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:
Collaboration diagram for chrono::fea::ChElementBeamIGA:

Public Types

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

Public Member Functions

 ChElementBeamIGA (const ChElementBeamIGA &)=delete
 
ChElementBeamIGAoperator= (const ChElementBeamIGA &)=delete
 
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 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< ChBeamSectionCosseratGetSection ()
 Get the section & material of the element.
 
ChVectorDynamicGetKnotSequence ()
 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, 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< ChVector3d > & GetStressN ()
 Get the stress, as cut-force [N], in a vector with as many elements as Gauss points.
 
std::vector< ChVector3d > & GetStressM ()
 Get the stress, as cut-torque [Nm], in a vector with as many elements as Gauss points.
 
std::vector< ChVector3d > & 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< ChVector3d > & 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 ComputeNodalMass () override
 Add contribution of element inertia to total nodal masses.
 
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 ChVector3d &G_acc) override
 Compute gravity forces, grouped in the Fg vector, one node after the other.
 
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 EvaluateSectionPoint (const double eta, ChVector3d &point)
 Gets the absolute xyz position of a point on the beam line, at abscissa '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 void EleDoIntegration () override
 This is optionally implemented if there is some internal state that requires integration.
 
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, 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...
 
- 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. More...
 

Friends

class ChExtruderBeamIGA
 

Additional Inherited Members

- 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::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

< here return N and dN/du

Parameters
Fioutput vector of internal forces
state_xstate position to evaluate Fi
state_wstate speed to evaluate Fi
used_for_differentiationused 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
Ueta parametric coordinate in line -1..+1
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::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
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.

◆ EvaluateSectionDisplacement()

virtual void chrono::fea::ChElementBeamIGA::EvaluateSectionDisplacement ( const double  eta,
ChVector3d u_displ,
ChVector3d 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,
ChVector3d Fforce,
ChVector3d 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,
ChVector3d 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.

Implements chrono::fea::ChElementBeam.

◆ EvaluateSectionPoint()

virtual void chrono::fea::ChElementBeamIGA::EvaluateSectionPoint ( const double  eta,
ChVector3d 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

◆ GetNodeNumCoordsPosLevel()

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

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->GetNumCoordsPosLevel(), 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, 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.

Member Data Documentation

◆ add_gyroscopic_terms

bool chrono::fea::ChElementBeamIGA::add_gyroscopic_terms = true
static

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)


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