Class for creating a 2D finite kinematic four-node quadrilateral element in a mesh. More...

#include <kin2DQuad4.hpp>

Inheritance diagram for kin2DQuad4:

Collaboration diagram for kin2DQuad4:

[legend]

Public Member Functions
	kin2DQuad4 (const std::vector< unsigned int > nodes, std::unique_ptr< Material > &material, const double th, const std::string quadrature="GAUSS", const unsigned int nGauss=4)
	Creates a kin2DQuad4 in a finite element Mesh. More...

	~kin2DQuad4 ()
	Destroys this kin2DQuad4 object. More...

void	CommitState ()
	Save the material states in the element. More...

void	ReverseState ()
	Reverse the material/section states to previous converged state in this element. More...

void	InitialState ()
	Brings the material/section state to its initial state in this element. More...

void	UpdateState ()
	Update the material states in the element. More...

void	SetDomain (std::map< unsigned int, std::shared_ptr< Node > > &nodes)
	Sets the finite element dependance among objects. More...

void	SetDamping (const std::shared_ptr< Damping > &damping)
	Sets the damping model. More...

std::vector< unsigned int >	GetTotalDegreeOfFreedom () const
	Gets the list of total-degree of freedom of this Element. More...

Eigen::MatrixXd	GetStrain () const
	Gets the material/section (generalised) strain. More...

Eigen::MatrixXd	GetStress () const
	Gets the material/section (generalised) stress. More...

Eigen::MatrixXd	GetStrainRate () const
	Gets the material/section (generalised) strain-rate. More...

Eigen::MatrixXd	GetStrainAt (double x3, double x2) const
	Gets the material strain in section at coordinate (x3,x2). More...

Eigen::MatrixXd	GetStressAt (double x3, double x2) const
	Gets the material stress in section at coordinate (x3,x2). More...

Eigen::VectorXd	GetVTKResponse (std::string response) const
	Gets the element internal response in VTK format for Paraview display. More...

double	ComputeEnergy ()
	Computes the element energy for a given deformation. More...

Eigen::MatrixXd	ComputeMassMatrix ()
	Compute the lumped/consistent mass matrix of the element. More...

Eigen::MatrixXd	ComputeStiffnessMatrix ()
	Compute the stiffness matrix of the element using gauss-integration. More...

Eigen::MatrixXd	ComputeDampingMatrix ()
	Compute the damping matrix of the element using gauss-integration. More...

Eigen::MatrixXd	ComputePMLMatrix ()
	Compute the PML history matrix using gauss-integration. More...

Eigen::VectorXd	ComputeInternalForces ()
	Compute the internal (elastic) forces acting on the element. More...

Eigen::VectorXd	ComputeInternalDynamicForces ()
	Compute the elastic, inertial, and viscous forces acting on the element. More...

Eigen::VectorXd	ComputeSurfaceForces (const std::shared_ptr< Load > &surface, unsigned int face)
	Compute the surface forces acting on the element. More...

Eigen::VectorXd	ComputeBodyForces (const std::shared_ptr< Load > &body, unsigned int k=0)
	Compute the body forces acting on the element. More...

Eigen::VectorXd	ComputeDomainReductionForces (const std::shared_ptr< Load > &drm, unsigned int k)
	Compute the domain reduction forces acting on the element. More...

Public Member Functions inherited from Element
	Element (std::string name, const std::vector< unsigned int > nodes, unsigned int ndofs, unsigned int VTKcell, unsigned int SVLcell)
	Creates an Element in a finite element Mesh. More...

virtual	~Element ()=0
	Destroys this Element object. More...

std::string	GetName () const
	Gets the Element Name. More...

unsigned int	GetVTKCellType () const
	Gets the Element VTK cell type. More...

unsigned int	GetVTKGroupType () const
	Gets the Element VTK group type. More...

unsigned int	GetNumberOfNodes () const
	Returns the number of nodes in element. More...

unsigned int	GetNumberOfDegreeOfFreedom () const
	Returns total number of degree of freedom in the element. More...

const std::vector< unsigned int > &	GetNodes () const
	Returns the Node Connectivity Indexes. More...

bool	HasFixedNode (const std::vector< std::shared_ptr< Node > > &nodes) const
	Returns if the element has fixed nodes. More...

