Description

Simple ANCF beam element with two nodes and gradient-deficient formulation.

For this element, constant section and constant material are assumed along the beam coordinate. Torsional stiffness is impossible because of the formulation. Based on the formulation in: "Analysis of Thin Beams and Cables Using the Absolute Nodal Coordinate Formulation", J. Gerstmayr, A. Shabana, Nonlinear Dynamics (2006) 45: 109-130, DOI: 10.1007/s11071-006-1856-1

#include <ChElementCableANCF.h>

Inheritance diagram for chrono::fea::ChElementCableANCF:

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Collaboration diagram for chrono::fea::ChElementCableANCF:

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

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

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

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

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

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

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

virtual void	SetNodes (std::shared_ptr< ChNodeFEAxyzD > nodeA, std::shared_ptr< ChNodeFEAxyzD > nodeB)

void	SetSection (std::shared_ptr< ChBeamSectionCableANCF > section)
	Set the section & material of beam element. More...

std::shared_ptr< ChBeamSectionCableANCF >	GetSection ()
	Get the section & material of the element.

std::shared_ptr< ChNodeFEAxyzD >	GetNodeA ()
	Get the first node (beginning).

std::shared_ptr< ChNodeFEAxyzD >	GetNodeB ()
	Get the second node (ending).

double	GetCurrLength ()
	Get element length.

virtual void	ShapeFunctions (ShapeVector &N, double xi)
	Fill the N shape function matrix with the values of shape functions at abscissa 'xi'. More...

virtual void	ShapeFunctionsDerivatives (ShapeVector &Nd, double xi)
	Fill the N shape function derivative matrix with the values of shape function derivatives at abscissa 'xi'. More...

virtual void	ShapeFunctionsDerivatives2 (ShapeVector &Ndd, double xi)
	Fill the N shape function derivative matrix with the values of shape function 2nd derivatives at abscissa 'xi'. More...

virtual void	Update () override
	Update, called at least at each time step. More...

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

virtual void	ComputeInternalJacobians (double Kfactor, double Rfactor)
	Compute the stiffness matrix of the element. More...

virtual void	ComputeMassMatrix ()
	Compute the mass matrix of the element. More...

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

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

virtual void	ComputeInternalForces (ChVectorDynamic<> &Fi) override
	Compute the internal forces and set values in the Fi vector. More...

virtual void	ComputeGravityForces (ChVectorDynamic<> &Fg, const ChVector3d &G_acc) override
	Compute the generalized force vector due to gravity using the efficient ANCF specific method.

virtual void	EvaluateSectionDisplacement (const double eta, ChVector3d &displ, ChVector3d &rot) override
	Evaluate the xyz displacement of a point on the beam line and the rotation RxRyRz of section plane. More...

virtual void	EvaluateSectionVelocity (const double eta, ChVector3d &lin_vel, ChVector3d &ang_vel) override
	Evaluate the linear and angular velocity of a point on the beam line. More...

virtual void	EvaluateSectionFrame (const double eta, ChVector3d &point, ChQuaternion<> &rot) override
	Evaluate the absolute xyz position of a point on the beam line and the absolute rotation of section plane. More...

virtual void	EvaluateSectionForceTorque (const double eta, ChVector3d &force, ChVector3d &torque) override
	Evaluate 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. More...

virtual void	EvaluateSectionStrain (const double eta, ChVector3d &strain) override
	Evaluate the axial and bending strain of the ANCF element torque (torsion on x, bending on y, on bending on z) at a section along the beam line. More...

void	SetAlphaDamp (double a)
	Set structural damping.

virtual unsigned int	GetLoadableNumCoordsPosLevel () override
	Get the number of DOFs affected by this element (position part).

virtual unsigned int	GetLoadableNumCoordsVelLevel () override
	Get the number of DOFs affected by this element (speed part).

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

virtual void	LoadableGetStateBlockVelLevel (int block_offset, ChStateDelta &mD) override
	Get 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 unsigned int	GetNumFieldCoords () override
	Return the number of coordinates in the interpolated field.

virtual unsigned int	GetNumSubBlocks () override
	Get the number of DOFs sub-blocks.

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

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

virtual bool	IsSubBlockActive (unsigned 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 vector of variables.

virtual void	ComputeNF (const double U, 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 coordinates of the surface, each ranging in -1..+1. More...

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. More...

virtual double	GetDensity () override
	Return the material density for this element.

Public Member Functions inherited from chrono::fea::ChElementBeam
double	GetMass () const
	Return the full mass of the beam element.

double	GetRestLength () const
	Return the rest length of the beam element.

void	SetRestLength (double l)
	Set the rest length of the bar. More...

