Shape function for 1D line elements in 3D space. More...

#include "Line3D.h"

Inheritance diagram for Line3D:

Collaboration diagram for Line3D:

[legend]

Public Member Functions
	Line3D (const String &name, const Properties &conf, const Properties &props)
	Constructs a new Line3D shape object.

idx_t	globalRank () const override
	Get the global rank (spatial dimension).

idx_t	localRank () const override
	Get the local rank of the line element.

idx_t	nodeCount () const override
	Get the number of nodes in the line element.

idx_t	vertexCount () const override
	Get the number of vertices in the line element.

idx_t	ipointCount () const override
	Get the number of integration points.

idx_t	shapeFuncCount () const override
	Get the number of shape functions.

Matrix	getVertexCoords () const override
	Get the local coordinates of the vertices.

Matrix	getIntegrationScheme () const override
	Get the integration scheme.

bool	containsLocalPoint (const Vector &u) const override
	Check whether a local point is inside the element.

void	getIntegrationWeights (const Vector &w, const Matrix &c) const override
	Compute integration weights for numerical integration.

Matrix	getVertexFunctions () const override
	Get shape function values at the integration points.

Matrix	getShapeFunctions () const override
	Get shape function values at the integration points.

void	getGlobalPoint (const Vector &x, const Vector &u, const Matrix &c) const override
	Transform local coordinates to global coordinates.

void	getShapeGradients (const Matrix &g, const Vector &w, const Matrix &c) const
	get the gradients of the shape functions at the integration points

void	getRotations (const Cubix &Ri, const Cubix &Rn) const
	return the rotations at the integration points

void	getXi (const Quadix &Xi, const Vector &w, const Matrix &u, const Matrix &c) const
	Get the Xi at the integration points.

void	getXi (const Quadix &Xi, const Matrix &grads, const Matrix &phiP) const
	Xi from precomputed shape gradients and tangent (allocation free)

void	getPsi (const Quadix &Psi, const Vector &w, const Matrix &c) const
	Get the Psi at the integration points.

void	getPi (const Cubix &Pi, const Cubix &Ri, const Cubix &Rn) const
	Get the Pi at the integration points.

void	getPi (const Cubix &Pi, const Cubix &Rn) const
	Get the Pi at the integration points.

void	getRotationGradients (const Cubix &LambdaP, const Vector &w, const Matrix &c, const Cubix &nodeLambda) const
	Get the rotation gradients at the integration points from the rotations (Crisfield/Jelenic)

void	getRotationsAndGradients (const Cubix &Ri, const Cubix &LambdaP, const Matrix &grads, const Cubix &nodeLambda) const
	Get the rotations and the rotation gradients at the integration points using one evaluation of the node rotation vectors.

void	evalShapeFunctions (const Vector &h, const Vector &u) const override
	Evaluate shape functions at given local coordinates.

void	evalShapeGradients (const Vector &h, const Vector &g, const Vector &u) const
	Evaluate shape functions and their gradients at local coordinates.

void	evalShapeGradGrads (const Vector &h, const Vector &g, const Vector &gg, const Vector &u) const
	Evaluate shape functions, gradients, and second derivatives.

Static Public Attributes
static const String	PROP_NODES = "numPoints"
	Property name for number of nodes.

static const String	PROP_INT = "intScheme"
	Property name for integration scheme.

static const String	PROP_LOCAL
	Property name for local coordinates.

static const idx_t	GLOB_RANK = 3
	Global rank (always 3 for 3D space)

Protected Attributes
jem::Ref< ParametricLine >	intLine_
	internal line element for some standard functions

Matrix	nodePsi_
	relative rotation vectors of the nodes, 3 x nodeCount

Matrix	lambdaR_
	reference rotation, 3 x 3

Matrix	ipPsi_
	rotation vectors at the integration points, 3 x ipointCount

MatmulChain< double, 2 >	matmul_
	matrix products without allocations

Matrix	relRot_
	relative rotation, 3 x 3

Matrix	skewP_
	skew symmetric matrix of the tangent, 3 x 3

Vector	phiIJ_
	relative rotation vector between the reference nodes

Memo of the last getShapeGradients() call
The gradients only depend on the node coordinates, and the same coordinates are requested several times in a row (strains, Xi, rotation gradients of one element). A hit needs bit-identical coordinates, so the results are exactly those of a fresh evaluation. Not thread safe.
bool	gradMemoValid_ = false

Matrix	gradMemoCoords_

Matrix	gradMemoGrads_

Vector	gradMemoWeights_

Detailed Description

Provides shape functions and geometric operations for line elements embedded in 3D space. Supports 2, 3, and 4-node line elements with configurable integration schemes and rotational control functions.

