1D FemElement based on a beam volume discretization with a fixed cross section More...

#include <Fem1DElementBeam.h>

Inheritance diagram for SurgSim::Physics::Fem1DElementBeam:

Public Member Functions
	Fem1DElementBeam ()
	Constructor.

	Fem1DElementBeam (std::array< size_t, 2 > nodeIds)
	Constructor. More...

	Fem1DElementBeam (std::shared_ptr< FemElementStructs::FemElementParameter > elementData)
	Constructor for FemElement object factory. More...

void	setRadius (double radius)
	Sets the beam's circular cross-section radius. More...

double	getRadius () const
	Gets the beam's circular cross-section radius. 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...

bool	getShearingEnabled () const
	Gets whether shearing is enabled for the element. More...

void	setShearingEnabled (bool enabled)
	Enables or disables shearing for the element. 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...

const SurgSim::Math::Matrix33d &	getInitialRotation () const

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	computeInitialRotation (const SurgSim::Math::OdeState &state)
	Computes the beam element's initial rotation. More...

void	computeStiffness (const SurgSim::Math::OdeState &state)
	Computes the beam's stiffness matrix. More...

void	computeMass (const SurgSim::Math::OdeState &state)
	Computes the beam's mass matrix. More...

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

SurgSim::Math::Matrix33d	m_R0
	Initial rotation matrix for the element.

Eigen::Matrix< double, 12, 12 >	m_MLocal
	Stiffness matrix (in local coordinate frame)

Eigen::Matrix< double, 12, 12 >	m_KLocal
	Stiffness matrix (in local coordinate frame)

double	m_restLength
	Rest length.

double	m_radius
	radius for a circular Beam

double	m_A
	Cross sectional area = PI.radius.radius if circular.

bool	m_haveShear
	Does this beam element have shear.

double	m_shearFactor
	Shear factor (usually 5/8)

double	m_J
	Polar moment of inertia.

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

1D FemElement based on a beam volume discretization with a fixed cross section

The inertia property (mass) and the stiffness matrices are derived from "Theory of Matrix Structural Analysis" from J.S. Przemieniecki. The deformation is based on linear elasticity theory and not on visco-elasticity theory; therefore, the element does not have any damping components.

Note: The element is considered to have a circular cross section.

Constructor & Destructor Documentation

§ Fem1DElementBeam() [1/2]

SurgSim::Physics::Fem1DElementBeam::Fem1DElementBeam ( std::array< size_t, 2 > nodeIds )

explicit

Constructor.

Parameters

nodeIds An array of 2 node ids defining this beam element with respect to a DeformableRepresentationState which is passed to the initialize method.

§ Fem1DElementBeam() [2/2]

SurgSim::Physics::Fem1DElementBeam::Fem1DElementBeam ( std::shared_ptr< FemElementStructs::FemElementParameter > elementData )

explicit

Constructor for FemElement object factory.

Parameters

elementData A FemElement struct defining this beam element with respect to a DeformableRepresentationState which is passed to the initialize method.

Exceptions

SurgSim::Framework::AssertionFailure if nodeIds has a size different than 2

Member Function Documentation

§ computeCartesianCoordinate()

SurgSim::Math::Vector SurgSim::Physics::Fem1DElementBeam::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.

§ computeInitialRotation()

void SurgSim::Physics::Fem1DElementBeam::computeInitialRotation ( const SurgSim::Math::OdeState & state )

protected

Computes the beam element's initial rotation.

Parameters

state The state to compute the rotation from

Note: This method stores the result in m_R0

§ computeMass()

void SurgSim::Physics::Fem1DElementBeam::computeMass ( const SurgSim::Math::OdeState & state )

protected

Computes the beam's mass matrix.

Parameters

state The state to compute the stiffness matrix from

§ computeNaturalCoordinate()

SurgSim::Math::Vector SurgSim::Physics::Fem1DElementBeam::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.

§ computeStiffness()

void SurgSim::Physics::Fem1DElementBeam::computeStiffness ( const SurgSim::Math::OdeState & state )

protected

Computes the beam's stiffness matrix.

Parameters

state The state to compute the stiffness matrix from

Cross sectional moment of inertia

The shear area in the y and z directions (=0 => no shear) http://en.wikipedia.org/wiki/Timoshenko_beam_theory

Shear deformation parameters

§ doUpdateFMDK()

void SurgSim::Physics::Fem1DElementBeam::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.

§ getInitialRotation()

const SurgSim::Math::Matrix33d & SurgSim::Physics::Fem1DElementBeam::getInitialRotation ( ) const

Returns: the initial beam rotation

§ getRadius()

double SurgSim::Physics::Fem1DElementBeam::getRadius ( ) const

Gets the beam's circular cross-section radius.

Returns: The radius of the beam

§ getShearingEnabled()

bool SurgSim::Physics::Fem1DElementBeam::getShearingEnabled ( ) const

Gets whether shearing is enabled for the element.

Returns: True if shearing is enabled

§ getVolume()

double SurgSim::Physics::Fem1DElementBeam::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::Fem1DElementBeam::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.

§ setRadius()

void SurgSim::Physics::Fem1DElementBeam::setRadius ( double radius )

Sets the beam's circular cross-section radius.

Parameters

radius The radius of the beam

§ setShearingEnabled()

void SurgSim::Physics::Fem1DElementBeam::setShearingEnabled ( bool enabled )

Enables or disables shearing for the element.

Shearing can only be meaningfully enabled or disabled before the element has had initialize called.

Parameters

enabled Boolean determining whether shearing is enabled

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

SurgSim/Physics/Fem1DElementBeam.h
SurgSim/Physics/Fem1DElementBeam.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

§ Fem1DElementBeam() [1/2]

§ Fem1DElementBeam() [2/2]

Member Function Documentation

§ computeCartesianCoordinate()

§ computeInitialRotation()

§ computeMass()

§ computeNaturalCoordinate()

§ computeStiffness()

§ doUpdateFMDK()

§ getInitialRotation()

§ getRadius()

§ getShearingEnabled()

§ getVolume()

§ initialize()

§ setRadius()

§ setShearingEnabled()