Description

Simple beam element with two nodes and Euler-Bernoulli formulation.

For this 'basic' implementation, constant section and constant material are assumed.

Further information in the white paper PDF

Note that there are also ChElementCableANCF if no torsional effects are needed, as in cables.

#include <ChElementBeamEuler.h>

Inheritance diagram for chrono::fea::ChElementBeamEuler:

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Collaboration diagram for chrono::fea::ChElementBeamEuler:

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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...

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

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

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

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

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

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

void	SetNodeAreferenceRot (ChQuaternion<> mrot)
	Set the reference rotation of nodeA respect to the element rotation.

ChQuaternion	GetNodeAreferenceRot ()

void	SetNodeBreferenceRot (ChQuaternion<> mrot)
	Set the reference rotation of nodeB respect to the element rotation.

ChQuaternion	GetNodeBreferenceRot ()

ChQuaternion	GetAbsoluteRotation ()
	Get the absolute rotation of element in space This is not the same of Rotation() , that expresses the accumulated rotation from starting point.

ChQuaternion	GetRefRotation ()
	Get the original reference rotation of element in space.

void	SetDisableCorotate (bool md)
	Set this as true to have the beam behave like a non-corotated beam hence do not update the corotated reference. More...

void	SetForceSymmetricStiffness (bool md)
	Set this as true to force the tangent stiffness matrix to be inexact, but symmetric. More...

void	SetUseGeometricStiffness (bool md)
	Set this as false to disable the contribution of geometric stiffness to the total tangent stiffness. More...

void	ShapeFunctions (ShapeVector &N, double eta)
	Fills the N matrix (compressed! single row, 12 columns) with the values of shape functions at abscissa 'eta'. More...

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

virtual void	UpdateRotation () override
	Compute large rotation of element for corotational approach The reference frame of this Euler-Bernoulli beam has X aligned to two nodes and Y parallel to Y of 1st node.

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...

void	GetField_dt (ChVectorDynamic<> &mD_dt)
	Fills the Ddt vector with the current time derivatives of field values at the nodes of the element, with proper ordering. More...

void	ComputeStiffnessMatrix ()
	Computes the local (material) stiffness matrix of the element: K = integral( [B]' * [D] * [B] ), Note: in this 'basic' implementation, constant section and constant material are assumed, so the explicit result of quadrature is used. More...

void	ComputeGeometricStiffnessMatrix ()
	Computes the local geometric stiffness Kg of the element. 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 (e.g. More...

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	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 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, 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 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.

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.

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.

Friends
class	ChExtruderBeamEuler

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

double	length

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

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

Member Function Documentation

◆ ComputeGeometricStiffnessMatrix()

void chrono::fea::ChElementBeamEuler::ComputeGeometricStiffnessMatrix ( )

Computes the local geometric stiffness Kg of the element.

Note: this->Kg will be set as the geometric stiffness EXCLUDING the multiplication by the P pull force, in fact P multiplication happens in all terms, thus this allows making the Kg as a constant matrix that is computed only at the beginning, and later it is multiplied by P all times the real Kg is needed. If you later change some material property, call this or InitialSetup().

◆ ComputeInternalForces()

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

overridevirtual

Computes the internal forces (e.g.

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::ChElementBeamEuler::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::ChElementBeamEuler::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, 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	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::ChElementBeamEuler::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::ChElementBeamEuler::ComputeStiffnessMatrix ( )

Computes the local (material) stiffness matrix of the element: K = integral( [B]' * [D] * [B] ), Note: in this 'basic' implementation, constant section and constant material are assumed, so the explicit result of quadrature is used.

Also, this local material stiffness matrix is constant, computed only at the beginning for performance reasons; if you later change some material property, call this or InitialSetup().

◆ EvaluateSectionDisplacement()

void chrono::fea::ChElementBeamEuler::EvaluateSectionDisplacement	(	const double	eta,
		ChVector<> &	u_displ,
		ChVector<> &	u_rotaz
	)

overridevirtual

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. Results are not corotated.