Supported Elements

2-node linear line (StdLine2)
3-node quadratic line (StdLine3)
4-node cubic line (StdLine4)

Author: Til Gärtner

See also: Line Shapes

Constructor & Destructor Documentation

◆ Line3D()

Line3D::Line3D	(	const String &	name,
		const Properties &	conf,
		const Properties &	props
	)

explicit

Parameters

[in]	name	Shape instance name for identification
[out]	conf	Configuration properties container for output
[in]	props	Input properties containing shape parameters

Exceptions

jem::IllegalInputException if unsupported number of nodes is specified

Member Function Documentation

◆ containsLocalPoint()

bool Line3D::containsLocalPoint ( const Vector & u ) const

inlineoverride

Parameters

[in] u Local coordinate vector

Returns: Whether the point is contained in the element

◆ evalShapeFunctions()

void Line3D::evalShapeFunctions	(	const Vector &	h,
		const Vector &	u
	)		const

inlineoverride

Parameters

[out]	h	Shape function value vector
[in]	u	Local coordinate vector

◆ evalShapeGradGrads()

void Line3D::evalShapeGradGrads	(	const Vector &	h,
		const Vector &	g,
		const Vector &	gg,
		const Vector &	u
	)		const

inline

Parameters

[out]	h	Shape function value vector
[out]	g	Shape function gradient vector
[out]	gg	Shape function second derivative vector
[in]	u	Local coordinate vector

◆ evalShapeGradients()

void Line3D::evalShapeGradients	(	const Vector &	h,
		const Vector &	g,
		const Vector &	u
	)		const

inline

Parameters

[out]	h	Shape function value vector
[out]	g	Shape function gradient vector
[in]	u	Local coordinate vector

◆ getGlobalPoint()

void Line3D::getGlobalPoint	(	const Vector &	x,
		const Vector &	u,
		const Matrix &	c
	)		const

override

Parameters

[out]	x	Global coordinate vector
[in]	u	Local coordinate vector
[in]	c	Coordinates of the nodes, c(i,j) is the i-th coordinate of the j-th node

◆ getIntegrationScheme()

Matrix Line3D::getIntegrationScheme ( ) const

inlineoverride

Returns: Matrix describing the integration scheme

◆ getIntegrationWeights()

void Line3D::getIntegrationWeights	(	const Vector &	w,
		const Matrix &	c
	)		const

override

Parameters

[out]	w	Integration weights at the integration points
[in]	c	Node coordinates matrix, c(i,j) is the i-th coordinate of the j-th node

◆ getPi() [1/2]

void Line3D::getPi	(	const Cubix &	Pi,
		const Cubix &	Ri,
		const Cubix &	Rn
	)		const

Parameters

[out]	Pi	6 x 6 Pi(.,.,i) where i are the integration points
[out]	Ri	3 x 3 Ri(.,.,i) rotation at the i-th integration point
[in]	Rn	nodal rotations, Rn(.,.,i) is the 3 x 3 rotation matrix at the i-th node

◆ getPi() [2/2]

void Line3D::getPi	(	const Cubix &	Pi,
		const Cubix &	Rn
	)		const

Parameters

[out]	Pi	6 x 6 Pi(.,.,i) where i are the integration points
[in]	Rn	nodal rotations, Rn(.,.,i) is the 3 x 3 rotation matrix at the i-th node

◆ getPsi()

void Line3D::getPsi	(	const Quadix &	Psi,
		const Vector &	w,
		const Matrix &	c
	)		const

Parameters

[out]	Psi	6 x 9 Psi(.,.,j,i), where j are the nodes and i are the integration points
[out]	w	weights of the integration points
[in]	c	coordinates of the nodes, c(i,j) is the i-th coordinate of the j-th node

◆ getRotationGradients()

void Line3D::getRotationGradients	(	const Cubix &	LambdaP,
		const Vector &	w,
		const Matrix &	c,
		const Cubix &	nodeLambda
	)		const

Parameters

[out]	LambdaP	3 x 3 curvature at the integration points, LambdaP(.,.,i) is the gradient at the i-th point
[out]	w	integration weights
[in]	c	coordinates of the nodes, c(i,j) is the i-th coordinate of the j-th node
[in]	nodeLambda	nodal rotations, nodeLambda(.,.,i) is the 3 x 3 rotation matrix at the i-th node

◆ getRotations()

void Line3D::getRotations	(	const Cubix &	Ri,
		const Cubix &	Rn
	)		const

Parameters

[out]	Ri	3 x 3 Ri(.,.,i) rotational matrix at the i-th integration point
[in]	Rn	nodal rotations, Rn(.,.,i) is the 3 x 3 rotation matrix at the i-th node