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

virtual void	EleIntLoadResidual_F (ChVectorDynamic<> &R, const double c) override
	Add the internal forces (pasted at global nodes offsets) into a global vector R, multiplied by a scaling factor c, as R += forces * c This default implementation is SLIGHTLY INEFFICIENT.

virtual void	EleIntLoadResidual_Mv (ChVectorDynamic<> &R, const ChVectorDynamic<> &w, const double c) override
	Add the product of element mass M by a vector w (pasted at global nodes offsets) into a global vector R, multiplied by a scaling factor c, as R += M * w * c This default implementation is VERY INEFFICIENT.

virtual void	EleIntLoadLumpedMass_Md (ChVectorDynamic<> &Md, double &error, const double c) override
	Adds the lumped mass to a Md vector, representing a mass diagonal matrix. More...

virtual void	EleIntLoadResidual_F_gravity (ChVectorDynamic<> &R, const ChVector3d &G_acc, const double c) override
	Add the contribution of gravity loads, multiplied by a scaling factor c, as: R += M * g * c This default implementation is VERY INEFFICIENT. More...

virtual void	InjectKRMMatrices (ChSystemDescriptor &descriptor) override
	Register with the given system descriptor any ChKRMBlock objects associated with this item.

virtual void	LoadKRMMatrices (double Kfactor, double Rfactor, double Mfactor) override
	Compute and load current stiffnes (K), damping (R), and mass (M) matrices in encapsulated ChKRMBlock objects. More...

virtual void	VariablesFbLoadInternalForces (double factor=1.) override
	Add the internal forces, expressed as nodal forces, into the encapsulated ChVariables.

virtual void	VariablesFbIncrementMq () override
	Add M*q (internal masses multiplied current 'qb').

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. More...

virtual void	ElementUpdateEndStep (double time)
	For a given finite element, computes updates at the end of a time step. More...

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.

Public Attributes
bool	m_use_damping
	Boolean indicating whether internal damping is added.

double	m_alpha
	Scaling factor for internal damping.

Additional Inherited Members
Protected Attributes inherited from chrono::fea::ChElementANCF
int	m_element_dof
	actual number of degrees of freedom for the element

bool	m_full_dof
	true if all node variables are active (not fixed)

ChArray< int >	m_mapping_dof
	indices of active DOFs (set only is some are fixed)

Protected Attributes inherited from chrono::fea::ChElementBeam
double	mass

double	length

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

Member Function Documentation

◆ ComputeInternalForces()

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

overridevirtual

Compute the internal forces and set values in the Fi vector.

Note that the actual position of nodes is not in relaxed reference position.

Implements chrono::fea::ChElementBase.

◆ ComputeInternalJacobians()

void chrono::fea::ChElementCableANCF::ComputeInternalJacobians	(	double	Kfactor,
		double	Rfactor
	)

virtual

Compute the stiffness matrix of the element.

K = integral( .... ), Note: in this 'basic' implementation, constant section and constant material are assumed.

◆ ComputeKRMmatricesGlobal()

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

overridevirtual

Set 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.

◆ ComputeMassMatrix()

void chrono::fea::ChElementCableANCF::ComputeMassMatrix ( )

virtual

Compute the mass matrix of the element.

Note: in this 'basic' implementation, constant section and constant material are assumed.

◆ ComputeNF() [1/2]

void chrono::fea::ChElementCableANCF::ComputeNF	(	const double	U,
		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 coordinates of the surface, 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 line
Qi	result of Q = N'*F
detJ	Jacobian determinant
F	input F vector, size equal to number of field coordinates
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::ChLoadableU.

◆ ComputeNF() [2/2]

void chrono::fea::ChElementCableANCF::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	result of N'*F, maybe with offset block_offset
detJ	Jacobian determinant
F	input F vector, size equal to number of field coordinates
state_x	if != 0, update state (position part) to this, then evaluate Q
state_w	if != 0, update state (speed part) to this, then evaluate Q

Implements chrono::ChLoadableUVW.

◆ EvaluateSectionDisplacement()

void chrono::fea::ChElementCableANCF::EvaluateSectionDisplacement	(	const double	eta,
		ChVector3d &	displ,
		ChVector3d &	rot
	)

overridevirtual

Evaluate the xyz displacement of a point on the beam line and the rotation RxRyRz of section plane.

Notes:

eta=-1 at node1, eta=+1 at node2.
'displ' is the displacement state of 2 nodes (for example, obtained via GetStateBlock()). Results are not corotated.

Implements chrono::fea::ChElementBeam.

◆ EvaluateSectionForceTorque()

void chrono::fea::ChElementCableANCF::EvaluateSectionForceTorque	(	const double	eta,
		ChVector3d &	force,
		ChVector3d &	torque
	)

overridevirtual

Evaluate 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.

