chrono::fea::ChElementShellANCF_3443 Class Reference

## Description

ANCF shell element with four nodes.

The coordinates at each node are the position vector and 3 position vector gradients.

The node numbering is in ccw fashion as in the following scheme:

        v
^
|
D o-----+-----o C
|     |     |
--+-----+-----+----> u
|     |     |
A o-----+-----o B


#include <ChElementShellANCF_3443.h>

Inheritance diagram for chrono::fea::ChElementShellANCF_3443:
Collaboration diagram for chrono::fea::ChElementShellANCF_3443:

## Classes

class  Layer
Definition of a layer. More...

## Public Types

enum  IntFrcMethod { IntFrcMethod::ContInt, IntFrcMethod::PreInt }
Internal force calculation method. More...

template<typename T , int M, int N>
using ChMatrixNMc = Eigen::Matrix< T, M, N, Eigen::ColMajor >

using VectorN = ChVectorN< double, NSF >

using Vector3N = ChVectorN< double, 3 *NSF >

using VectorNIP = ChVectorN< double, NIP >

using Matrix3xN = ChMatrixNM< double, 3, NSF >

using MatrixNx3 = ChMatrixNM< double, NSF, 3 >

using MatrixNx3c = ChMatrixNMc< double, NSF, 3 >

using MatrixNx6 = ChMatrixNM< double, NSF, 6 >

using MatrixNxN = ChMatrixNM< double, NSF, NSF >

## 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< ChNodeFEAxyzDDD > nodeA, std::shared_ptr< ChNodeFEAxyzDDD > nodeB, std::shared_ptr< ChNodeFEAxyzDDD > nodeC, std::shared_ptr< ChNodeFEAxyzDDD > 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< ChNodeFEAxyzDDDGetNodeA () const
Get a handle to the first node of this element.

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

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

std::shared_ptr< ChNodeFEAxyzDDDGetNodeD () 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 SetMidsurfaceOffset (const double offset)
Offset the midsurface of the composite shell element. More...

Set the structural damping.

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

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

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

void SetIntFrcCalcMethod (IntFrcMethod method)
Set the calculation method to use for the generalized internal force and its Jacobian calculations. More...

IntFrcMethod GetIntFrcCalcMethod ()
Return the type of calculation method currently set for the generalized internal force and its Jacobian calculations.

ChMatrix33 GetGreenLagrangeStrain (const double xi, const double eta, const double zeta)
Get the Green-Lagrange strain tensor at the normalized element coordinates (xi, eta, zeta) at the current state of the element. More...

ChMatrix33 GetPK2Stress (const double layer, const double xi, const double eta, const double layer_zeta)
Get the 2nd Piola-Kirchoff stress tensor at the normalized layer coordinates (xi, eta, layer_zeta) at the current state of the element for the specified layer number (0 indexed) since the stress can be discontinuous at the layer boundary. More...

double GetVonMissesStress (const double layer, const double xi, const double eta, const double layer_zeta)
Get the von Mises stress value at the normalized layer coordinates (xi, eta, layer_zeta) at the current state of the element for the specified layer number (0 indexed) since the stress can be discontinuous at the layer boundary. More...

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

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

virtual void ComputeMmatrixGlobal (ChMatrixRef M) override
Set M equal to the global mass matrix.

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

virtual void ComputeInternalForces (ChVectorDynamic<> &Fi) override
Compute the generalized internal force vector for the current nodal coordinates as set the value in the Fi vector.

virtual void ComputeKRMmatricesGlobal (ChMatrixRef H, double Kfactor, double Rfactor=0, double Mfactor=0) override
Set H as a linear combination of M, K, and R. More...

virtual void ComputeGravityForces (ChVectorDynamic<> &Fg, const ChVector<> &G_acc) override
Compute the generalized force vector due to gravity using the efficient ANCF specific method.

