chrono::fea::ChElementBeamEuler Class Reference

## 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:
Collaboration diagram for chrono::fea::ChElementBeamEuler:

## Public Types

using ShapeVector = ChMatrixNM< double, 1, 10 >

## 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. More...

virtual int GetNodeNdofs (int n) override
Get the number of coordinates from the specified node that are used by this element. More...

virtual std::shared_ptr< ChNodeFEAbaseGetNodeN (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< ChBeamSectionEulerGetSection ()
Get the section & material of the element.

std::shared_ptr< ChNodeFEAxyzrotGetNodeA ()
Get the first node (beginning)

std::shared_ptr< ChNodeFEAxyzrotGetNodeB ()
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, 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
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, 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
ChKblockGenericKstiffness ()
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 EleIntLoadResidual_F_gravity (ChVectorDynamic<> &R, const ChVector<> &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 ComputeMmatrixGlobal (ChMatrixRef M) override
Calculate the mass matrix, expressed in global reference. More...

virtual void InjectKRMmatrices (ChSystemDescriptor &descriptor) 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
Add 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
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 int GetNdofs_active ()
Get the actual number of active degrees of freedom. More...

virtual int GetNodeNdofs_active (int n)
Get the actual number of active coordinates from the specified node that are used by this element. More...

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
ChMatrix33Rotation ()
Access the cumulative rotation matrix of the element. More...

## Public Attributes

bool use_numerical_diff_for_KR = false

## 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

## ◆ 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

Get the number of coordinates in the field used by the referenced nodes.

This is for example the size (number 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 specified node that are used by this element.

Note that this may be different from the value returned by GetNodeN(n)->GetNdofW().

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