Class for creating a 2D linearized two-node frame element in a mesh. More...

#include <lin2DFrame2.hpp>

Inheritance diagram for lin2DFrame2:

Collaboration diagram for lin2DFrame2:

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Public Member Functions
	lin2DFrame2 (const std::vector< unsigned int > nodes, std::unique_ptr< Section > &section, bool formulation=false, const std::string quadrature="GAUSS", unsigned int nGauss=3)
	Creates a lin2DFrame2 in a finite element Mesh. More...

	~lin2DFrame2 ()
	Destroys this lin2DFrame2 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
double	ComputeLength () const
	Compute the current length of the element. More...

Eigen::MatrixXd	ComputeLocalAxes () const
	Compute/update the local axis-1 of the element. More...

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	ComputeShapeFunctionMatrix (const double ri) const
	Evaluates the shape function matrix at a given Gauss point. More...

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

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

Private Attributes
double	L
	Length of the element. More...

bool	Formulation
	The element formulation. More...

double	Phi
	Section Shear Factor. 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< Section > >	theSection
	The Element's Section. More...

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

Detailed Description

Class for creating a 2D linearized two-node frame element in a mesh.

See also: Element.hpp Mesh.hpp

Constructor & Destructor Documentation

◆ lin2DFrame2()

lin2DFrame2::lin2DFrame2	(	const std::vector< unsigned int >	nodes,
		std::unique_ptr< Section > &	section,
		bool	formulation = `false`,
		const std::string	quadrature = `"GAUSS"`,
		unsigned int	nGauss = `3`
	)

Creates a lin2DFrame2 in a finite element Mesh.

Parameters

nodes	The Node connectivity array of this Element.
section	Pointer to the Section that this Element is made out of.
formulation	The frame formulation: "Bernoulli", "Timoshenko".
quadrature	The integration rule to be employed.
nGauss	Number of Gauss points for Element integration.

Note: More details can be found at lin2DFrame2.

See also: lin2DFrame2::theNodes, lin2DFrame2::theSection, lin2DFrame2::QuadraturePoints.

◆ ~lin2DFrame2()

lin2DFrame2::~lin2DFrame2 ( )

Destroys this lin2DFrame2 object.

Member Function Documentation

◆ CommitState()

void lin2DFrame2::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 lin2DFrame2::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 lin2DFrame2::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 lin2DFrame2.

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

Implements Element.

◆ ComputeDomainReductionForces()

Eigen::VectorXd lin2DFrame2::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 lin2DFrame2::ComputeEnergy ( )

virtual

Computes the element energy for a given deformation.

Returns: Scalar with the element deformation energy.

Implements Element.

◆ ComputeInitialStiffnessMatrix()

Eigen::MatrixXd lin2DFrame2::ComputeInitialStiffnessMatrix ( ) const

private

Compute the initial stiffness matrix of the element.

Returns: Matrix with the initial Tanget stiffness matrix.

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

◆ ComputeInternalDynamicForces()

Eigen::VectorXd lin2DFrame2::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 lin2DFrame2::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 lin2DFrame2.

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

Implements Element.

◆ ComputeLength()

double lin2DFrame2::ComputeLength ( ) const

private

Compute the current length of the element.

◆ ComputeLocalAxes()

Eigen::MatrixXd lin2DFrame2::ComputeLocalAxes ( ) const

private

Compute/update the local axis-1 of the element.

Returns: Matrix with the local axis transformation.

Note: Axes transformation are according to lin2DFrame2.

◆ ComputeMassMatrix()

Eigen::MatrixXd lin2DFrame2::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 lin2DFrame2.

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

Implements Element.

◆ ComputePMLMatrix()

Eigen::MatrixXd lin2DFrame2::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.

◆ ComputeShapeFunctionMatrix()

Eigen::MatrixXd lin2DFrame2::ComputeShapeFunctionMatrix ( const double ri ) const

private

Evaluates the shape function matrix at a given Gauss point.

Parameters

ri	The Gauss coordinate in the r-axis.

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

◆ ComputeStiffnessMatrix()

Eigen::MatrixXd lin2DFrame2::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 lin2DFrame2.

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

Implements Element.

◆ ComputeStrain()

Eigen::VectorXd lin2DFrame2::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 lin2DFrame2::ComputeStrainDisplacementMatrix ( const double ri ) const

private

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

Parameters

ri	The Gauss coordinate in the r-axis.

Returns: Matrix with the strain-displacement operator.

◆ ComputeStrainRate()

Eigen::VectorXd lin2DFrame2::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 lin2DFrame2::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 lin2DFrame2::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 lin2DFrame2::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 lin2DFrame2::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 lin2DFrame2::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 lin2DFrame2::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> lin2DFrame2::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 lin2DFrame2::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 lin2DFrame2::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 lin2DFrame2::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 lin2DFrame2::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 lin2DFrame2::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 lin2DFrame2::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

◆ Formulation

bool lin2DFrame2::Formulation

private

The element formulation.

◆ L

double lin2DFrame2::L

private

Length of the element.

◆ Phi

double lin2DFrame2::Phi

private

Section Shear Factor.

◆ QuadraturePoints

std::unique_ptr<QuadratureRule> lin2DFrame2::QuadraturePoints

private

Coordinate of Gauss points.

◆ theDamping

std::shared_ptr<Damping> lin2DFrame2::theDamping

private

The Damping model.

◆ theNodes

std::vector<std::shared_ptr<Node> > lin2DFrame2::theNodes

private

The Element's Nodes.

◆ theSection

std::vector<std::unique_ptr<Section> > lin2DFrame2::theSection

private

The Element's Section.

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ lin2DFrame2()

◆ ~lin2DFrame2()

Member Function Documentation

◆ CommitState()

◆ ComputeBodyForces()

◆ ComputeDampingMatrix()

◆ ComputeDomainReductionForces()

◆ ComputeEnergy()

◆ ComputeInitialStiffnessMatrix()

◆ ComputeInternalDynamicForces()

◆ ComputeInternalForces()

◆ ComputeLength()

◆ ComputeLocalAxes()

◆ ComputeMassMatrix()

◆ ComputePMLMatrix()

◆ ComputeShapeFunctionMatrix()

◆ ComputeStiffnessMatrix()

◆ ComputeStrain()

◆ ComputeStrainDisplacementMatrix()

◆ ComputeStrainRate()

◆ ComputeSurfaceForces()

◆ GetStrain()

◆ GetStrainAt()

◆ GetStrainRate()

◆ GetStress()

◆ GetStressAt()

◆ GetTotalDegreeOfFreedom()

◆ GetVTKResponse()

◆ InitialState()

◆ ReverseState()

◆ SetDamping()

◆ SetDomain()

◆ UpdateState()

Member Data Documentation

◆ Formulation

◆ L

◆ Phi

◆ QuadraturePoints

◆ theDamping

◆ theNodes

◆ theSection