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 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. More...
 
virtual unsigned int GetNodeNumCoordsPosLevel (unsigned int n) override
 Get the number of coordinates from the specified node that are used by this element. More...
 
virtual std::shared_ptr< ChNodeFEAbaseGetNode (unsigned 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 GetFieldDt (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...
 
virtual void ComputeNodalMass () override
 Add contribution of element inertia to total nodal masses.
 
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 ChVector3d &G_acc) override
 Compute gravity forces, grouped in the Fg vector, one node after the other. More...
 
virtual void EvaluateSectionDisplacement (const double eta, ChVector3d &u_displ, ChVector3d &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, ChVector3d &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, ChVector3d &Fforce, ChVector3d &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, ChVector3d &StrainV) override
 Gets the axial and bending strain of the ANCF "cable" element.
 
virtual unsigned int GetLoadableNumCoordsPosLevel () override
 Gets the number of DOFs affected by this element (position part)
 
virtual unsigned int GetLoadableNumCoordsVelLevel () override
 Gets the number of DOFs affected by this element (speed part)
 
virtual void LoadableGetStateBlockPosLevel (int block_offset, ChState &mD) override
 Gets all the DOFs packed in a single vector (position part)
 
virtual void LoadableGetStateBlockVelLevel (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 unsigned int GetNumFieldCoords () 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 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 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
ChKRMBlockKstiffness ()
 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 ComputeMmatrixGlobal (ChMatrixRef M) override
 Calculate the mass matrix, expressed in global reference. 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 unsigned int GetNumCoordsPosLevelActive ()
 Get the actual number of active degrees of freedom. More...
 
virtual unsigned int GetNodeNumCoordsPosLevelActive (unsigned int n)
 Get the actual number of active coordinates from the specified node that are used by this element. More...
 
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
ChKRMBlock 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().

◆ ComputeGravityForces()

void chrono::fea::ChElementBeamEuler::ComputeGravityForces ( ChVectorDynamic<> &  Fg,
const ChVector3d G_acc 
)
overridevirtual

Compute gravity forces, grouped in the Fg vector, one node after the other.

TODO for the lumped mass matrix case, the mM * mG product can be unrolled into few multiplications as mM mostly zero, and same for mG

Reimplemented from chrono::fea::ChElementGeneric.

◆ 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
Uparametric coordinate in line
QiReturn result of Q = N'*F here
detJReturn det[J] here
FInput F vector, size is =n. field coords.
state_xif != 0, update state (pos. part) to this, then evaluate Q
state_wif != 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
Uparametric coordinate in volume
Vparametric coordinate in volume
Wparametric coordinate in volume
QiReturn result of N'*F here, maybe with offset block_offset
detJReturn det[J] here
FInput F vector, size is = n.field coords.
state_xif != 0, update state (pos. part) to this, then evaluate Q
state_wif != 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,
ChVector3d u_displ,
ChVector3d 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,
ChVector3d Fforce,
ChVector3d 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,
ChVector3d 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.

◆ GetFieldDt()

void chrono::fea::ChElementBeamEuler::GetFieldDt ( 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->GetNumCoordsPosLevel(), 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}

◆ GetNodeNumCoordsPosLevel()

virtual unsigned int chrono::fea::ChElementBeamEuler::GetNodeNumCoordsPosLevel ( unsigned 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 GetNode(n)->GetNumCoordsVelLevel().

Implements chrono::fea::ChElementBase.

◆ GetNumCoordsPosLevel()

virtual unsigned int chrono::fea::ChElementBeamEuler::GetNumCoordsPosLevel ( )
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.

◆ 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->GetNumCoordsPosLevel(), 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