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_3423.h>

Inheritance diagram for chrono::fea::ChElementShellANCF_3423:

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Collaboration diagram for chrono::fea::ChElementShellANCF_3423:

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Classes
class	Layer
	Definition of a layer. More...

Public Types
using	ShapeVector = ChMatrixNM< double, 1, NSF >

using	VectorN = ChVectorN< double, NSF >

using	MatrixNx3 = ChMatrixNM< double, NSF, 3 >

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.

virtual unsigned int	GetNumCoordsPosLevelActive () override
	Get the number of active coordinates in the field used by the referenced nodes.

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

virtual unsigned int	GetNodeNumCoordsPosLevelActive (unsigned int n) override
	Get the number of active 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< ChNodeFEAbase >	GetNode (unsigned int n) override
	Access the n-th node of this element.

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

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

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

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

void	AddLayer (double thickness, double theta, std::shared_ptr< ChMaterialShellANCF > material)
	Add a layer. More...

size_t	GetNumLayers () const
	Get the number of layers.

const Layer &	GetLayer (size_t i) const
	Get a handle to the specified layer.

void	SetAlphaDamp (double a)
	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 (ShapeVector &N, double x, double y, double z)
	Fills the N shape function matrix. More...

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

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

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

ChStrainStress3D	EvaluateSectionStrainStress (const ChVector3d &loc, int layer_id)
	Return a struct with 6-component strain and stress vectors evaluated at a given quadrature point and layer number. More...

void	EvaluateDeflection (double &defVec)

virtual void	GetStateBlock (ChVectorDynamic<> &mD) override
	Fill 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
	Set H as the stiffness matrix K, scaled by Kfactor. More...

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

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

virtual void	ComputeGravityForces (ChVectorDynamic<> &Fg, const ChVector3d &G_acc) override
	Compute the generalized force vector due to gravity using the efficient ANCF specific method.

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

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

virtual void	EvaluateSectionDisplacement (const double u, const double v, ChVector3d &u_displ, ChVector3d &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, ChVector3d &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, ChVector3d &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	ComputeGravityForceScale ()
	Compute the matrix to scale gravity by to get the generalized gravitational force.

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, ShapeVector &Nx, ShapeVector &Ny, ShapeVector &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	CalcCoordDtMatrix (ChVectorN< double, 24 > &dt)

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 (velocity 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 (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 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	EvaluateSectionVelNorm (double U, double V, ChVector3d &Result) override
	Virtual method to plot velocity field distribution. More...

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 ChVector3d	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::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
ChKRMBlock &	Kstiffness ()
	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	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 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	NSF = 8
	number of shape functions

Friends
class	ShellANCF_Mass

class	ShellANCF_Gravity

class	ShellANCF_Force

class	ShellANCF_Jacobian

Additional Inherited Members
Protected Attributes inherited from chrono::fea::ChElementANCF
int	m_element_dof
	actual number of degrees of freedom for the element

bool	m_full_dof
	true if all node variables are active (not fixed)

ChArray< int >	m_mapping_dof
	indices of active DOFs (set only is some are fixed)

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

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

Member Function Documentation

◆ AddLayer()

void chrono::fea::ChElementShellANCF_3423::AddLayer	(	double	thickness,
		double	theta,
		std::shared_ptr< ChMaterialShellANCF >	material
	)

Add a layer.

Parameters

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

◆ ComputeInternalForces()

void chrono::fea::ChElementShellANCF_3423::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.

◆ ComputeInternalJacobians()

void chrono::fea::ChElementShellANCF_3423::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().

◆ ComputeKRMmatricesGlobal()

void chrono::fea::ChElementShellANCF_3423::ComputeKRMmatricesGlobal	(	ChMatrixRef	H,
		double	Kfactor,
		double	Rfactor = `0`,
		double	Mfactor = `0`
	)

overridevirtual

Set 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.

Implements chrono::fea::ChElementBase.

◆ ComputeMassMatrix()

void chrono::fea::ChElementShellANCF_3423::ComputeMassMatrix ( )

Compute the mass matrix of the element.

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

◆ ComputeNF() [1/2]

void chrono::fea::ChElementShellANCF_3423::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.

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

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

Implements chrono::ChLoadableUV.

◆ ComputeNF() [2/2]

void chrono::fea::ChElementShellANCF_3423::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.

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

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

Implements chrono::ChLoadableUVW.

◆ ComputeNodalMass()

void chrono::fea::ChElementShellANCF_3423::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.

