chrono::fea::ChElementShellANCF Class Reference

## Description

ANCF laminated shell element with four nodes.

This class implements composite material elastic force formulations.

The node numbering is in ccw fashion as in the following scheme: v ^ D o--—+--—o C | | | –+--—+--—+-> u | | | A o--—+--—o B

#include <ChElementShellANCF.h>

Inheritance diagram for chrono::fea::ChElementShellANCF:
Collaboration diagram for chrono::fea::ChElementShellANCF:

## Classes

class  Layer
Definition of a layer. More...

## 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.

virtual int GetNodeNdofs (int n) override
Get the number of coordinates from the n-th node used by this element.

void SetNodes (std::shared_ptr< ChNodeFEAxyzD > nodeA, std::shared_ptr< ChNodeFEAxyzD > nodeB, std::shared_ptr< ChNodeFEAxyzD > nodeC, std::shared_ptr< ChNodeFEAxyzD > nodeD)
Specify the nodes of this element.

void SetDimensions (double lenX, double lenY)
Specify the element dimensions.

virtual std::shared_ptr< ChNodeFEAbaseGetNodeN (int n) override
Access the n-th node of this element.

std::shared_ptr< ChNodeFEAxyzDGetNodeA () const
Get a handle to the first node of this element.

std::shared_ptr< ChNodeFEAxyzDGetNodeB () const
Get a handle to the second node of this element.

std::shared_ptr< ChNodeFEAxyzDGetNodeC () const
Get a handle to the third node of this element.

std::shared_ptr< ChNodeFEAxyzDGetNodeD () const
Get a handle to the fourth node of this element.

void AddLayer (double thickness, double theta, std::shared_ptr< ChMaterialShellANCF > material)

size_t GetNumLayers () const
Get the number of layers.

const LayerGetLayer (size_t i) const
Get a handle to the specified layer.

void SetGravityOn (bool val)
Turn gravity on/off.

Set the structural damping.

double GetLengthX () const
Get the element length in the X direction.

double GetLengthY () const
Get the element length in the Y direction.

double GetThickness ()
Get the total thickness of the shell element.

void ShapeFunctions (ChMatrix<> &N, double x, double y, double z)
Fills the N shape function matrix. More...

void ShapeFunctionsDerivativeX (ChMatrix<> &Nx, double x, double y, double z)
Fills the Nx shape function derivative matrix with respect to X. More...

void ShapeFunctionsDerivativeY (ChMatrix<> &Ny, double x, double y, double z)
Fills the Ny shape function derivative matrix with respect to Y. More...

void ShapeFunctionsDerivativeZ (ChMatrix<> &Nz, double x, double y, double z)
Fills the Nz shape function derivative matrix with respect to Z. More...

ChVector EvaluateSectionStrains ()
Return a vector with three strain components. More...

virtual void GetStateBlock (ChMatrixDynamic<> &mD) override
Fills the D vector (column matrix) with the current field values at the nodes of the element, with proper ordering. More...

virtual void ComputeKRMmatricesGlobal (ChMatrix<> &H, double Kfactor, double Rfactor=0, double Mfactor=0) override
Sets H as the stiffness matrix K, scaled by Kfactor. More...

virtual void ComputeMmatrixGlobal (ChMatrix<> &M) override
Returns the global mass matrix. More...

virtual void ComputeNodalMass () override
Add contribution of element inertia to total nodal masses. More...

virtual void ComputeInternalForces (ChMatrixDynamic<> &Fi) override
Computes the internal forces. More...

virtual void SetupInitial (ChSystem *system) override
Initial setup. More...

virtual void Update () override
Update the state of this element.

virtual void EvaluateSectionDisplacement (const double u, const double v, ChVector<> &u_displ, ChVector<> &u_rotaz) override
Gets the xyz displacement of a point on the shell, and the rotation RxRyRz of section reference, at parametric coordinates 'u' and 'v'. More...

virtual void EvaluateSectionFrame (const double u, const double v, ChVector<> &point, ChQuaternion<> &rot) override
Gets the absolute xyz position of a point on the shell, and the absolute rotation of section reference, at parametric coordinates 'u' and 'v'. More...

virtual void EvaluateSectionPoint (const double u, const double v, ChVector<> &point) override
Gets the absolute xyz position of a point on the shell, at parametric coordinates 'u' and 'v'. More...

void ComputeInternalJacobians (double Kfactor, double Rfactor)
Compute Jacobians of the internal forces. More...