Protected Member Functions
Eigen::VectorXd	TransformTensorToVector (const Eigen::MatrixXd &vector) const
	Transform tensor components into vector. More...

Eigen::MatrixXd	TransformVectorToTensor (const Eigen::VectorXd &vector) const
	Transform vector components into tensor. More...

Private Member Functions
Eigen::VectorXd	ComputeStrain (const double ri, const double si, const Eigen::MatrixXd &Jij) const
	Update strain in the element. More...

Eigen::VectorXd	ComputeStrainRate (const double ri, const double si, const Eigen::MatrixXd &Bij) const
	Update strain rate in the element. More...

Eigen::MatrixXd	ComputeJacobianMatrix (const double ri, const double si) const
	Computes the jacobian of the transformation. More...

Eigen::MatrixXd	ComputeDeformationGradientMatrix (const double ri, const double si, const Eigen::MatrixXd &Jij) const
	Computes the deformation gradient. More...

Eigen::MatrixXd	ComputeSecondPiolaKirchhoffMatrix (const Eigen::VectorXd &Stress) const
	Compute the Second Piola-Kirchhoff Stress Tensor. More...

Eigen::MatrixXd	ComputeShapeFunctionMatrix (const double ri, const double si) const
	Evaluates the shape function matrix at a given Gauss point. More...

Eigen::MatrixXd	ComputeLinearStrainDisplacementMatrix (const double ri, const double si, const Eigen::MatrixXd &Jij) const
	Evaluates the strain-displacement matrix at a given Gauss point. More...

Eigen::MatrixXd	ComputeNonLinearStrainDisplacementMatrix (const double ri, const double si, const Eigen::MatrixXd &Jij) const
	Evaluates the strain-displacement matrix at a given Gauss point. More...

Eigen::MatrixXd	ComputeLinearizedStrainDisplacementMatrix (const double ri, const double si, const Eigen::MatrixXd &Jij) const
	Evaluates the linearized (small strain) strain-displacement matrix at a given Gauss point. More...

Eigen::MatrixXd	ComputeInitialStiffnessMatrix () const
	Compute the initial stiffness matrix of the element using gauss-integration. More...

Private Attributes
double	t
	Element thickness. More...

std::shared_ptr< Damping >	theDamping
	The Damping model. More...

std::vector< std::shared_ptr< Node > >	theNodes
	The Element's Nodes. More...

std::vector< std::unique_ptr< Material > >	theMaterial
	The Element's material. More...

std::unique_ptr< QuadratureRule >	QuadraturePoints
	Coordinate of Gauss points. More...

Detailed Description

Class for creating a 2D finite kinematic four-node quadrilateral element in a mesh.

See also: Element.hpp Mesh.hpp

Constructor & Destructor Documentation

◆ kin2DQuad4()

kin2DQuad4::kin2DQuad4	(	const std::vector< unsigned int >	nodes,
		std::unique_ptr< Material > &	material,
		const double	th,
		const std::string	quadrature = `"GAUSS"`,
		const unsigned int	nGauss = `4`
	)

Creates a kin2DQuad4 in a finite element Mesh.

Parameters

nodes	The Node connectivity array of this Element.
material	Pointer to the Material that this Element is made out of.
th	The thickness of the lin2DQuad4 Element.
quadrature	The integration rule to be employed.
nGauss	Number of Gauss points for Element integration.

Note: More details can be found at kin2DQuad4.

See also: kin2DQuad4::theNodes, kin2DQuad4::theMaterial, kin2DQuad4::QuadraturePoints.

◆ ~kin2DQuad4()

kin2DQuad4::~kin2DQuad4 ( )

Destroys this kin2DQuad4 object.

