTetrahedron::computeNaturalCoordinate	(	const SurgSim::Math::OdeState &	state,
		const SurgSim::Math::Vector &	cartesianCoordinate
	)		const

overridevirtual

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

Implements SurgSim::Physics::FemElement.

§ computeShapeFunctions()

void SurgSim::Physics::Fem3DElementTetrahedron::computeShapeFunctions	(	const SurgSim::Math::OdeState &	state,
		double *	volume,
		std::array< double, 4 > *	ai,
		std::array< double, 4 > *	bi,
		std::array< double, 4 > *	ci,
		std::array< double, 4 > *	di
	)		const

protected

Computes the tetrahedron shape functions.

Parameters

	state	The deformable rest state to compute the shape function from
[out]	volume	the volume calculated with the given state
[out]	ai	from the shape function, Ni(x, y, z) = 1/6*volume (ai + bi.x + ci.y + di.z)
[out]	bi	from the shape function, Ni(x, y, z) = 1/6*volume (ai + bi.x + ci.y + di.z)
[out]	ci	from the shape function, Ni(x, y, z) = 1/6*volume (ai + bi.x + ci.y + di.z)
[out]	di	from the shape function, Ni(x, y, z) = 1/6*volume (ai + bi.x + ci.y + di.z)

§ computeStiffness()

void SurgSim::Physics::Fem3DElementTetrahedron::computeStiffness	(	const SurgSim::Math::OdeState &	state,
		SurgSim::Math::Matrix *	k
	)

protected

Computes the tetrahedron stiffness matrix.

Parameters

	state	The state to compute the stiffness matrix from
[out]	k	The stiffness matrix to store the result into

Elasticity material matrix (contains the elastic properties of the material)

Shape functions: Tetrahedron rest volume

Shape functions coefficients Ni(x,y,z) = 1/6V ( ai + x.bi + y.ci + z.di )

§ doUpdateFMDK()

void SurgSim::Physics::Fem3DElementTetrahedron::doUpdateFMDK	(	const Math::OdeState &	state,
		int	options
	)

overrideprotectedvirtual

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

Implements SurgSim::Physics::FemElement.

§ getVolume()

double SurgSim::Physics::Fem3DElementTetrahedron::getVolume ( const SurgSim::Math::OdeState & state ) const

overridevirtual

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)

Implements SurgSim::Physics::FemElement.

§ initialize()

void SurgSim::Physics::Fem3DElementTetrahedron::initialize ( const SurgSim::Math::OdeState & state )

overridevirtual

Initialize the FemElement once everything has been set.

Parameters

state The state to initialize the FemElement with

Reimplemented from SurgSim::Physics::FemElement.

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

SurgSim/Physics/Fem3DElementTetrahedron.h
SurgSim/Physics/Fem3DElementTetrahedron.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

§ Fem3DElementTetrahedron() [1/2]

§ Fem3DElementTetrahedron() [2/2]

Member Function Documentation

§ computeCartesianCoordinate()

§ computeMass()

§ computeNaturalCoordinate()

§ computeShapeFunctions()

§ computeStiffness()

§ doUpdateFMDK()

§ getVolume()

§ initialize()