Description

ANCF beam element with three nodes.

The coordinates at each node are the position vector and the 2 position vector gradients in the cross-section.

The node numbering, as follows:

              v
              ^
              |
A o-----+-----o-----+-----o B -> u
             /C
            w

where C is the third and central node.

#include <ChElementBeamANCF_3333.h>

Inheritance diagram for chrono::fea::ChElementBeamANCF_3333:

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Collaboration diagram for chrono::fea::ChElementBeamANCF_3333:

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Public Types
enum	IntFrcMethod { IntFrcMethod::ContInt, IntFrcMethod::PreInt }
	Internal force calculation method. More...

template<typename T , int M, int N>
using	ChMatrixNMc = Eigen::Matrix< T, M, N, Eigen::ColMajor >

using	VectorN = ChVectorN< double, NSF >

using	Vector3N = ChVectorN< double, 3 *NSF >

using	VectorNIP_D0 = ChVectorN< double, NIP_D0 >

using	VectorNIP_Dv = ChVectorN< double, NIP_Dv >

using	Matrix3xN = ChMatrixNM< double, 3, NSF >

using	MatrixNx3 = ChMatrixNM< double, NSF, 3 >

using	MatrixNx3c = ChMatrixNMc< double, NSF, 3 >

using	MatrixNx6 = ChMatrixNM< double, NSF, 6 >

using	MatrixNxN = ChMatrixNM< double, NSF, NSF >

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

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

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

void	SetNodes (std::shared_ptr< ChNodeFEAxyzDD > nodeA, std::shared_ptr< ChNodeFEAxyzDD > nodeB, std::shared_ptr< ChNodeFEAxyzDD > nodeC)
	Specify the nodes of this element.

void	SetDimensions (double lenX, double thicknessY, double thicknessZ)
	Specify the element dimensions.

void	SetMaterial (std::shared_ptr< ChMaterialBeamANCF > beam_mat)
	Specify the element material.

std::shared_ptr< ChMaterialBeamANCF >	GetMaterial () const
	Return the material.

virtual std::shared_ptr< ChNodeFEAbase >	GetNodeN (int n) override
	Access the n-th node of this element.

std::shared_ptr< ChNodeFEAxyzDD >	GetNodeA () const
	Get a handle to the first node of this element.

std::shared_ptr< ChNodeFEAxyzDD >	GetNodeB () const
	Get a handle to the second node of this element.

std::shared_ptr< ChNodeFEAxyzDD >	GetNodeC () const
	Get a handle to the third (middle) node of this element.

void	SetAlphaDamp (double a)
	Set the structural damping.

double	GetLengthX () const
	Get the element length in the xi direction (when there is no deformation of the element)

double	GetThicknessY ()
	Get the total thickness of the beam element in the eta direction (when there is no deformation of the element)

double	GetThicknessZ ()
	Get the total thickness of the beam element in the zeta direction (when there is no deformation of the element)

void	SetIntFrcCalcMethod (IntFrcMethod method)
	Set the calculation method to use for the generalized internal force and its Jacobian calculations. More...

IntFrcMethod	GetIntFrcCalcMethod ()
	Return the type of calculation method currently set for the generalized internal force and its Jacobian calculations.

ChMatrix33	GetGreenLagrangeStrain (const double xi, const double eta, const double zeta)
	Get the Green-Lagrange strain tensor at the normalized element coordinates (xi, eta, zeta) at the current state of the element. More...

ChMatrix33	GetPK2Stress (const double xi, const double eta, const double zeta)
	Get the 2nd Piola-Kirchoff stress tensor at the normalized element coordinates (xi, eta, zeta) at the current state of the element. More...

double	GetVonMissesStress (const double xi, const double eta, const double zeta)
	Get the von Mises stress value at the normalized element coordinates (xi, eta, zeta) at the current state of the element. More...

virtual void	GetStateBlock (ChVectorDynamic<> &mD) override
	Fill the D vector (column matrix) with the current field values at the nodes of the element, with proper ordering. More...

virtual void	Update () override
	Update the state of this element.

virtual void	ComputeMmatrixGlobal (ChMatrixRef M) override
	Set M equal to the global mass matrix.

virtual void	ComputeNodalMass () override
	Add contribution of element inertia to total nodal masses.

virtual void	ComputeInternalForces (ChVectorDynamic<> &Fi) override
	Compute the generalized internal force vector for the current nodal coordinates as set the value in the Fi vector.

virtual void	ComputeKRMmatricesGlobal (ChMatrixRef H, double Kfactor, double Rfactor=0, double Mfactor=0) override
	Set H as a linear combination of M, K, and R. More...

virtual void	ComputeGravityForces (ChVectorDynamic<> &Fg, const ChVector<> &G_acc) override
	Compute the generalized force vector due to gravity using the efficient ANCF specific method.

