Class for creating a 2D linearized four-node perfectly matched layer element in a mesh. More...

#include <PML2DQuad4.hpp>

Inheritance diagram for PML2DQuad4:

Collaboration diagram for PML2DQuad4:

[legend]

Public Member Functions
	PML2DQuad4 (const std::vector< unsigned int > nodes, std::unique_ptr< Material > &material, const std::vector< double > parameters, const std::string quadrature="GAUSS", const unsigned int nGauss=4)
	Creates a PML2DQuad4 in a finite element Mesh. More...

	~PML2DQuad4 ()
	Destroys this PML2DQuad4 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...

Private Member Functions
Eigen::VectorXd	ComputeStrain (const Eigen::MatrixXd &Bij) const
	Update strain in the element. More...

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

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

Eigen::VectorXd	ComputePMLStretchingFactors (const double ri, const double si, const double rho, const double mu, const double lambda) const
	Evaluates the stretching parameters of PML. More...

Private Attributes
double	t
	Element thickness. More...

double	m_pml
	Polynomial degree of thePerfectly Match Layer. More...

double	L_pml
	Thickness of the PML region. More...

double	R_pml
	Reflection coefficient for the PML. More...

double	x0_pml
	Coordinates x0 of reference point. More...

double	y0_pml
	Coordinates y0 of reference point. More...

double	nx_pml
	Horizontal normal components for outward normal. More...

double	ny_pml
	Vertical normal components for outward normal. 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 linearized four-node perfectly matched layer element in a mesh.

See also: Element.hpp Mesh.hpp

Constructor & Destructor Documentation

◆ PML2DQuad4()

PML2DQuad4::PML2DQuad4	(	const std::vector< unsigned int >	nodes,
		std::unique_ptr< Material > &	material,
		const std::vector< double >	parameters,
		const std::string	quadrature = `"GAUSS"`,
		const unsigned int	nGauss = `4`
	)

Creates a PML2DQuad4 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.
parameters	The list of PML parameters.
quadrature	The integration rule to be employed.
nGauss	Number of Gauss points for Element integration.

Note: More details can be found at PML2DQuad4.

See also: PML2DQuad4::theNodes, PML2DQuad4::theMaterial, PML2DQuad4::QuadraturePoints.

◆ ~PML2DQuad4()

PML2DQuad4::~PML2DQuad4 ( )

Destroys this PML2DQuad4 object.

Member Function Documentation

◆ CommitState()

void PML2DQuad4::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 PML2DQuad4::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 PML2DQuad4::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 PML2DQuad4.

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

Implements Element.

◆ ComputeDomainReductionForces()

Eigen::VectorXd PML2DQuad4::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 PML2DQuad4::ComputeEnergy ( )

virtual

Computes the element energy for a given deformation.

Returns: Scalar with the element deformation energy.

Implements Element.

◆ ComputeInternalDynamicForces()

Eigen::VectorXd PML2DQuad4::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 PML2DQuad4::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 PML2DQuad4.

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

Implements Element.

◆ ComputeJacobianMatrix()

Eigen::MatrixXd PML2DQuad4::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).

◆ ComputeMassMatrix()

Eigen::MatrixXd PML2DQuad4::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 PML2DQuad4.

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

Implements Element.

◆ ComputePMLMatrix()

Eigen::MatrixXd PML2DQuad4::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.

◆ ComputePMLStretchingFactors()

Eigen::VectorXd PML2DQuad4::ComputePMLStretchingFactors	(	const double	ri,
		const double	si,
		const double	rho,
		const double	mu,
		const double	lambda
	)		const

private

Evaluates the stretching parameters of PML.

Parameters

ri	The i-th Gauss coordinate in the r-axis.
si	The i-th Gauss coordinate in the s-axis.
rho	The material density.
mu	The second Lame constant.
lambda	The first Lame constant.

Returns: Vector with the stretching parameters.

◆ ComputeShapeFunctionMatrix()

Eigen::MatrixXd PML2DQuad4::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 PML2DQuad4::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 PML2DQuad4.