Member Function Documentation

◆ CommitState()

void kin2DQuad4::CommitState ( )

virtual

Save the material states in the element.

Note: This function sets the trial states as converged ones in Material.

Implements Element.

◆ ComputeBodyForces()

Eigen::VectorXd kin2DQuad4::ComputeBodyForces	(	const std::shared_ptr< Load > &	body,
		unsigned int	k = `0`
	)

virtual

Compute the body forces acting on the element.

Parameters

body	Pointer to the Load object that contains this information.
k	The time step at which the body load is evaluated.

Returns: Vector with the Element surface force.

Note: The body force vector can be revisited in ZeroLength1D.

See also: Assembler::ComputeExternalForceVector(), Integrator::ComputeEffectiveForce().

Implements Element.

◆ ComputeDampingMatrix()

Eigen::MatrixXd kin2DQuad4::ComputeDampingMatrix ( )

virtual

Compute the damping matrix of the element using gauss-integration.

Returns: Matrix with the Element damping matrix.

Note: The damping matrix can be revisited in kin2DQuad4.

See also: Assembler::ComputeDampingMatrix(), Integrator::ComputeEffectiveStiffness().

Implements Element.

◆ ComputeDeformationGradientMatrix()

Eigen::MatrixXd kin2DQuad4::ComputeDeformationGradientMatrix	(	const double	ri,
		const double	si,
		const Eigen::MatrixXd &	Jij
	)		const

private

Computes the deformation gradient.

Parameters

ri	The i-th Gauss coordinate in the r-axis.
si	The i-th Gauss coordinate in the s-axis.
Jij	The Jacobian matrix evaluated at (ri,si).

Returns: Matrix with the deformation gradient.

◆ ComputeDomainReductionForces()

Eigen::VectorXd kin2DQuad4::ComputeDomainReductionForces	(	const std::shared_ptr< Load > &	drm,
		unsigned int	k
	)

virtual

Compute the domain reduction forces acting on the element.

Parameters

drm	Pointer to the DRM Load object that contains this information.
k	The time step at which the body load is evaluated.

Returns: Vector with the Element domain reduction forces.

Note: The DRM force vector can be revisited in ZeroLength1D.

See also: Assembler::ComputeExternalForceVector(), Integrator::ComputeEffectiveForce().

Implements Element.

◆ ComputeEnergy()

double kin2DQuad4::ComputeEnergy ( )

virtual

Computes the element energy for a given deformation.

Returns: Scalar with the element deformation energy.

Implements Element.

◆ ComputeInitialStiffnessMatrix()

Eigen::MatrixXd kin2DQuad4::ComputeInitialStiffnessMatrix ( ) const

private

Compute the initial stiffness matrix of the element using gauss-integration.

Returns: Matrix with the initial Tanget stiffness matrix.

Note: This matrix is computed when the strain deformation is zero.

◆ ComputeInternalDynamicForces()

Eigen::VectorXd kin2DQuad4::ComputeInternalDynamicForces ( )

virtual

Compute the elastic, inertial, and viscous forces acting on the element.

Returns: Vector with the Element dynamic internal force.

Note: The internal force vector can be revisited in Element.

See also: Assembler::ComputeDynamicInternalForceVector().

Implements Element.

◆ ComputeInternalForces()

Eigen::VectorXd kin2DQuad4::ComputeInternalForces ( )

virtual

Compute the internal (elastic) forces acting on the element.

Returns: Vector with the Element internal force.

Note: The internal force vector can be revisited in kin2DQuad4.

See also: Assembler::ComputeInternalForceVector(), Integrator::ComputeEffectiveForce().

Implements Element.

◆ ComputeJacobianMatrix()

Eigen::MatrixXd kin2DQuad4::ComputeJacobianMatrix	(	const double	ri,
		const double	si
	)		const

private

Computes the jacobian of the transformation.