◆ ComputeNormal()

ChVector3d chrono::fea::ChElementShellANCF_3423::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.

Implements chrono::ChLoadableUV.

◆ EvaluateSectionDisplacement()

void chrono::fea::ChElementShellANCF_3423::EvaluateSectionDisplacement	(	const double	u,
		const double	v,
		ChVector3d &	u_displ,
		ChVector3d &	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 parametric coordinates, except if triangular shell, where u=0..+1, v=0..+1, natural triangle coords. Results are not corotated.

Implements chrono::fea::ChElementShell.

◆ EvaluateSectionFrame()

void chrono::fea::ChElementShellANCF_3423::EvaluateSectionFrame	(	const double	u,
		const double	v,
		ChVector3d &	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 parametric coordinates, except if triangular shell, where u=0..+1, v=0..+1, natural triangle coords. Results are corotated.

Implements chrono::fea::ChElementShell.

◆ EvaluateSectionPoint()

void chrono::fea::ChElementShellANCF_3423::EvaluateSectionPoint	(	const double	u,
		const double	v,
		ChVector3d &	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 parametric coordinates, except if triangular shell, where u=0..+1, v=0..+1, natural triangle coords. Results are corotated.

Implements chrono::fea::ChElementShell.

◆ EvaluateSectionStrainStress()

ChStrainStress3D chrono::fea::ChElementShellANCF_3423::EvaluateSectionStrainStress	(	const ChVector3d &	loc,
		int	layer_id
	)

Return a struct with 6-component strain and stress vectors evaluated at a given quadrature point and layer number.

Beta

◆ EvaluateSectionVelNorm()

void chrono::fea::ChElementShellANCF_3423::EvaluateSectionVelNorm	(	double	U,
		double	V,
		ChVector3d &	Result
	)

overridevirtual

Virtual method to plot velocity field distribution.

Note, u=-1..+1 , v= -1..+1 parametric coordinates, except if triangular shell, where u=0..+1, v=0..+1, natural triangle coords.

Implements chrono::fea::ChElementShell.

◆ GetDensity()

double chrono::fea::ChElementShellANCF_3423::GetDensity ( )

overridevirtual

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

Density is mass per unit surface.

Implements chrono::ChLoadableUVW.

◆ GetStateBlock()

void chrono::fea::ChElementShellANCF_3423::GetStateBlock ( ChVectorDynamic<> & mD )

overridevirtual

Fill 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. {x_a y_a z_a Dx_a Dx_a Dx_a x_b y_b z_b Dx_b Dy_b Dz_b}

Implements chrono::fea::ChElementBase.

◆ ShapeFunctions()

void chrono::fea::ChElementShellANCF_3423::ShapeFunctions	(	ShapeVector &	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!

◆ ShapeFunctionsDerivativeX()

void chrono::fea::ChElementShellANCF_3423::ShapeFunctionsDerivativeX	(	ShapeVector &	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!

◆ ShapeFunctionsDerivativeY()

void chrono::fea::ChElementShellANCF_3423::ShapeFunctionsDerivativeY	(	ShapeVector &	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!

◆ ShapeFunctionsDerivativeZ()

void chrono::fea::ChElementShellANCF_3423::ShapeFunctionsDerivativeZ	(	ShapeVector &	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!

The documentation for this class was generated from the following files:

/builds/uwsbel/chrono/src/chrono/fea/ChElementShellANCF_3423.h
/builds/uwsbel/chrono/src/chrono/fea/ChElementShellANCF_3423.cpp

Description

Classes

Public Types

Public Member Functions

Static Public Attributes

Friends

Additional Inherited Members

Member Function Documentation

◆ AddLayer()

◆ ComputeInternalForces()

◆ ComputeInternalJacobians()

◆ ComputeKRMmatricesGlobal()

◆ ComputeMassMatrix()

◆ ComputeNF() [1/2]

◆ ComputeNF() [2/2]

◆ ComputeNodalMass()

◆ ComputeNormal()

◆ EvaluateSectionDisplacement()

◆ EvaluateSectionFrame()

◆ EvaluateSectionPoint()

◆ EvaluateSectionStrainStress()

◆ EvaluateSectionVelNorm()

◆ GetDensity()

◆ GetStateBlock()

◆ ShapeFunctions()

◆ ShapeFunctionsDerivativeX()

◆ ShapeFunctionsDerivativeY()

◆ ShapeFunctionsDerivativeZ()