Description

Tetrahedron FEA element with 4 nodes.

This is a classical element with linear displacement, hence with constant stress and constant strain. It can be easily used for 3D FEA problems.

#include <ChElementTetra_4.h>

Inheritance diagram for chrono::fea::ChElementTetra_4:

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Collaboration diagram for chrono::fea::ChElementTetra_4:

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Public Types
using	ShapeVector = ChMatrixNM< double, 1, 4 >

Public Member Functions
virtual int	GetNnodes () override
	Gets the number of nodes used by this element.

virtual int	GetNdofs () override
	Gets the number of coordinates in the field used by the referenced nodes. More...

virtual int	GetNodeNdofs (int n) override
	Get the number of coordinates from the n-th node that are used by this element. More...

virtual std::shared_ptr< ChNodeFEAbase >	GetNodeN (int n) override
	Access the nth node.

virtual void	SetNodes (std::shared_ptr< ChNodeFEAxyz > nodeA, std::shared_ptr< ChNodeFEAxyz > nodeB, std::shared_ptr< ChNodeFEAxyz > nodeC, std::shared_ptr< ChNodeFEAxyz > nodeD)

void	ShapeFunctions (ShapeVector &N, double r, double s, double t)
	Fills the N shape function matrix with the values of shape functions at r,s,t 'volume' coordinates, where r=1 at 2nd vertex, s=1 at 3rd, t = 1 at 4th. More...

virtual void	GetStateBlock (ChVectorDynamic<> &mD) override
	Fills the D vector (displacement) with the currentfield values at the nodes of the element, with proper ordering. More...

double	ComputeVolume ()

virtual void	ComputeStiffnessMatrix ()
	Computes the local STIFFNESS MATRIX of the element: K = Volume * [B]' * [D] * [B].

virtual void	UpdateRotation () override
	compute large rotation of element for corotational approach

virtual void	ComputeKRMmatricesGlobal (ChMatrixRef H, double Kfactor, double Rfactor=0, double Mfactor=0) override
	Sets H as the global stiffness matrix K, scaled by Kfactor. More...

virtual void	ComputeInternalForces (ChVectorDynamic<> &Fi) override
	Computes the internal forces (ex. More...

void	SetMaterial (std::shared_ptr< ChContinuumElastic > my_material)
	Set the material of the element.

std::shared_ptr< ChContinuumElastic >	GetMaterial ()

const ChMatrixDynamic &	GetMatrB () const
	Get the partial derivatives matrix MatrB and the StiffnessMatrix.

const ChMatrixDynamic &	GetStiffnessMatrix () const

ChStrainTensor	GetStrain ()
	Returns the strain tensor (note that the tetrahedron 4 nodes is a linear element, thus the strain is constant in the entire volume). More...

ChStressTensor	GetStress ()
	Returns the stress tensor (note that the tetrahedron 4 nodes is a linear element, thus the stress is constant in the entire volume). More...

void	ComputeNodalMass () override
	This function computes and adds corresponding masses to ElementBase member m_TotalMass.

virtual int	LoadableGet_ndof_x () override
	Gets the number of DOFs affected by this element (position part)

virtual int	LoadableGet_ndof_w () override
	Gets the number of DOFs affected by this element (speed part)

virtual void	LoadableGetStateBlock_x (int block_offset, ChState &mD) override
	Gets all the DOFs packed in a single vector (position part)

virtual void	LoadableGetStateBlock_w (int block_offset, ChStateDelta &mD) override
	Gets all the DOFs packed in a single vector (speed part)

virtual void	LoadableStateIncrement (const unsigned int off_x, ChState &x_new, const ChState &x, const unsigned int off_v, const ChStateDelta &Dv) override
	Increment all DOFs using a delta.

virtual int	Get_field_ncoords () override
	Number of coordinates in the interpolated field: here the {x,y,z} displacement.

virtual int	GetSubBlocks () override
	Tell the number of DOFs blocks (ex. =1 for a body, =4 for a tetrahedron, etc.)

virtual unsigned int	GetSubBlockOffset (int nblock) override
	Get the offset of the i-th sub-block of DOFs in global vector.

virtual unsigned int	GetSubBlockSize (int nblock) override
	Get the size of the i-th sub-block of DOFs in global vector.

virtual void	LoadableGetVariables (std::vector< ChVariables * > &mvars) override
	Get the pointers to the contained ChVariables, appending to the mvars vector.

virtual void	ComputeNF (const double U, const double V, const double W, ChVectorDynamic<> &Qi, double &detJ, const ChVectorDynamic<> &F, ChVectorDynamic<> state_x, ChVectorDynamic<> state_w) override
	Evaluate N'F , where N is some type of shape function evaluated at U,V,W coordinates of the volume, each ranging in 0..+1 F is a load, N'F is the resulting generalized load Returns also det[J] with J=[dx/du,..], that might be useful in gauss quadrature. More...

virtual double	GetDensity () override
	This is needed so that it can be accessed by ChLoaderVolumeGravity.

virtual bool	IsTetrahedronIntegrationNeeded () override
	If true, use quadrature over u,v,w in [0..1] range as tetrahedron volumetric coords, with z=1-u-v-w otherwise use quadrature over u,v,w in [-1..+1] as box isoparametric coords.