Parameters

ri	The i-th Gauss coordinate in the r-axis.
si	The i-th Gauss coordinate in the s-axis.

Returns: The Jacobian matrix evaluated at i-th Gauss point (ri,si).

◆ ComputeLinearizedStrainDisplacementMatrix()

Eigen::MatrixXd kin2DQuad4::ComputeLinearizedStrainDisplacementMatrix	(	const double	ri,
		const double	si,
		const Eigen::MatrixXd &	Jij
	)		const

private

Evaluates the linearized (small strain) strain-displacement matrix at a given Gauss point.

Parameters

ri	The i-th Gauss coordinate in the r-axis.
si	The i-th Gauss coordinate in the s-axis.
Jij	The Jacobian matrix evaluated at (ri,si).

Returns: Matrix with the linear strain-displacement operator.

◆ ComputeLinearStrainDisplacementMatrix()

Eigen::MatrixXd kin2DQuad4::ComputeLinearStrainDisplacementMatrix	(	const double	ri,
		const double	si,
		const Eigen::MatrixXd &	Jij
	)		const

private

Evaluates the strain-displacement matrix at a given Gauss point.

Parameters

ri	The i-th Gauss coordinate in the r-axis.
si	The i-th Gauss coordinate in the s-axis.
Jij	The Jacobian matrix evaluated at (ri,si).

Returns: Matrix with the linear strain-displacement operator.

◆ ComputeMassMatrix()

Eigen::MatrixXd kin2DQuad4::ComputeMassMatrix ( )

virtual

Compute the lumped/consistent mass matrix of the element.

Returns: Matrix with the Element mass matrix.

Note: The mass matrix can be revisited in kin2DQuad4.

See also: Assembler::ComputeMassMatrix(), Integrator::ComputeEffectiveStiffness().

Implements Element.

◆ ComputeNonLinearStrainDisplacementMatrix()

Eigen::MatrixXd kin2DQuad4::ComputeNonLinearStrainDisplacementMatrix	(	const double	ri,
		const double	si,
		const Eigen::MatrixXd &	Jij
	)		const

private

Evaluates the strain-displacement matrix at a given Gauss point.

Parameters

ri	The i-th Gauss coordinate in the r-axis.
si	The i-th Gauss coordinate in the s-axis.
Jij	The Jacobian matrix evaluated at (ri,si).

Returns: Matrix with the geometric strain-displacement operator.

◆ ComputePMLMatrix()

Eigen::MatrixXd kin2DQuad4::ComputePMLMatrix ( )

virtual

Compute the PML history matrix using gauss-integration.

Returns: Matrix with the PML Element matrix.

Note: The PML matrix is none existent for this element.

See also: Assembler::ComputePMLHistoryMatrix(), Integrator::ComputeEffectiveStiffness().

Implements Element.

◆ ComputeSecondPiolaKirchhoffMatrix()

Eigen::MatrixXd kin2DQuad4::ComputeSecondPiolaKirchhoffMatrix ( const Eigen::VectorXd & Stress ) const

private

Compute the Second Piola-Kirchhoff Stress Tensor.

Parameters

Stress The stress vector to be mapped to current configuration.

◆ ComputeShapeFunctionMatrix()

Eigen::MatrixXd kin2DQuad4::ComputeShapeFunctionMatrix	(	const double	ri,
		const double	si
	)		const

private

Evaluates the shape function matrix at a given Gauss point.

Parameters

ri	The i-th Gauss coordinate in the r-axis.
si	The i-th Gauss coordinate in the s-axis.

Returns: Matrix with the shape function at the Gauss coordinate.

◆ ComputeStiffnessMatrix()

Eigen::MatrixXd kin2DQuad4::ComputeStiffnessMatrix ( )

virtual

Compute the stiffness matrix of the element using gauss-integration.

Returns: Matrix with the Element stiffness matrix.

Note: The stiffness matrix can be revisited in kin2DQuad4.

See also: Assembler::ComputeStiffnessMatrix(), Integrator::ComputeEffectiveStiffness().

