chrono::fea::ChElementBeamIGA Class Reference

## 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

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

## Public Member Functions

ChElementBeamIGA (const ChElementBeamIGA &)=delete

ChElementBeamIGAoperator= (const ChElementBeamIGA &)=delete

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 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< 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.

Gets the number of DOFs affected by this element (position part)

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, 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.

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

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.

Set if the element forces will include the gyroscopic and centrifugal terms (slower performance, but might be needed esp. More...

## Friends

class ChExtruderBeamIGA

Protected Attributes inherited from chrono::fea::ChElementBeam
double mass

double length

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

## ◆ 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
 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

## ◆ 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

## ◆ 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

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::ChElementBeamIGA::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()

 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, 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.