virtual void EvaluateSectionDisplacement (const double xi, const double eta, ChVector<> &u_displ, ChVector<> &u_rotaz) override
Gets the xyz displacement of a point on the shell midsurface, and the rotation RxRyRz of section plane, at abscissa '(xi,eta,0)'.

virtual void EvaluateSectionFrame (const double xi, const double eta, ChVector<> &point, ChQuaternion<> &rot) override
Gets the absolute xyz position of a point on the shell midsurface, and the absolute rotation of section plane, at abscissa '(xi,eta,0)'. More...

virtual void EvaluateSectionPoint (const double xi, const double eta, ChVector<> &point) override
Gets the absolute xyz position of a point on the shell midsurface specified in normalized coordinates.

virtual void EvaluateSectionVelNorm (const double xi, const double eta, ChVector<> &Result) override
Gets the absolute xyz velocity of a point on the shell midsurface specified in normalized coordinates.

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.

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 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 xi, const double eta, 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 xi,eta coordinates of the midsurface, 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 xi, const double eta, const double zeta, 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 xi,eta,zeta 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 xi, const double eta) override
Gets the normal to the surface at the parametric coordinate xi,eta. More...

Public Member Functions inherited from chrono::fea::ChElementShell
virtual bool IsTriangleShell ()
Return false if quadrilateral shell - hence u,v parametric coordinates assumed in -1..+1, return true if triangular shell - hence u,v are triangle natural coordinates assumed in 0..+1.

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 EleIntLoadResidual_F_gravity (ChVectorDynamic<> &R, const ChVector<> &G_acc, const double c) override
(This is a default (VERY UNOPTIMAL) book keeping so that in children classes you can avoid implementing this EleIntLoadResidual_F_gravity function, unless you need faster code. More...

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.

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 z=1-u-v) otherwise use default quadrature over u,v in [-1..+1] as rectangular isoparametric coords.

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 const int NP = 4
number of Gauss quadrature points for each midsurface direction

static const int NT = 2
number of quadrature points through the thickness

static const int NIP = NP * NP * NT

static const int NSF = 16
number of shape functions

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

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

## ◆ IntFrcMethod

 strong

Internal force calculation method.

Enumerator
ContInt

"Continuous Integration" style method - Fastest for a small number of layers

PreInt

"Pre-Integration" style method - Fastest for a large number of layers

## Member Function Documentation

 void chrono::fea::ChElementShellANCF_3443::AddLayer ( double thickness, double theta, std::shared_ptr< ChMaterialShellANCF > material )

Layers should be added prior to the start of the simulation since can be a significant amount of pre-calculation overhead required.

Parameters
 thickness layer thickness theta fiber angle (radians) material layer material

## ◆ ComputeKRMmatricesGlobal()

 void chrono::fea::ChElementShellANCF_3443::ComputeKRMmatricesGlobal ( ChMatrixRef H, double Kfactor, double Rfactor = 0, double Mfactor = 0 )
overridevirtual

Set H as a linear combination of M, K, and R.

H = Mfactor * [M] + Kfactor * [K] + Rfactor * [R], where [M] is the mass matrix, [K] is the stiffness matrix, and [R] is the damping matrix.

Implements chrono::fea::ChElementBase.

## ◆ ComputeNF() [1/2]

 void chrono::fea::ChElementShellANCF_3443::ComputeNF ( const double xi, const double eta, 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 xi,eta coordinates of the midsurface, 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.

For this ANCF element, only the first 6 entries in F are used in the calculation. The first three entries is the applied force in global coordinates and the second 3 entries is the applied moment in global space.

Parameters
 xi parametric coordinate in surface eta 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 state_w if != 0, update state (speed part) to this, then evaluate

## ◆ ComputeNF() [2/2]

 void chrono::fea::ChElementShellANCF_3443::ComputeNF ( const double xi, const double eta, const double zeta, 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 xi,eta,zeta 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.