Implements Element.

◆ ComputeStrain()

Eigen::VectorXd kin2DQuad4::ComputeStrain	(	const double	ri,
		const double	si,
		const Eigen::MatrixXd &	Jij
	)		const

private

Update strain in the element.

Parameters

ri	The i-th Gauss coordinate in the r-axis.
si	The i-th Gauss coordinate in the s-axis.
Jij	The Jacobian matrix evaluated at (ri,si).

Returns: Vector with the strain at integration point.

◆ ComputeStrainRate()

Eigen::VectorXd kin2DQuad4::ComputeStrainRate	(	const double	ri,
		const double	si,
		const Eigen::MatrixXd &	Bij
	)		const

private

Update strain rate in the element.

Parameters

ri	The i-th Gauss coordinate in the r-axis.
si	The i-th Gauss coordinate in the s-axis.
Bij	The strain-displacement matrix.

Returns: Vector with the strain-rate at integration point.

◆ ComputeSurfaceForces()

Eigen::VectorXd kin2DQuad4::ComputeSurfaceForces	(	const std::shared_ptr< Load > &	surface,
		unsigned int	face
	)

virtual

Compute the surface forces acting on the element.

Parameters

surface	Pointer to the Load object that contains this information.
k	The time step at which the surface load is evaluated.

Returns: Vector with the Element surface force.

Note: The surface force vector can be revisited in ZeroLength1D.

See also: Assembler::ComputeExternalForceVector(), Integrator::ComputeEffectiveForce().

Implements Element.

◆ GetStrain()

Eigen::MatrixXd kin2DQuad4::GetStrain ( ) const

virtual

Gets the material/section (generalised) strain.

Returns: Matrix with the strain at each integration point.

Note: The index (i,j) are the strain and Gauss-point respectively.

Implements Element.

◆ GetStrainAt()

Eigen::MatrixXd kin2DQuad4::GetStrainAt	(	double	x3,
		double	x2
	)		const

virtual

Gets the material strain in section at coordinate (x3,x2).

Parameters

x3	Local coordinate along the x3-axis.
x2	Local coordinate along the x2-axis.

Returns: Matrix with the strain at coordinate (x3,x2).

Note: The strains are interpolated at this coordinate.

Implements Element.

◆ GetStrainRate()

Eigen::MatrixXd kin2DQuad4::GetStrainRate ( ) const

virtual

Gets the material/section (generalised) strain-rate.

Returns: Matrix with the strain-rate at each integration point.

Note: The index (i,j) are the strain-rate and Gauss-point respectively.

Implements Element.

◆ GetStress()

Eigen::MatrixXd kin2DQuad4::GetStress ( ) const

virtual

Gets the material/section (generalised) stress.

Returns: Matrix with the stress at each integration point.

Note: The index (i,j) are the stress and Gauss-point respectively.

Implements Element.

◆ GetStressAt()

Eigen::MatrixXd kin2DQuad4::GetStressAt	(	double	x3,
		double	x2
	)		const

virtual

Gets the material stress in section at coordinate (x3,x2).

Parameters

x3	Local coordinate along the x3-axis.
x2	Local coordinate along the x2-axis.

Returns: Matrix with the stresses at coordinate (x3,x2).

Note: The stresses are interpolated at this coordinate.

Implements Element.

◆ GetTotalDegreeOfFreedom()

std::vector<unsigned int> kin2DQuad4::GetTotalDegreeOfFreedom ( ) const

virtual

Gets the list of total-degree of freedom of this Element.

Returns: Vector with the list of degree-of-freedom of this Element.

Implements Element.

◆ GetVTKResponse()

Eigen::VectorXd kin2DQuad4::GetVTKResponse ( std::string response ) const

virtual

Gets the element internal response in VTK format for Paraview display.

Parameters

response The response to be display in Paraview.

Returns: Vector with the response at the Element center.

Note: The current responses are: "Strain", "Stress".

Implements Element.