Implements chrono::fea::ChElementBeam.

◆ EvaluateSectionForceTorque()

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

overridevirtual

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. Results are not corotated, and are expressed in the reference system of beam.

Implements chrono::fea::ChElementBeam.

◆ EvaluateSectionFrame()

void chrono::fea::ChElementBeamEuler::EvaluateSectionFrame	(	const double	eta,
		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 'eta'.

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

Implements chrono::fea::ChElementBeam.

◆ GetField_dt()

void chrono::fea::ChElementBeamEuler::GetField_dt ( ChVectorDynamic<> & mD_dt )

Fills the Ddt vector with the current time derivatives of 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! Give that this element includes rotations at nodes, this gives: {v_a v_a v_a wx_a wy_a wz_a v_b v_b v_b wx_b wy_b wz_b}

◆ GetNdofs()

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

overridevirtual

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. For corotational elements, field is assumed in local reference! Given that this element includes rotations at nodes, this gives: {x_a y_a z_a Rx_a Ry_a Rz_a x_b y_b z_b Rx_b Ry_b Rz_b}

Implements chrono::fea::ChElementBase.

◆ SetDisableCorotate()

void chrono::fea::ChElementBeamEuler::SetDisableCorotate ( bool md )

inline

Set this as true to have the beam behave like a non-corotated beam hence do not update the corotated reference.

Just for benchmarks!

◆ SetForceSymmetricStiffness()

void chrono::fea::ChElementBeamEuler::SetForceSymmetricStiffness ( bool md )

inline

Set this as true to force the tangent stiffness matrix to be inexact, but symmetric.

This allows the use of faster solvers. For systems close to the equilibrium, the tangent stiffness would be symmetric anyway.

◆ SetSection()

void chrono::fea::ChElementBeamEuler::SetSection ( std::shared_ptr< ChBeamSectionEuler > my_material )

inline

Set the section & material of beam element .

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

◆ SetUseGeometricStiffness()

void chrono::fea::ChElementBeamEuler::SetUseGeometricStiffness ( bool md )

inline

Set this as false to disable the contribution of geometric stiffness to the total tangent stiffness.

By default it is on.

◆ ShapeFunctions()

void chrono::fea::ChElementBeamEuler::ShapeFunctions	(	ShapeVector &	N,
		double	eta
	)

Fills the N matrix (compressed! single row, 12 columns) with the values of shape functions at abscissa 'eta'.

Note, eta=-1 at node1, eta=+1 at node2. Given u = 12-d state block {u1,r1,u2,r2}' , d = 6-d field {u,r}, one has f(eta) = [S(eta)]*u where one fills the sparse [S] matrix with the N shape functions in this pattern: | 0 . . . . . 3 . . . . . | | . 1 . . . 2 . 4 . . . 5 | [S] =| . . 1 . -2 . . . 4 . -5 . | | . . . 0 . . . . . 3 . . | | . . -6 . 8 . . . -7 . 9 . | | . 6 . . . 8 . 7 . . . 9 |

◆ Update()

void chrono::fea::ChElementBeamEuler::Update ( )

overridevirtual

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

Description

Public Types

Public Member Functions

Friends

Additional Inherited Members

Member Function Documentation

◆ ComputeGeometricStiffnessMatrix()

◆ ComputeInternalForces()

◆ ComputeKRMmatricesGlobal()

◆ ComputeNF() [1/2]

◆ ComputeNF() [2/2]

◆ ComputeStiffnessMatrix()

◆ EvaluateSectionDisplacement()

◆ EvaluateSectionForceTorque()

◆ EvaluateSectionFrame()

◆ GetField_dt()

◆ GetNdofs()

◆ GetNodeNdofs()

◆ GetStateBlock()

◆ SetDisableCorotate()

◆ SetForceSymmetricStiffness()

◆ SetSection()

◆ SetUseGeometricStiffness()

◆ ShapeFunctions()

◆ Update()