Description

Isogeometric formulation (IGA) of a Cosserat rod, with large displacements, based on the Geometrically Exact Beam Theory.

User-defined order n (ex: 1=linear 2=quadratic, 3=cubic), where each element is a span of a b-spline, so each element uses n+1 control points, ie. nodes of chrono::fea::ChNodeFEAxyzrot type. As a thick beam, shear effects are possible, v. Timoshenko theory. Reduced integration to correct shear locking (*note, use order 1 for the moment, this must be improved) Initial curved configuration is supported. The section is defined in a modular way, via a chrono::fea::ChBeamSectionCosserat object that is composed via an elastic model, an inertial model, a damping (optional) model, a plastic (optional) model. Some of the ready-to-use implementation of those models allow a very generic beam where the center of mass, center of shear etc. are arbitrarily offset from the beam centerline, thus allowing the simulation of advanced cases like helicopter blades etc.

#include <ChElementBeamIGA.h>

Inheritance diagram for chrono::fea::ChElementBeamIGA:

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Collaboration diagram for chrono::fea::ChElementBeamIGA:

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Public Types
enum	QuadratureType { FULL_OVER, FULL_EXACT, REDUCED, SELECTIVE, CUSTOM1, URI2 }
	For testing purposes:

Public Member Functions
	ChElementBeamIGA (const ChElementBeamIGA &)=delete

ChElementBeamIGA &	operator= (const ChElementBeamIGA &)=delete

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 std::vector< std::shared_ptr< ChNodeFEAxyzrot > > &	GetNodes ()

virtual void	SetNodesCubic (std::shared_ptr< ChNodeFEAxyzrot > nodeA, std::shared_ptr< ChNodeFEAxyzrot > nodeB, std::shared_ptr< ChNodeFEAxyzrot > nodeC, std::shared_ptr< ChNodeFEAxyzrot > nodeD, double knotA1, double knotA2, double knotB1, double knotB2, double knotB3, double knotB4, double knotB5, double knotB6)

virtual void	SetNodesGenericOrder (std::vector< std::shared_ptr< ChNodeFEAxyzrot >> mynodes, std::vector< double > myknots, int myorder)

void	SetIntegrationPoints (int npoints_s, int npoints_b)
	Set the integration points, for shear components and for bending components:

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

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

ChVectorDynamic &	GetKnotSequence ()
	Access the local knot sequence of this element (ex.for diagnostics)

double	GetU1 ()
	Get the parametric coordinate at the beginning of the span.

double	GetU2 ()
	Get the parametric coordinate at the end of the span.

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

std::vector< std::unique_ptr< ChBeamMaterialInternalData > > &	GetPlasticData ()
	Get the plastic data, in a vector with as many elements as Gauss points.

std::vector< ChVector<> > &	GetStressN ()
	Get the stress, as cut-force [N], in a vector with as many elements as Gauss points.

std::vector< ChVector<> > &	GetStressM ()
	Get the stress, as cut-torque [Nm], in a vector with as many elements as Gauss points.

std::vector< ChVector<> > &	GetStrainE ()
	Get the strain (total=elastic+plastic), as deformation (x is axial strain), in a vector with as many elements as Gauss points.

std::vector< ChVector<> > &	GetStrainK ()
	Get the strain (total=elastic+plastic), as curvature (x is torsion), in a vector with as many elements as Gauss points.

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

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	ComputeInternalForces_impl (ChVectorDynamic<> &Fi, ChState &state_x, ChStateDelta &state_w, bool used_for_differentiation=false)

virtual void	ComputeGravityForces (ChVectorDynamic<> &Fg, const ChVector<> &G_acc) override
	Compute gravity forces, grouped in the Fg vector, one node after the other.

virtual void	EvaluateSectionDisplacement (const double eta, 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 abscyssa 'eta'. More...

virtual void	EvaluateSectionPoint (const double eta, ChVector<> &point)
	Gets the absolute xyz position of a point on the beam line, at abscissa 'eta'. More...

virtual void	EvaluateSectionFrame (const double eta, 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 'eta'. More...

virtual void	EvaluateSectionForceTorque (const double eta, ChVector<> &Fforce, ChVector<> &Mtorque) override
	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) override
	Gets the axial and bending strain of the ANCF "cable" element.

virtual void	EleDoIntegration () override
	This is optionally implemented if there is some internal state that requires integration.

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, 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 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, 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 coordinates of the line, 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 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.