◆ InitialState()

void kin2DQuad4::InitialState ( )

virtual

Brings the material/section state to its initial state in this element.

Note: This function returns the meterial states to the beginning.

Implements Element.

◆ ReverseState()

void kin2DQuad4::ReverseState ( )

virtual

Reverse the material/section states to previous converged state in this element.

Note: This function returns the trial states to previous converged states at the Material level.

Implements Element.

◆ SetDamping()

void kin2DQuad4::SetDamping ( const std::shared_ptr< Damping > & damping )

virtual

Sets the damping model.

Parameters

damping Pointer to the damping model.

Note: Several Element objects can share the same damping model.

Implements Element.

◆ SetDomain()

void kin2DQuad4::SetDomain ( std::map< unsigned int, std::shared_ptr< Node > > & nodes )

virtual

Sets the finite element dependance among objects.

Parameters

nodes The Node list of the Mesh object.

Note: This function sets the relation between Node and Element objects.

See also: lin2DQuad4::theNodes.

Implements Element.

◆ TransformTensorToVector()

Eigen::VectorXd kin2DQuad4::TransformTensorToVector ( const Eigen::MatrixXd & vector ) const

protected

Transform tensor components into vector.

Parameters

vector The tensor to be transformed into a vector.

Returns: The equivalent vector object.

◆ TransformVectorToTensor()

Eigen::MatrixXd kin2DQuad4::TransformVectorToTensor ( const Eigen::VectorXd & vector ) const

protected

Transform vector components into tensor.

Parameters

vector The vector to be transformed into a tensor.

Returns: The equivalent tensor object.

◆ UpdateState()

void kin2DQuad4::UpdateState ( )

virtual

Update the material states in the element.

Note: This function update the trial states at the Material level.

Implements Element.

Member Data Documentation

◆ QuadraturePoints

std::unique_ptr<QuadratureRule> kin2DQuad4::QuadraturePoints

private

Coordinate of Gauss points.

◆ t

double kin2DQuad4::t

private

Element thickness.

◆ theDamping

std::shared_ptr<Damping> kin2DQuad4::theDamping

private

The Damping model.

◆ theMaterial

std::vector<std::unique_ptr<Material> > kin2DQuad4::theMaterial

private

The Element's material.

◆ theNodes

std::vector<std::shared_ptr<Node> > kin2DQuad4::theNodes

private

The Element's Nodes.

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ kin2DQuad4()

◆ ~kin2DQuad4()

Member Function Documentation

◆ CommitState()

◆ ComputeBodyForces()

◆ ComputeDampingMatrix()

◆ ComputeDeformationGradientMatrix()

◆ ComputeDomainReductionForces()

◆ ComputeEnergy()

◆ ComputeInitialStiffnessMatrix()

◆ ComputeInternalDynamicForces()

◆ ComputeInternalForces()

◆ ComputeJacobianMatrix()

◆ ComputeLinearizedStrainDisplacementMatrix()

◆ ComputeLinearStrainDisplacementMatrix()

◆ ComputeMassMatrix()

◆ ComputeNonLinearStrainDisplacementMatrix()

◆ ComputePMLMatrix()

◆ ComputeSecondPiolaKirchhoffMatrix()

◆ ComputeShapeFunctionMatrix()

◆ ComputeStiffnessMatrix()

◆ ComputeStrain()

◆ ComputeStrainRate()

◆ ComputeSurfaceForces()

◆ GetStrain()

◆ GetStrainAt()

◆ GetStrainRate()

◆ GetStress()

◆ GetStressAt()

◆ GetTotalDegreeOfFreedom()

◆ GetVTKResponse()

◆ InitialState()

◆ ReverseState()

◆ SetDamping()

◆ SetDomain()

◆ TransformTensorToVector()

◆ TransformVectorToTensor()

◆ UpdateState()

Member Data Documentation

◆ QuadraturePoints

◆ t

◆ theDamping

◆ theMaterial

◆ theNodes