virtual void	EvaluateSectionStrain (const double, chrono::ChVector< double > &) override

virtual void	EvaluateSectionForceTorque (const double, chrono::ChVector< double > &, chrono::ChVector< double > &) override

virtual void	EvaluateSectionDisplacement (const double xi, ChVector<> &u_displ, ChVector<> &u_rotaz) override
	Gets the xyz displacement of a point on the beam line, and the rotation RxRyRz of section plane, at abscissa '(xi,0,0)'. More...

virtual void	EvaluateSectionFrame (const double xi, ChVector<> &point, ChQuaternion<> &rot) override
	Gets the absolute xyz position of a point on the beam line, and the absolute rotation of section plane, at abscissa '(xi,0,0)'. More...

void	EvaluateSectionPoint (const double xi, ChVector<> &point)
	Gets the absolute xyz position of a point on the beam line specified in normalized coordinates xi = -1 at node A and xi = 1 at node B.

void	EvaluateSectionVel (const double xi, ChVector<> &Result)
	Gets the absolute xyz velocity of a point on the beam line specified in normalized coordinates xi = -1 at node A and xi = 1 at node B.

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 (velocity 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 (velocity 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, ex=3 for a tetrahedron finite element or a cable, = 1 for a thermal problem, etc.

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 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 xi, 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 xi coordinate of the beam line, 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 void	ComputeNF (const double xi, const double eta, const double zeta, 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 xi,eta,zeta 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. More...

ChVector	ComputeTangent (const double xi)
	Gets the tangent to the beam axis at the parametric coordinate xi. More...

Public Member Functions inherited from chrono::fea::ChElementBeam
virtual void	EvaluateSectionForceTorque (const double eta, ChVector<> &Fforce, ChVector<> &Mtorque)=0
	Gets the force (traction x, shear y, shear z) and the torque (torsion on x, bending on y, on bending on z) at a section along the beam line, at abscissa 'eta'. More...

virtual void	EvaluateSectionStrain (const double eta, ChVector<> &StrainV)=0
	Gets the axial and bending strain of the ANCF "cable" element.

double	GetMass ()
	The full mass of the beam, (with const. section, density, etc.)

double	GetRestLength ()
	The rest length of the bar.

void	SetRestLength (double ml)
	Set the rest length of the bar (usually this should be automatically done when SetupInitial is called on beams element, given the current state, but one might need to override this, ex for precompressed beams etc).

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

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.

Static Public Attributes
static const int	NP = 3
	number of Gauss quadrature along beam axis

static const int	NT = 2
	number of quadrature points through cross section

static const int	NIP_D0 = NP * NT * NT
	number of Gauss quadrature points excluding the Poisson effect for the Enhanced Continuum Mechanics method

static const int	NIP_Dv
	number of Gauss quadrature points including the Poisson effect for reduced integration along the beam axis for the Enhanced Continuum Mechanics method (Full Gauss quadrature points along the beam axis (xi direction) and 1 point Gauss quadrature in the eta and zeta directions) More...

static const int	NIP
	total number of integration points for the Enhanced Continuum Mechanics method More...

static const int	NSF = 9
	number of shape functions

Additional Inherited Members
Protected Attributes inherited from chrono::fea::ChElementBeam
double	mass

double	length

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

Member Enumeration Documentation

◆ IntFrcMethod

enum chrono::fea::ChElementBeamANCF_3333::IntFrcMethod

strong

Internal force calculation method.

Enumerator
ContInt	"Continuous Integration" style method - Typically fastest for this element
PreInt	"Pre-Integration" style method

Member Function Documentation

◆ ComputeKRMmatricesGlobal()

void chrono::fea::ChElementBeamANCF_3333::ComputeKRMmatricesGlobal	(	ChMatrixRef	H,
		double	Kfactor,
		double	Rfactor = `0`,
		double	Mfactor = `0`
	)

overridevirtual

Set H as a linear combination of M, K, and R.

H = Mfactor * [M] + Kfactor * [K] + Rfactor * [R], where [M] is the mass matrix, [K] is the stiffness matrix, and [R] is the damping matrix.

Implements chrono::fea::ChElementBase.

◆ ComputeNF() [1/2]

void chrono::fea::ChElementBeamANCF_3333::ComputeNF	(	const double	xi,
		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 xi coordinate of the beam line, 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.

For this ANCF element, only the first 6 entries in F are used in the calculation. The first three entries is the applied force in global coordinates and the second 3 entries is the applied moment in global space.

Parameters

xi	parametric coordinate along the beam axis
Qi	Return result of Q = N'*F here
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
state_w	if != 0, update state (speed part) to this, then evaluate

Implements chrono::ChLoadableU.

◆ ComputeNF() [2/2]

void chrono::fea::ChElementBeamANCF_3333::ComputeNF	(	const double	xi,
		const double	eta,
		const double	zeta,
		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 xi,eta,zeta 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.

For this ANCF element, only the first 6 entries in F are used in the calculation. The first three entries is the applied force in global coordinates and the second 3 entries is the applied moment in global space.