void ComputeMassMatrix ()
Compute the mass matrix of the element. More...

void ComputeGravityForce (const ChVector<> &g_acc)
Compute the gravitational forces.

void ShapeFunctionANSbilinearShell (ChMatrixNM< double, 1, 4 > &S_ANS, double x, double y)

void CalcStrainANSbilinearShell ()

void Basis_M (ChMatrixNM< double, 6, 5 > &M, double x, double y, double z)

double Calc_detJ0 (double x, double y, double z)

double Calc_detJ0 (double x, double y, double z, ChMatrixNM< double, 1, 8 > &Nx, ChMatrixNM< double, 1, 8 > &Ny, ChMatrixNM< double, 1, 8 > &Nz, ChMatrixNM< double, 1, 3 > &Nx_d0, ChMatrixNM< double, 1, 3 > &Ny_d0, ChMatrixNM< double, 1, 3 > &Nz_d0)

void CalcCoordMatrix (ChMatrixNM< double, 8, 3 > &d)

void CalcCoordDerivMatrix (ChMatrixNM< double, 24, 1 > &dt)

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

Gets the number of DOFs affected by this element (velocity 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 (velocity 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. More...

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 EvaluateSectionVelNorm (double U, double V, ChVector<> &Result) override
Virtual method to plot velocity field distribution.

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, const double V, 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 coordinates of the surface, 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. More...

virtual ChVector ComputeNormal (const double U, const double V) override
Gets the normal to the surface at the parametric coordinate U,V. More...

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
(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 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 EleDoIntegration ()
This is optionally implemented if there is some internal state that requires integration. More...

Public Member Functions inherited from chrono::ChLoadableUV
virtual bool IsTriangleIntegrationNeeded ()
If true, use quadrature over u,v in [0..1] range as triangle area coords, with w=1-u-v otherwise use quadrature over u,v in [-1..+1] as rectangular isoparametric coords. 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 quadrature over u,v,w in [-1..+1] as box isoparametric coords. More...

## Static Public Member Functions

static void Inverse55_Numerical (ChMatrixNM< double, 5, 5 > &a, int n)
Numerical inverse for a 5x5 matrix.

static void Inverse55_Analytical (ChMatrixNM< double, 5, 5 > &A, ChMatrixNM< double, 5, 5 > &B)
Analytical inverse for a 5x5 matrix.

## Friends

class MyMass

class MyGravity

class MyForce

class MyJacobian

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

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

## Member Function Documentation

 void chrono::fea::ChElementShellANCF::AddLayer ( double thickness, double theta, std::shared_ptr< ChMaterialShellANCF > material )

Parameters
 thickness layer thickness theta fiber angle (radians) material layer material
 void chrono::fea::ChElementShellANCF::ComputeInternalForces ( ChMatrixDynamic<> & 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.

 void chrono::fea::ChElementShellANCF::ComputeInternalJacobians ( double Kfactor, double Rfactor )

Compute Jacobians of the internal forces.

This function calculates a linear combination of the stiffness (K) and damping (R) matrices, J = Kfactor * K + Rfactor * R for given coefficients Kfactor and Rfactor. This Jacobian will be further combined with the global mass matrix M and included in the global stiffness matrix H in the function ComputeKRMmatricesGlobal().

 void chrono::fea::ChElementShellANCF::ComputeKRMmatricesGlobal ( ChMatrix<> & H, double Kfactor, double Rfactor = 0, double Mfactor = 0 )
overridevirtual

Sets H as the stiffness matrix K, scaled by Kfactor.

Optionally, also superimposes global damping matrix R, scaled by Rfactor, and mass matrix M, scaled by Mfactor. Matrices are expressed in global reference. Corotational elements can take the local Kl & Rl matrices and rotate them. CHLDREN CLASSES MUST IMPLEMENT THIS!!!

Implements chrono::fea::ChElementBase.

 void chrono::fea::ChElementShellANCF::ComputeMassMatrix ( )

Compute the mass matrix of the element.

Note: in this 'basic' implementation, constant section and constant material are assumed

 void chrono::fea::ChElementShellANCF::ComputeMmatrixGlobal ( ChMatrix<> & M )
overridevirtual

Returns the global mass matrix.

This is the default implementation, POTENTIALLY VERY INEFFICIENT. Children classes may need to override this with a more efficient version.

