Description

Tetrahedron FEA element with 10 nodes.

This is a quadratic element for displacements; stress and strain are interpolated depending on Gauss points.

#include <ChElementTetraCorot_10.h>

Inheritance diagram for chrono::fea::ChElementTetraCorot_10:

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Collaboration diagram for chrono::fea::ChElementTetraCorot_10:

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Public Types
using	ShapeVector = ChMatrixNM< double, 1, 10 >

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...

double	GetVolume ()

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

virtual std::shared_ptr< ChNodeFEAxyz >	GetTetrahedronNode (int n) override
	Return the specified tetrahedron node (0 <= n <= 3).

virtual void	SetNodes (std::shared_ptr< ChNodeFEAxyz > nodeA, std::shared_ptr< ChNodeFEAxyz > nodeB, std::shared_ptr< ChNodeFEAxyz > nodeC, std::shared_ptr< ChNodeFEAxyz > nodeD, std::shared_ptr< ChNodeFEAxyz > nodeE, std::shared_ptr< ChNodeFEAxyz > nodeF, std::shared_ptr< ChNodeFEAxyz > nodeG, std::shared_ptr< ChNodeFEAxyz > nodeH, std::shared_ptr< ChNodeFEAxyz > nodeI, std::shared_ptr< ChNodeFEAxyz > nodeJ)

virtual void	Update () override
	Update element at each time step.

void	ShapeFunctions (ShapeVector &N, double r, double s, double t)
	Fills the N shape function matrix with the values of shape functions at zi parametric 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 current field values at the nodes of the element, with proper ordering. More...

double	ComputeVolume ()
	Approximation!! not the exact volume This returns an exact value only in case of Constant Metric Tetrahedron.

virtual void	ComputeJacobian (ChMatrixDynamic<> &Jacobian, double zeta1, double zeta2, double zeta3, double zeta4)
	Puts inside 'Jacobian' the Jacobian matrix of the element zeta1,...,zeta4 are the four natural coordinates of the integration point note: in case of tetrahedral elements natural coord. More...

virtual void	ComputeMatrB (ChMatrixDynamic<> &mmatrB, double zeta1, double zeta2, double zeta3, double zeta4, double &JacobianDet)
	Computes the matrix of partial derivatives and puts data in "mmatrB" evaluated at natural coordinates zeta1,...,zeta4 note: in case of tetrahedral elements natural coord. More...

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

void	GetParameterForNodeID (const int nodeID, double &z1, double &z2, double &z3, double &z4)
	Given the node ID, gets the 4 parameters of the shape function.

ChStrainTensor	GetStrain (double z1, double z2, double z3, double z4)
	Returns the strain tensor at given parameters. More...

ChStressTensor	GetStress (double z1, double z2, double z3, double z4)
	Returns the stress tensor at given parameters. More...

virtual void	UpdateRotation () override
	Given the actual position of the nodes, recompute the cumulative rotation matrix A.

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 (int n) const
	Get the partial derivatives matrix MatrB and the StiffnessMatrix.

const ChMatrixDynamic &	GetStiffnessMatrix () const

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
	Get the number of DOFs sub-blocks.

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

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

virtual bool	IsSubBlockActive (int nblock) const override
	Check if the specified sub-block of DOFs is active.

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 -1..+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::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	ComputeNodalMass ()
	Compute element's nodal masses.

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. More...

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::ChElementGeneric
ChKblockGeneric	Kmatr

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

Member Function Documentation

◆ ComputeInternalForces()

void chrono::fea::ChElementTetraCorot_10::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.

◆ ComputeJacobian()

void chrono::fea::ChElementTetraCorot_10::ComputeJacobian	(	ChMatrixDynamic<> &	Jacobian,
		double	zeta1,
		double	zeta2,
		double	zeta3,
		double	zeta4
	)

virtual

Puts inside 'Jacobian' the Jacobian matrix of the element zeta1,...,zeta4 are the four natural coordinates of the integration point note: in case of tetrahedral elements natural coord.

vary in the range 0 ... +1

◆ ComputeKRMmatricesGlobal()

void chrono::fea::ChElementTetraCorot_10::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.

◆ ComputeMatrB()

void chrono::fea::ChElementTetraCorot_10::ComputeMatrB	(	ChMatrixDynamic<> &	mmatrB,
		double	zeta1,
		double	zeta2,
		double	zeta3,
		double	zeta4,
		double &	JacobianDet
	)

virtual

Computes the matrix of partial derivatives and puts data in "mmatrB" evaluated at natural coordinates zeta1,...,zeta4 note: in case of tetrahedral elements natural coord.

vary in the range 0 ... +1

◆ ComputeNF()

void chrono::fea::ChElementTetraCorot_10::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 -1..+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.

◆ ComputeStiffnessMatrix()

void chrono::fea::ChElementTetraCorot_10::ComputeStiffnessMatrix ( )

virtual

Computes the local STIFFNESS MATRIX of the element: K = sum (w_i * [B]' * [D] * [B])

!! => because the canonical interval is -1 ... +1, but we want to integrate

◆ GetNdofs()

virtual int chrono::fea::ChElementTetraCorot_10::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::ChElementTetraCorot_10::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::ChElementTetraCorot_10::GetStateBlock ( ChVectorDynamic<> & mD )

overridevirtual

Fills the D vector (displacement) with the current field 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::ChElementTetraCorot_10::GetStrain	(	double	z1,
		double	z2,
		double	z3,
		double	z4
	)

Returns the strain tensor at given parameters.

The tensor is in the original undeformed unrotated reference.

◆ GetStress()

ChStressTensor chrono::fea::ChElementTetraCorot_10::GetStress	(	double	z1,
		double	z2,
		double	z3,
		double	z4
	)

Returns the stress tensor at given parameters.

The tensor is in the original undeformed unrotated reference.

◆ ShapeFunctions()

void chrono::fea::ChElementTetraCorot_10::ShapeFunctions	(	ShapeVector &	N,
		double	r,
		double	s,
		double	t
	)

Fills the N shape function matrix with the values of shape functions at zi parametric coordinates, where r=1 at 2nd vertex, s=1 at 3rd, t=1 at 4th.

All ranging in [0...1]. The last, u (=1 at 1st vertex) is computed form the first 3. It stores the Ni(r,s,t) values in a 1 row, 10 columns matrix.

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

/builds/uwsbel/chrono/src/chrono/fea/ChElementTetraCorot_10.h
/builds/uwsbel/chrono/src/chrono/fea/ChElementTetraCorot_10.cpp

Description

Public Types

Public Member Functions

Additional Inherited Members

Member Function Documentation

◆ ComputeInternalForces()

◆ ComputeJacobian()

◆ ComputeKRMmatricesGlobal()

◆ ComputeMatrB()

◆ ComputeNF()

◆ ComputeStiffnessMatrix()

◆ GetNdofs()

◆ GetNodeNdofs()

◆ GetStateBlock()

◆ GetStrain()

◆ GetStress()

◆ ShapeFunctions()