Public Member Functions inherited from chrono::fea::ChElementBeam
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	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.

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 QuadratureType	quadrature_type = ChElementBeamIGA::QuadratureType::FULL_EXACT
	For testing purposes:

static double	Delta = 1e-10
	For testing purposes:

static bool	lumped_mass = true
	Set if the element mass matrix is computed in lumped or consistent way.

static bool	add_gyroscopic_terms = true
	Set if the element forces will include the gyroscopic and centrifugal terms (slower performance, but might be needed esp. when center of mass is offset)

Friends
class	ChExtruderBeamIGA

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

double	length

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

Member Function Documentation

◆ ComputeInternalForces()

void chrono::fea::ChElementBeamIGA::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.

◆ ComputeInternalForces_impl()

void chrono::fea::ChElementBeamIGA::ComputeInternalForces_impl	(	ChVectorDynamic<> &	Fi,
		ChState &	state_x,
		ChStateDelta &	state_w,
		bool	used_for_differentiation = `false`
	)

< here return N and dN/du

Parameters

Fi	output vector of internal forces
state_x	state position to evaluate Fi
state_w	state speed to evaluate Fi
used_for_differentiation	used during FD Jacobian evaluation?

◆ ComputeKRMmatricesGlobal()

void chrono::fea::ChElementBeamIGA::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() [1/2]

void chrono::fea::ChElementBeamIGA::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 coordinates of the line, 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.

< h

Parameters

U	eta parametric coordinate in line -1..+1
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 Q
state_w	if != 0, update state (speed part) to this, then evaluate Q

Implements chrono::ChLoadableU.

◆ ComputeNF() [2/2]

void chrono::fea::ChElementBeamIGA::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.

◆ EvaluateSectionDisplacement()

virtual void chrono::fea::ChElementBeamIGA::EvaluateSectionDisplacement	(	const double	eta,
		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 abscyssa 'eta'.

Note, eta=-1 at node1, eta=+1 at node2. Note, 'displ' is the displ.state of 2 nodes, ex. get it as GetStateBlock() Results are not corotated.

Implements chrono::fea::ChElementBeam.

◆ EvaluateSectionForceTorque()

virtual void chrono::fea::ChElementBeamIGA::EvaluateSectionForceTorque	(	const double	eta,
		ChVector<> &	Fforce,
		ChVector<> &	Mtorque
	)

inlineoverridevirtual

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'.

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

Implements chrono::fea::ChElementBeam.

◆ EvaluateSectionFrame()

virtual void chrono::fea::ChElementBeamIGA::EvaluateSectionFrame	(	const double	eta,
		ChVector<> &	point,
		ChQuaternion<> &	rot
	)

inlineoverridevirtual

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

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

< here return in N

Implements chrono::fea::ChElementBeam.

◆ EvaluateSectionPoint()

virtual void chrono::fea::ChElementBeamIGA::EvaluateSectionPoint	(	const double	eta,
		ChVector<> &	point
	)

inlinevirtual

Gets the absolute xyz position of a point on the beam line, at abscissa 'eta'.

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

< here return in N

◆ GetNdofs()

virtual int chrono::fea::ChElementBeamIGA::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::ChElementBeamIGA::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()

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

inlineoverridevirtual

Fills 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->GetNdofs(), it will be resized.

Implements chrono::fea::ChElementBase.

◆ SetSection()

void chrono::fea::ChElementBeamIGA::SetSection ( std::shared_ptr< ChBeamSectionCosserat > my_material )

inline

Set the section & material of beam element .

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

◆ Update()

virtual void chrono::fea::ChElementBeamIGA::Update ( )

inlineoverridevirtual

Update: this is 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 is the proper place.

Reimplemented from chrono::fea::ChElementBase.

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

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

Description

Public Types

Public Member Functions

Static Public Attributes

Friends

Additional Inherited Members

Member Function Documentation

◆ ComputeInternalForces()

◆ ComputeInternalForces_impl()

◆ ComputeKRMmatricesGlobal()

◆ ComputeNF() [1/2]

◆ ComputeNF() [2/2]

◆ EvaluateSectionDisplacement()

◆ EvaluateSectionForceTorque()

◆ EvaluateSectionFrame()

◆ EvaluateSectionPoint()

◆ GetNdofs()

◆ GetNodeNdofs()

◆ GetStateBlock()

◆ SetSection()

◆ Update()