Reimplemented from chrono::fea::ChElementGeneric.

 void chrono::fea::ChElementShellANCF::ComputeNF ( const double U, const double V, 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 coordinates of the surface, 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 surface V parametric coordinate in surface 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

 void chrono::fea::ChElementShellANCF::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

 void chrono::fea::ChElementShellANCF::ComputeNodalMass ( )
overridevirtual

Add contribution of element inertia to total nodal masses.

This class computes and adds corresponding masses to ElementGeneric member m_TotalMass.

Reimplemented from chrono::fea::ChElementBase.

 ChVector chrono::fea::ChElementShellANCF::ComputeNormal ( const double U, const double V )
overridevirtual

Gets the normal to the surface at the parametric coordinate U,V.

Each coordinate ranging in -1..+1.

 void chrono::fea::ChElementShellANCF::EvaluateSectionDisplacement ( const double u, const double v, ChVector<> & u_displ, ChVector<> & u_rotaz )
overridevirtual

Gets the xyz displacement of a point on the shell, and the rotation RxRyRz of section reference, at parametric coordinates 'u' and 'v'.

Note, u=-1..+1 , v= -1..+1. Results are not corotated.

Implements chrono::fea::ChElementShell.

 void chrono::fea::ChElementShellANCF::EvaluateSectionFrame ( const double u, const double v, ChVector<> & point, ChQuaternion<> & rot )
overridevirtual

Gets the absolute xyz position of a point on the shell, and the absolute rotation of section reference, at parametric coordinates 'u' and 'v'.

Note, u=-1..+1 , v= -1..+1. Results are corotated.

Implements chrono::fea::ChElementShell.

 void chrono::fea::ChElementShellANCF::EvaluateSectionPoint ( const double u, const double v, ChVector<> & point )
overridevirtual

Gets the absolute xyz position of a point on the shell, at parametric coordinates 'u' and 'v'.

Note, u=-1..+1 , v= -1..+1. Results are corotated.

Implements chrono::fea::ChElementShell.

 ChVector chrono::fea::ChElementShellANCF::EvaluateSectionStrains ( )

Return a vector with three strain components.

Beta

 virtual int chrono::fea::ChElementShellANCF::Get_field_ncoords ( )
overridevirtual

Number of coordinates in the interpolated field, ex=3 for a tetrahedron finite element or a cable, = 1 for a thermal problem, etc.

 double chrono::fea::ChElementShellANCF::GetDensity ( )
overridevirtual

This is needed so that it can be accessed by ChLoaderVolumeGravity.

Density is mass per unit surface.

 void chrono::fea::ChElementShellANCF::GetStateBlock ( ChMatrixDynamic<> & mD )
overridevirtual

Fills the D vector (column matrix) 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! CHLDREN CLASSES MUST IMPLEMENT THIS!!!

Implements chrono::fea::ChElementBase.

 void chrono::fea::ChElementShellANCF::SetupInitial ( ChSystem * system )
overridevirtual

Initial setup.

This is used mostly to precompute matrices that do not change during the simulation, such as the local stiffness of each element (if any), the mass, etc.

Reimplemented from chrono::fea::ChElementBase.

 void chrono::fea::ChElementShellANCF::ShapeFunctions ( ChMatrix<> & N, double x, double y, double z )

Fills the N shape function matrix.

NOTE! actually N should be a 3row, 24 column sparse matrix, as N = [s1*eye(3) s2*eye(3) s3*eye(3) s4*eye(3)...]; , but to avoid wasting zero and repeated elements, here it stores only the s1 through s8 values in a 1 row, 8 columns matrix!

 void chrono::fea::ChElementShellANCF::ShapeFunctionsDerivativeX ( ChMatrix<> & Nx, double x, double y, double z )

Fills the Nx shape function derivative matrix with respect to X.

NOTE! to avoid wasting zero and repeated elements, here it stores only the four values in a 1 row, 8 columns matrix!

 void chrono::fea::ChElementShellANCF::ShapeFunctionsDerivativeY ( ChMatrix<> & Ny, double x, double y, double z )

Fills the Ny shape function derivative matrix with respect to Y.

NOTE! to avoid wasting zero and repeated elements, here it stores only the four values in a 1 row, 8 columns matrix!

 void chrono::fea::ChElementShellANCF::ShapeFunctionsDerivativeZ ( ChMatrix<> & Nz, double x, double y, double z )

Fills the Nz shape function derivative matrix with respect to Z.

NOTE! to avoid wasting zero and repeated elements, here it stores only the four values in a 1 row, 8 columns matrix!