Description

A Kirchhoff-Love thin shell element of triangular shape.

This is based on the BST Basic Shell Triangle idea of Onate et al., where 3 purely translational nodes are used for the triangle itself, and 3 other purely translational nodes are used from the neighbouring triangles to infer curvature.

The node numbering is as in the following scheme, where 0-1-2 are the nodes of the triangle, and 3-4-5 are the nodes from neighbouring elements in the mesh:

         2
  4 o----o---o 3
     \   |\  |
      \  | \ |
       \ |  |
       0 o---o 1
          \  |
           \ |
            |
             o 5

#include <ChElementShellBST.h>

Inheritance diagram for chrono::fea::ChElementShellBST:

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Collaboration diagram for chrono::fea::ChElementShellBST:

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

Public Types
using	ShapeVector = ChMatrixNM< double, 1, 3 >

Public Member Functions
void	SetNodes (std::shared_ptr< ChNodeFEAxyz > node0, std::shared_ptr< ChNodeFEAxyz > node1, std::shared_ptr< ChNodeFEAxyz > node2, std::shared_ptr< ChNodeFEAxyz > node3, std::shared_ptr< ChNodeFEAxyz > node4, std::shared_ptr< ChNodeFEAxyz > node5)
	Specify the nodes of this element. More...

virtual unsigned int	GetNumNodes () override
	Get the number of nodes used by this element, not considering those marked with "nullptr" ex. if at boundary.

virtual unsigned int	GetNumCoordsPosLevel () override
	Get the number of 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 std::shared_ptr< ChNodeFEAbase >	GetNode (unsigned int n) override
	Access the n-th node of this element, not considering those marked with "nullptr" ex. if at boundary n=0..5.

std::shared_ptr< ChNodeFEAxyz >	GetNodeMainTriangle (unsigned int n) const
	Get a handle to the n node of this element, among the three of the triangle part, n=0..2.

std::shared_ptr< ChNodeFEAxyz >	GetNodeNeighbour (unsigned int n) const
	Get a handle to the n node from the three of the neighbouring triangles, n=0..2. Even if nullptr.

void	SetAsNeutral ()
	Sets the neutral rotations of nodes at once, assuming the current element position is for zero strain.

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

void	SetLayerZreferenceCentered ()
	Impose the reference z level of shell element as centered along the total thickness. More...

void	SetLayerZreference (double z_from_bottom)
	Impose the reference z level of shell element respect to the lower face of bottom layer Note! Use after you added all layers.

size_t	GetNumLayers () const
	Get the number of layers.

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

double	GetThickness ()
	Get the total thickness of the shell element (might be sum of multiple layer thicknesses)

void	ShapeFunctions (ShapeVector &N, const double u, const double v)
	Fills the N shape function matrix, evaluated in "natural" triangle coordinates U and V.

void	ShapeFunctionsDerivativeU (ShapeVector &Nu, const double u, const double v)
	Fills the Nu shape function derivative matrix with respect to U. Note, may remove u,v parms cause constant.

void	ShapeFunctionsDerivativeV (ShapeVector &Nv, const double u, const double v)
	Fills the Nv shape function derivative matrix with respect to V. Note, may remove u,v parms cause constant.

void	ShapeFunctionsDerivativeX (ShapeVector &Nx, const ChMatrixNM< double, 2, 2 > &Jux, const double u, const double v)
	Fills the Nx shape function derivative matrix with respect to X local element direction. More...

void	ShapeFunctionsDerivativeY (ShapeVector &Ny, const ChMatrixNM< double, 2, 2 > &Jux, const double u, const double v)
	Fills the Ny shape function derivative matrix with respect to Y local element direction. More...

virtual void	GetStateBlock (ChVectorDynamic<> &mD) override
	Fill the D vector with the current field values at thenodes 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	ComputeInternalForces (ChVectorDynamic<> &Fi) override
	Computes the internal forces. More...

void	ComputeInternalForces_impl (ChVectorDynamic<> &Fi, ChState &state_x, ChStateDelta &state_w, bool used_for_differentiation=false)

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

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	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...

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

virtual bool	IsTriangleShell () override
	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.

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

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	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...

virtual bool	IsTriangleIntegrationNeeded () override
	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.

virtual bool	IsTrianglePrismIntegrationNeeded () override
	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.

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	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	ComputeGravityForces (ChVectorDynamic<> &Fg, const ChVector3d &G_acc) override
	Compute the gravitational forces. 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...

virtual void	ComputeNodalMass ()
	Compute element's nodal masses.

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

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.

Public Attributes
std::vector< std::shared_ptr< ChNodeFEAxyz > >	m_nodes
	element nodes

std::vector< Layer >	m_layers
	element layers

std::vector< double >	m_layers_z
	layer separation z values (not scaled, default centered tot thickness)

double	tot_thickness
	total element thickness

ChMatrixNM< double, 2, 2 >	Jux
	jacobian [d{u,v}/d{x,y}], as inverse of [d{x,y}/d{u,v}]

double	area
	initial element triangle area

ChVector3d	l0
	initial lengths

ChVector3d	cM [3]
	cM coefficients

ChVector3d	cI [3]
	cI coefficients

ChVector3d	rI
	rI coefficients = RIi/(RMi/RIi) = (1/hIi)/((1/hMi)(1/hIi))

ChVector3d	phi0
	initial edge bendings

ChVector3d	phi
	actual edge bendings (last computed)

ChVector3d	k0
	initial curvature (not needed?)