For this ANCF element, only the first 6 entries in F are used in the calculation. The first three entries is the applied force in global coordinates and the second 3 entries is the applied moment in global space.

Parameters
 xi parametric coordinate in volume eta parametric coordinate in volume zeta 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

## ◆ ComputeNormal()

 ChVector chrono::fea::ChElementShellANCF_3443::ComputeNormal ( const double xi, const double eta )
overridevirtual

Gets the normal to the surface at the parametric coordinate xi,eta.

Each coordinate ranging in -1..+1.

## ◆ EvaluateSectionFrame()

 void chrono::fea::ChElementShellANCF_3443::EvaluateSectionFrame ( const double xi, const double eta, ChVector<> & point, ChQuaternion<> & rot )
overridevirtual

Gets the absolute xyz position of a point on the shell midsurface, and the absolute rotation of section plane, at abscissa '(xi,eta,0)'.

Note, nodeA = (xi=-1, eta=-1) Note, nodeB = (xi=1, eta=-1) Note, nodeC = (xi=1, eta=1) Note, nodeD = (xi=-1, eta=1)

Implements chrono::fea::ChElementShell.

## ◆ GetDensity()

 double chrono::fea::ChElementShellANCF_3443::GetDensity ( )
overridevirtual

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

Density is the average mass per unit volume for the entire shell in the reference state of the element.

## ◆ GetGreenLagrangeStrain()

 ChMatrix33 chrono::fea::ChElementShellANCF_3443::GetGreenLagrangeStrain ( const double xi, const double eta, const double zeta )

Get the Green-Lagrange strain tensor at the normalized element coordinates (xi, eta, zeta) at the current state of the element.

Normalized element coordinates span from -1 to 1.

## ◆ GetPK2Stress()

 ChMatrix33 chrono::fea::ChElementShellANCF_3443::GetPK2Stress ( const double layer, const double xi, const double eta, const double layer_zeta )

Get the 2nd Piola-Kirchoff stress tensor at the normalized layer coordinates (xi, eta, layer_zeta) at the current state of the element for the specified layer number (0 indexed) since the stress can be discontinuous at the layer boundary.

"layer_zeta" spans -1 to 1 from the bottom surface to the top surface

## ◆ GetStateBlock()

 void chrono::fea::ChElementShellANCF_3443::GetStateBlock ( ChVectorDynamic<> & mD )
overridevirtual

Fill 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. {Pos_a Du_a Dv_a Dw_a Pos_b Du_b Dv_b Dw_b Pos_c Du_c Dv_c Dw_c Pos_d Du_d Dv_d Dw_d}

Implements chrono::fea::ChElementBase.

## ◆ GetVonMissesStress()

 double chrono::fea::ChElementShellANCF_3443::GetVonMissesStress ( const double layer, const double xi, const double eta, const double layer_zeta )

Get the von Mises stress value at the normalized layer coordinates (xi, eta, layer_zeta) at the current state of the element for the specified layer number (0 indexed) since the stress can be discontinuous at the layer boundary.

"layer_zeta" spans -1 to 1 from the bottom surface to the top surface

## ◆ SetIntFrcCalcMethod()

 void chrono::fea::ChElementShellANCF_3443::SetIntFrcCalcMethod ( IntFrcMethod method )

Set the calculation method to use for the generalized internal force and its Jacobian calculations.

This should be set prior to the start of the simulation since can be a significant amount of pre-calculation overhead required.

## ◆ SetMidsurfaceOffset()

 void chrono::fea::ChElementShellANCF_3443::SetMidsurfaceOffset ( const double offset )

Offset the midsurface of the composite shell element.

A positive value shifts the element's midsurface upward along the elements zeta direction. The offset should be provided in model units.

The documentation for this class was generated from the following files:
• /builds/uwsbel/chrono/src/chrono/fea/ChElementShellANCF_3443.h
• /builds/uwsbel/chrono/src/chrono/fea/ChElementShellANCF_3443.cpp