Results are not corotated, and are expressed in the reference system of beam. This is not mandatory for the element to work, but it can be useful for plotting, showing results, etc. Note that eta=-1 at node1, eta=+1 at node2.

Implements chrono::fea::ChElementBeam.

◆ EvaluateSectionFrame()

void chrono::fea::ChElementCableANCF::EvaluateSectionFrame	(	const double	eta,
		ChVector3d &	point,
		ChQuaternion<> &	rot
	)

overridevirtual

Evaluate the absolute xyz position of a point on the beam line and the absolute rotation of section plane.

Results are corotated (expressed in world reference). Notes that eta=-1 at node1, eta=+1 at node2.

Implements chrono::fea::ChElementBeam.

◆ EvaluateSectionStrain()

void chrono::fea::ChElementCableANCF::EvaluateSectionStrain	(	const double	eta,
		ChVector3d &	strain
	)

overridevirtual

Evaluate the axial and bending strain of the ANCF element torque (torsion on x, bending on y, on bending on z) at a section along the beam line.

Results are not corotated, and are expressed in the reference system of beam. This is not mandatory for the element to work, but it can be useful for plotting, showing results, etc. Note that eta=-1 at node1, eta=+1 at node2.

Implements chrono::fea::ChElementBeam.

◆ EvaluateSectionVelocity()

void chrono::fea::ChElementCableANCF::EvaluateSectionVelocity	(	const double	eta,
		ChVector3d &	lin_vel,
		ChVector3d &	ang_vel
	)

overridevirtual

Evaluate the linear and angular velocity of a point on the beam line.

Note that eta=-1 at node1, eta=+1 at node2.

Reimplemented from chrono::fea::ChElementBeam.

◆ GetStateBlock()

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

overridevirtual

Fill the D vector with the current field values at the nodes of the element, with proper ordering.

If the D vector has not the size of this->GetNumCoordsPosLevel(), it will be resized. {x_a y_a z_a Dx_a Dx_a Dx_a x_b y_b z_b Dx_b Dy_b Dz_b}

Implements chrono::fea::ChElementBase.

◆ SetSection()

void chrono::fea::ChElementCableANCF::SetSection ( std::shared_ptr< ChBeamSectionCableANCF > section )

inline

Set the section & material of beam element.

It is a shared property, so it can be shared between other beams.

◆ ShapeFunctions()

void chrono::fea::ChElementCableANCF::ShapeFunctions	(	ShapeVector &	N,
		double	xi
	)

virtual

Fill the N shape function matrix with the values of shape functions at abscissa 'xi'.

Note, xi=0 at node1, xi=+1 at node2. N should be a 3x12 parse matrix, N = [s1*eye(3) s2*eye(3) s3*eye(3) s4*eye(3)], but is stored here in a compressed form: only the s1 s2 s3 s4 values in a 4x1 column vector.

◆ ShapeFunctionsDerivatives()

void chrono::fea::ChElementCableANCF::ShapeFunctionsDerivatives	(	ShapeVector &	Nd,
		double	xi
	)

virtual

Fill the N shape function derivative matrix with the values of shape function derivatives at abscissa 'xi'.

Note, xi=0 at node1, xi=+1 at node2. In a compressed form, only four values are stored in a 4x1 column vector.

◆ ShapeFunctionsDerivatives2()

void chrono::fea::ChElementCableANCF::ShapeFunctionsDerivatives2	(	ShapeVector &	Ndd,
		double	xi
	)

virtual

Fill the N shape function derivative matrix with the values of shape function 2nd derivatives at abscissa 'xi'.

Note, xi=0 at node1, xi=+1 at node2. In a compressed form, only four values are stored in a 4x1 column vector.

◆ Update()

void chrono::fea::ChElementCableANCF::Update ( )

overridevirtual

Update, called at least at each time step.

If the element has to keep updated some auxiliary data, such as the rotation matrices for corotational approach, this should be implemented in this function.

Reimplemented from chrono::fea::ChElementBase.

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

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

Description

Public Types

Public Member Functions

Public Attributes

Additional Inherited Members

Member Function Documentation

◆ ComputeInternalForces()

◆ ComputeInternalJacobians()

◆ ComputeKRMmatricesGlobal()

◆ ComputeMassMatrix()

◆ ComputeNF() [1/2]

◆ ComputeNF() [2/2]

◆ EvaluateSectionDisplacement()

◆ EvaluateSectionForceTorque()

◆ EvaluateSectionFrame()

◆ EvaluateSectionStrain()

◆ EvaluateSectionVelocity()

◆ GetStateBlock()

◆ SetSection()

◆ ShapeFunctions()

◆ ShapeFunctionsDerivatives()

◆ ShapeFunctionsDerivatives2()

◆ Update()