ChVector3d	e0
	initial strain

ChVector3d	k
	actual curvature (last computed)

ChVector3d	e
	actual strain (last computed)

ChVector3d	n
	actual stress, membrane (last computed)

ChVector3d	m
	actual stress, bending (last computed)

Additional Inherited Members
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::ChElementShellBST::AddLayer	(	double	thickness,
		double	theta,
		std::shared_ptr< ChMaterialShellKirchhoff >	material
	)

Add a layer.

By default, when adding more than one layer, the reference z level of the shell element is centered along the total thickness.

Parameters

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

◆ ComputeInternalForces()

void chrono::fea::ChElementShellBST::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.

◆ ComputeInternalForces_impl()

void chrono::fea::ChElementShellBST::ComputeInternalForces_impl	(	ChVectorDynamic<> &	Fi,
		ChState &	state_x,
		ChStateDelta &	state_w,
		bool	used_for_differentiation = `false`
	)

Parameters

Fi	vector of internal forces
state_x	state position to evaluate Fi
state_w	state speed to evaluate Fi
used_for_differentiation	true if called during finite-difference Jacobian approximation

◆ ComputeInternalJacobians()

void chrono::fea::ChElementShellBST::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::ChElementShellBST::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.

◆ ComputeNF() [1/2]

void chrono::fea::ChElementShellBST::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

Implements chrono::ChLoadableUV.

◆ ComputeNF() [2/2]

void chrono::fea::ChElementShellBST::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

Implements chrono::ChLoadableUVW.

◆ ComputeNormal()

ChVector3d chrono::fea::ChElementShellBST::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.

◆ EleIntLoadLumpedMass_Md()

void chrono::fea::ChElementShellBST::EleIntLoadLumpedMass_Md	(	ChVectorDynamic<> &	Md,
		double &	error,
		const double	c
	)

overridevirtual

Adds the lumped mass to a Md vector, representing a mass diagonal matrix.

Used by lumped explicit integrators. If mass lumping is impossible or approximate, adds scalar error to "error" parameter. Md += c*diag(M) or Md += c*HRZ(M) or other lumping heuristics This default implementation is VERY INEFFICIENT.

Reimplemented from chrono::fea::ChElementGeneric.

◆ EvaluateSectionDisplacement()

void chrono::fea::ChElementShellBST::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::ChElementShellBST::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::ChElementShellBST::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.

◆ EvaluateSectionVelNorm()

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

overridevirtual

Fill the D vector with the current field values at thenodes 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 x_b y_b z_b ....}

Implements chrono::fea::ChElementBase.

◆ SetLayerZreferenceCentered()

void chrono::fea::ChElementShellBST::SetLayerZreferenceCentered ( )

Impose the reference z level of shell element as centered along the total thickness.

This is the default behavior each time you call AddLayer(); Note! Use after you added all layers.

◆ SetNodes()

void chrono::fea::ChElementShellBST::SetNodes	(	std::shared_ptr< ChNodeFEAxyz >	node0,
		std::shared_ptr< ChNodeFEAxyz >	node1,
		std::shared_ptr< ChNodeFEAxyz >	node2,
		std::shared_ptr< ChNodeFEAxyz >	node3,
		std::shared_ptr< ChNodeFEAxyz >	node4,
		std::shared_ptr< ChNodeFEAxyz >	node5
	)

Specify the nodes of this element.

The node numbering is as in the following scheme, where 0-1-2 are the nodes of the triangle, and 3-4-5 are the nodes from neighbouring elements in the mesh: On the boundary, one or more of nodes 3,4,5 might be "nullptr".

         2
  4 o----o---o 3
     \   |\  |
      \  | \ |
       \ |  |
       0 o---o 1
          \  |
           \ |
            |
             o 5

◆ ShapeFunctionsDerivativeX()

void chrono::fea::ChElementShellBST::ShapeFunctionsDerivativeX	(	ShapeVector &	Nx,
		const ChMatrixNM< double, 2, 2 > &	Jux,
		const double	u,
		const double	v
	)

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

The jacobian Jux = [d{u,v}/d{x,y}] must be provided, often from inverse of Jxu = [d{x,y}/d{u,v}], so that [Nx;Ny]=[Jux]*[Nu;Nv]. Note, may remove u,v parms cause constant

◆ ShapeFunctionsDerivativeY()

void chrono::fea::ChElementShellBST::ShapeFunctionsDerivativeY	(	ShapeVector &	Ny,
		const ChMatrixNM< double, 2, 2 > &	Jux,
		const double	u,
		const double	v
	)

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

The jacobian Jux = [d{u,v}/d{x,y}] must be provided, often from inverse of Jxu = [d{x,y}/d{u,v}], so that [Nx;Ny]=[Jux]*[Nu;Nv]. Note, may remove u,v parms cause constant

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

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

Description

Classes

Public Types

Public Member Functions

Public Attributes

Additional Inherited Members

Member Function Documentation

◆ AddLayer()

◆ ComputeInternalForces()

◆ ComputeInternalForces_impl()

◆ ComputeInternalJacobians()

◆ ComputeKRMmatricesGlobal()

◆ ComputeNF() [1/2]

◆ ComputeNF() [2/2]

◆ ComputeNormal()

◆ EleIntLoadLumpedMass_Md()

◆ EvaluateSectionDisplacement()

◆ EvaluateSectionFrame()

◆ EvaluateSectionPoint()

◆ EvaluateSectionVelNorm()

◆ GetDensity()

◆ GetStateBlock()

◆ SetLayerZreferenceCentered()

◆ SetNodes()

◆ ShapeFunctionsDerivativeX()

◆ ShapeFunctionsDerivativeY()