◆ getRotationsAndGradients()

void Line3D::getRotationsAndGradients	(	const Cubix &	Ri,
		const Cubix &	LambdaP,
		const Matrix &	grads,
		const Cubix &	nodeLambda
	)		const

Parameters

[out]	Ri	3 x 3 Ri(.,.,i) rotation at the i-th integration point (Pi = diag(Ri, Ri), see getPi)
[out]	LambdaP	3 x 3 curvature at the integration points, LambdaP(.,.,i) is the gradient at the i-th point
[in]	grads	shape gradients, shapeFuncCount x ipointCount (see getShapeGradients)
[in]	nodeLambda	nodal rotations, nodeLambda(.,.,i) is the 3 x 3 rotation matrix at the i-th node

◆ getShapeFunctions()

Matrix Line3D::getShapeFunctions ( ) const

inlineoverride

Returns: Matrix of shape function values

◆ getShapeGradients()

void Line3D::getShapeGradients	(	const Matrix &	g,
		const Vector &	w,
		const Matrix &	c
	)		const

Parameters

[out]	g	gradient of the shape functions at the integration points g(i,j) i-th shape function at the j-th int point
[out]	w	weights of the integration points
[in]	c	coordinates of the nodes, c(i,j) is the i-th coordinate of the j-th node

◆ getVertexCoords()

Matrix Line3D::getVertexCoords ( ) const

inlineoverride

Returns: Matrix of vertex coordinates

◆ getVertexFunctions()

Matrix Line3D::getVertexFunctions ( ) const

inlineoverride

Get the vertex shape function values at the integration points.

Returns: Matrix of shape function values

◆ getXi() [1/2]

void Line3D::getXi	(	const Quadix &	Xi,
		const Matrix &	grads,
		const Matrix &	phiP
	)		const

Parameters

[out]	Xi	Xi matrices, 6 x 6 x nodeCount x ipointCount
[in]	grads	Shape gradients, shapeFuncCount x ipointCount
[in]	phiP	Tangent of the deformed line at the integration points, 3 x ipointCount

◆ getXi() [2/2]

void Line3D::getXi	(	const Quadix &	Xi,
		const Vector &	w,
		const Matrix &	u,
		const Matrix &	c
	)		const

Parameters

[out]	Xi	6 x 6 Xi(.,.,j,i), where j are the nodes and i are the integration points
[out]	w	weights of the integration points
[in]	u	displacements of the nodes, u(i,j) is the i-th displacement of the j-th node
[in]	c	coordinates of the nodes, c(i,j) is the i-th coordinate of the j-th node

◆ globalRank()

idx_t Line3D::globalRank ( ) const

inlineoverride

Returns: Global rank (always 3 for 3D space); Global rank

◆ ipointCount()

idx_t Line3D::ipointCount ( ) const

inlineoverride

Returns: Number of integration points

◆ localRank()

idx_t Line3D::localRank ( ) const

inlineoverride

Returns: Local coordinate dimension

◆ nodeCount()

idx_t Line3D::nodeCount ( ) const

inlineoverride

Returns: Number of nodes

◆ shapeFuncCount()

idx_t Line3D::shapeFuncCount ( ) const

inlineoverride

Returns: Number of shape functions

◆ vertexCount()

idx_t Line3D::vertexCount ( ) const

inlineoverride

Returns: Number of vertices

mutableprotected

◆ skewP_

Matrix Line3D::skewP_

mutableprotected

Public Member Functions

Static Public Attributes

Protected Attributes

Detailed Description

Supported Elements

Constructor & Destructor Documentation

◆ Line3D()

Member Function Documentation

◆ containsLocalPoint()

◆ evalShapeFunctions()

◆ evalShapeGradGrads()

◆ evalShapeGradients()

◆ getGlobalPoint()

◆ getIntegrationScheme()

◆ getIntegrationWeights()

◆ getPi() [1/2]

◆ getPi() [2/2]

◆ getPsi()

◆ getRotationGradients()

◆ getRotations()

◆ getRotationsAndGradients()

◆ getShapeFunctions()

◆ getShapeGradients()

◆ getVertexCoords()

◆ getVertexFunctions()

◆ getXi() [1/2]

◆ getXi() [2/2]

◆ globalRank()

◆ ipointCount()

◆ localRank()

◆ nodeCount()

◆ shapeFuncCount()

◆ vertexCount()

Member Data Documentation

◆ GLOB_RANK

◆ gradMemoCoords_

◆ gradMemoGrads_

◆ gradMemoValid_

◆ gradMemoWeights_

◆ intLine_

◆ ipPsi_

◆ lambdaR_

◆ matmul_

◆ nodePsi_

◆ phiIJ_

◆ PROP_INT

◆ PROP_LOCAL

◆ PROP_NODES

◆ relRot_

◆ skewP_