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

Implements Element.

◆ ComputeStrain()

Eigen::VectorXd PML2DQuad4::ComputeStrain ( const Eigen::MatrixXd & Bij ) const

private

Update strain in the element.

Parameters

Bij	The strain-displacement matrix.

Returns: Vector with the strain at integration point.

◆ ComputeStrainDisplacementMatrix()

Eigen::MatrixXd PML2DQuad4::ComputeStrainDisplacementMatrix	(	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 strain-displacement operator.

◆ ComputeStrainRate()

Eigen::VectorXd PML2DQuad4::ComputeStrainRate ( const Eigen::MatrixXd & Bij ) const

private

Update strain rate in the element.

Parameters

Bij	The strain-displacement matrix.

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

◆ ComputeSurfaceForces()

Eigen::VectorXd PML2DQuad4::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 PML2DQuad4::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 PML2DQuad4::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 PML2DQuad4::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 PML2DQuad4::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 PML2DQuad4::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> PML2DQuad4::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 PML2DQuad4::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 PML2DQuad4::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 PML2DQuad4::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 PML2DQuad4::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 PML2DQuad4::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.

◆ UpdateState()

void PML2DQuad4::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

◆ L_pml

double PML2DQuad4::L_pml

private

Thickness of the PML region.

◆ m_pml

double PML2DQuad4::m_pml

private

Polynomial degree of thePerfectly Match Layer.

◆ nx_pml

double PML2DQuad4::nx_pml

private

Horizontal normal components for outward normal.

◆ ny_pml

double PML2DQuad4::ny_pml

private

Vertical normal components for outward normal.

◆ QuadraturePoints

std::unique_ptr<QuadratureRule> PML2DQuad4::QuadraturePoints

private

Coordinate of Gauss points.

◆ R_pml

double PML2DQuad4::R_pml

private

Reflection coefficient for the PML.

◆ t

double PML2DQuad4::t

private

Element thickness.

◆ theDamping

std::shared_ptr<Damping> PML2DQuad4::theDamping

private

The Damping model.

◆ theMaterial

std::vector<std::unique_ptr<Material> > PML2DQuad4::theMaterial

private

The Element's material.

◆ theNodes

std::vector<std::shared_ptr<Node> > PML2DQuad4::theNodes

private

The Element's Nodes.

◆ x0_pml

double PML2DQuad4::x0_pml

private

Coordinates x0 of reference point.

◆ y0_pml

double PML2DQuad4::y0_pml

private

Coordinates y0 of reference point.

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ PML2DQuad4()

◆ ~PML2DQuad4()

Member Function Documentation

◆ CommitState()

◆ ComputeBodyForces()

◆ ComputeDampingMatrix()

◆ ComputeDomainReductionForces()

◆ ComputeEnergy()

◆ ComputeInternalDynamicForces()

◆ ComputeInternalForces()

◆ ComputeJacobianMatrix()

◆ ComputeMassMatrix()

◆ ComputePMLMatrix()

◆ ComputePMLStretchingFactors()

◆ ComputeShapeFunctionMatrix()

◆ ComputeStiffnessMatrix()

◆ ComputeStrain()

◆ ComputeStrainDisplacementMatrix()

◆ ComputeStrainRate()

◆ ComputeSurfaceForces()

◆ GetStrain()

◆ GetStrainAt()

◆ GetStrainRate()

◆ GetStress()

◆ GetStressAt()

◆ GetTotalDegreeOfFreedom()

◆ GetVTKResponse()

◆ InitialState()

◆ ReverseState()

◆ SetDamping()

◆ SetDomain()

◆ UpdateState()

Member Data Documentation

◆ L_pml

◆ m_pml

◆ nx_pml

◆ ny_pml

◆ QuadraturePoints

◆ R_pml

◆ t

◆ theDamping

◆ theMaterial

◆ theNodes

◆ x0_pml

◆ y0_pml