Parameters

xi	parametric coordinate in volume
eta	parametric coordinate in volume
zeta	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.

◆ ComputeTangent()

ChVector chrono::fea::ChElementBeamANCF_3333::ComputeTangent ( const double xi )

Gets the tangent to the beam axis at the parametric coordinate xi.

xi = -1 at node A and xi = 1 at node B

◆ EvaluateSectionDisplacement()

virtual void chrono::fea::ChElementBeamANCF_3333::EvaluateSectionDisplacement	(	const double	xi,
		ChVector<> &	u_displ,
		ChVector<> &	u_rotaz
	)

inlineoverridevirtual

Gets the xyz displacement of a point on the beam line, and the rotation RxRyRz of section plane, at abscissa '(xi,0,0)'.

xi = -1 at node A and xi = 1 at node B

Implements chrono::fea::ChElementBeam.

◆ EvaluateSectionFrame()

void chrono::fea::ChElementBeamANCF_3333::EvaluateSectionFrame	(	const double	xi,
		ChVector<> &	point,
		ChQuaternion<> &	rot
	)

overridevirtual

Gets the absolute xyz position of a point on the beam line, and the absolute rotation of section plane, at abscissa '(xi,0,0)'.

xi = -1 at node A and xi = 1 at node B

Implements chrono::fea::ChElementBeam.

◆ GetDensity()

double chrono::fea::ChElementBeamANCF_3333::GetDensity ( )

overridevirtual

This is needed so that it can be accessed by ChLoaderVolumeGravity.

Density is the average mass per unit volume in the reference state of the element.

Implements chrono::ChLoadableUVW.

◆ GetGreenLagrangeStrain()

ChMatrix33 chrono::fea::ChElementBeamANCF_3333::GetGreenLagrangeStrain	(	const double	xi,
		const double	eta,
		const double	zeta
	)

Get the Green-Lagrange strain tensor at the normalized element coordinates (xi, eta, zeta) at the current state of the element.

Normalized element coordinates span from -1 to 1.

◆ GetPK2Stress()

ChMatrix33 chrono::fea::ChElementBeamANCF_3333::GetPK2Stress	(	const double	xi,
		const double	eta,
		const double	zeta
	)

Get the 2nd Piola-Kirchoff stress tensor at the normalized element coordinates (xi, eta, zeta) at the current state of the element.

Normalized element coordinates span from -1 to 1.

◆ GetStateBlock()

void chrono::fea::ChElementBeamANCF_3333::GetStateBlock ( ChVectorDynamic<> & mD )

overridevirtual

Fill the D vector (column matrix) 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. {Pos_a Dv_a Dw_a Pos_b Dv_b Dw_b Pos_c Dv_c Dw_c}

Implements chrono::fea::ChElementBase.

◆ GetVonMissesStress()

double chrono::fea::ChElementBeamANCF_3333::GetVonMissesStress	(	const double	xi,
		const double	eta,
		const double	zeta
	)

Get the von Mises stress value at the normalized element coordinates (xi, eta, zeta) at the current state of the element.

Normalized element coordinates span from -1 to 1.

◆ SetIntFrcCalcMethod()

void chrono::fea::ChElementBeamANCF_3333::SetIntFrcCalcMethod ( IntFrcMethod method )

Set the calculation method to use for the generalized internal force and its Jacobian calculations.

This should be set prior to the start of the simulation since can be a significant amount of pre-calculation overhead required.

Member Data Documentation

◆ NIP

const int chrono::fea::ChElementBeamANCF_3333::NIP

static

Initial value:

=

NIP_D0 + NIP_Dv

total number of integration points for the Enhanced Continuum Mechanics method

◆ NIP_Dv

const int chrono::fea::ChElementBeamANCF_3333::NIP_Dv

static

Initial value:

=

NP

number of Gauss quadrature points including the Poisson effect for reduced integration along the beam axis for the Enhanced Continuum Mechanics method (Full Gauss quadrature points along the beam axis (xi direction) and 1 point Gauss quadrature in the eta and zeta directions)

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

/builds/uwsbel/chrono/src/chrono/fea/ChElementBeamANCF_3333.h
/builds/uwsbel/chrono/src/chrono/fea/ChElementBeamANCF_3333.cpp

Description

Public Types

Public Member Functions

Static Public Attributes

Additional Inherited Members

Member Enumeration Documentation

◆ IntFrcMethod

Member Function Documentation

◆ ComputeKRMmatricesGlobal()

◆ ComputeNF() [1/2]

◆ ComputeNF() [2/2]

◆ ComputeTangent()

◆ EvaluateSectionDisplacement()

◆ EvaluateSectionFrame()

◆ GetDensity()

◆ GetGreenLagrangeStrain()

◆ GetPK2Stress()

◆ GetStateBlock()

◆ GetVonMissesStress()

◆ SetIntFrcCalcMethod()

Member Data Documentation

◆ NIP

◆ NIP_Dv