Public Member Functions inherited from chrono::fea::ChElementTetrahedron
double	GetVolume ()

virtual void	Update ()
	Update: this is called at least at each time step. More...

Public Member Functions inherited from chrono::fea::ChElementGeneric
ChKblockGeneric &	Kstiffness ()
	Access the proxy to stiffness, for sparse solver.

virtual void	EleIntLoadResidual_F (ChVectorDynamic<> &R, const double c) override
	(This is a default (a bit unoptimal) book keeping so that in children classes you can avoid implementing this EleIntLoadResidual_F function, unless you need faster code)

virtual void	EleIntLoadResidual_Mv (ChVectorDynamic<> &R, const ChVectorDynamic<> &w, const double c) override
	(This is a default (VERY UNOPTIMAL) book keeping so that in children classes you can avoid implementing this EleIntLoadResidual_Mv function, unless you need faster code.)

virtual void	EleIntLoadResidual_F_gravity (ChVectorDynamic<> &R, const ChVector<> &G_acc, const double c) override
	(This is a default (VERY UNOPTIMAL) book keeping so that in children classes you can avoid implementing this EleIntLoadResidual_F_gravity function, unless you need faster code. More...

virtual void	ComputeGravityForces (ChVectorDynamic<> &Fg, const ChVector<> &G_acc) override
	(This is the default implementation (POTENTIALLY INEFFICIENT) so that in children classes you can avoid implementing this ComputeGravityForces() function, unless you need faster code.) This fallback implementation uses a temp ChLoaderGravity that applies the load to elements only if they are inherited by ChLoadableUVW so it can use GetDensity() and Gauss quadrature.

virtual void	ComputeMmatrixGlobal (ChMatrixRef M) override
	Returns the global mass matrix. More...

virtual void	InjectKRMmatrices (ChSystemDescriptor &mdescriptor) override
	Tell to a system descriptor that there are item(s) of type ChKblock in this object (for further passing it to a solver)

virtual void	KRMmatricesLoad (double Kfactor, double Rfactor, double Mfactor) override
	Adds the current stiffness K and damping R and mass M matrices in encapsulated ChKblock item(s), if any. More...

virtual void	VariablesFbLoadInternalForces (double factor=1.) override
	Adds the internal forces, expressed as nodal forces, into the encapsulated ChVariables, in the 'fb' part: qf+=forces*factor (This is a default (a bit unoptimal) book keeping so that in children classes you can avoid implementing this VariablesFbLoadInternalForces function, unless you need faster code)

virtual void	VariablesFbIncrementMq () override
	Adds M*q (internal masses multiplied current 'qb') to Fb, ex. More...

Public Member Functions inherited from chrono::fea::ChElementBase
virtual void	EleDoIntegration ()
	This is optionally implemented if there is some internal state that requires integration.

Public Member Functions inherited from chrono::fea::ChElementCorotational
ChMatrix33 &	Rotation ()
	Access the cumulative rotation matrix of the element, The rotation is expressed relative to initial reference position of element.

Public Member Functions inherited from chrono::ChLoadableUVW
virtual bool	IsTrianglePrismIntegrationNeeded ()
	If true, use quadrature over u,v in [0..1] range as triangle natural coords (with z=1-u-v), and use linear quadrature over w in [-1..+1], otherwise use default quadrature over u,v,w in [-1..+1] as box isoparametric coords.

Additional Inherited Members
Protected Attributes inherited from chrono::fea::ChElementTetrahedron
double	Volume

Protected Attributes inherited from chrono::fea::ChElementGeneric
ChKblockGeneric	Kmatr

Protected Attributes inherited from chrono::fea::ChElementCorotational
ChMatrix33	A

Member Function Documentation

◆ ComputeInternalForces()

void chrono::fea::ChElementTetra_4::ComputeInternalForces ( ChVectorDynamic<> & Fi )

overridevirtual

Computes the internal forces (ex.

the actual position of nodes is not in relaxed reference position) and set values in the Fi vector.

Implements chrono::fea::ChElementBase.

◆ ComputeKRMmatricesGlobal()

void chrono::fea::ChElementTetra_4::ComputeKRMmatricesGlobal	(	ChMatrixRef	H,
		double	Kfactor,
		double	Rfactor = `0`,
		double	Mfactor = `0`
	)

overridevirtual

Sets H as the global stiffness matrix K, scaled by Kfactor.

Optionally, also superimposes global damping matrix R, scaled by Rfactor, and global mass matrix M multiplied by Mfactor.

Implements chrono::fea::ChElementBase.

◆ ComputeNF()

void chrono::fea::ChElementTetra_4::ComputeNF	(	const double	U,
		const double	V,
		const double	W,
		ChVectorDynamic<> &	Qi,
		double &	detJ,
		const ChVectorDynamic<> &	F,
		ChVectorDynamic<> *	state_x,
		ChVectorDynamic<> *	state_w
	)

overridevirtual

Evaluate N'*F , where N is some type of shape function evaluated at U,V,W coordinates of the volume, each ranging in 0..+1 F is a load, N'*F is the resulting generalized load Returns also det[J] with J=[dx/du,..], that might be useful in gauss quadrature.

Parameters

U	parametric coordinate in volume
V	parametric coordinate in volume
W	parametric coordinate in volume
Qi	Return result of N'*F here, maybe with offset block_offset
detJ	Return det[J] here
F	Input F vector, size is = n.field coords.
state_x	if != 0, update state (pos. part) to this, then evaluate Q
state_w	if != 0, update state (speed part) to this, then evaluate Q

Implements chrono::ChLoadableUVW.

◆ GetNdofs()

virtual int chrono::fea::ChElementTetra_4::GetNdofs ( )

inlineoverridevirtual

Gets the number of coordinates in the field used by the referenced nodes.

This is for example the size (n.of rows/columns) of the local stiffness matrix.

Implements chrono::fea::ChElementBase.

◆ GetNodeNdofs()

virtual int chrono::fea::ChElementTetra_4::GetNodeNdofs ( int n )

inlineoverridevirtual

Get the number of coordinates from the n-th node that are used by this element.

Note that this may be different from the value returned by GetNodeN(n)->Get_ndof_w();

Implements chrono::fea::ChElementBase.

◆ GetStateBlock()

void chrono::fea::ChElementTetra_4::GetStateBlock ( ChVectorDynamic<> & mD )

overridevirtual

Fills the D vector (displacement) with the currentfield values at the nodes of the element, with proper ordering.

If the D vector has not the size of this->GetNdofs(), it will be resized.For corotational elements, field is assumed in local reference!

Implements chrono::fea::ChElementBase.

◆ GetStrain()

ChStrainTensor chrono::fea::ChElementTetra_4::GetStrain ( )

Returns the strain tensor (note that the tetrahedron 4 nodes is a linear element, thus the strain is constant in the entire volume).

The tensor is in the original undeformed unrotated reference.

◆ GetStress()

ChStressTensor chrono::fea::ChElementTetra_4::GetStress ( )

Returns the stress tensor (note that the tetrahedron 4 nodes is a linear element, thus the stress is constant in the entire volume).

The tensor is in the original undeformed unrotated reference.

◆ ShapeFunctions()

void chrono::fea::ChElementTetra_4::ShapeFunctions	(	ShapeVector &	N,
		double	r,
		double	s,
		double	t
	)

Fills the N shape function matrix with the values of shape functions at r,s,t 'volume' coordinates, where r=1 at 2nd vertex, s=1 at 3rd, t = 1 at 4th.

All ranging in [0...1]. The last (u, u=1 at 1st vertex) is computed form the first 3 as 1.0-r-s-t. NOTE! actually N should be a 3row, 12 column sparse matrix, as N = [n1*eye(3) n2*eye(3) n3*eye(3) n4*eye(3)]; , but to avoid wasting zero and repeated elements, here it stores only the n1 n2 n3 n4 values in a 1 row, 4 columns matrix.

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

/builds/uwsbel/chrono/src/chrono/fea/ChElementTetra_4.h
/builds/uwsbel/chrono/src/chrono/fea/ChElementTetra_4.cpp

Description

Public Types

Public Member Functions

Additional Inherited Members

Member Function Documentation

◆ ComputeInternalForces()

◆ ComputeKRMmatricesGlobal()

◆ ComputeNF()

◆ GetNdofs()

◆ GetNodeNdofs()

◆ GetStateBlock()

◆ GetStrain()

◆ GetStress()

◆ ShapeFunctions()