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

idx_t	nodeCount () const override

idx_t	vertexCount () const override

idx_t	ipointCount () const override

idx_t	shapeFuncCount () const override

Matrix	getVertexCoords () const override

Matrix	getIntegrationScheme () const override

bool	containsLocalPoint (const Vector &u) const override

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

Matrix	getVertexFunctions () const override

Matrix	getShapeFunctions () const override

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

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

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

◆ evalShapeFunctions()

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

inlineoverride

Parameters

[out]	h	Shape function values
[in]	u	Local coordinates

◆ evalShapeGradGrads()

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

inline

Parameters

[out]	h	Shape function values
[out]	g	Shape function gradients
[out]	gg	Shape function second derivatives
[in]	u	Local coordinates

◆ evalShapeGradients()

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

inline

Parameters

[out]	h	Shape function values
[out]	g	Shape function gradients
[in]	u	Local coordinates

◆ getGlobalPoint()

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

override

Parameters

[out]	x	Global coordinates vector
[in]	u	Local coordinates vector
[in]	c	Node coordinates matrix

◆ getIntegrationScheme()

Matrix Line3D::getIntegrationScheme ( ) const

inlineoverride

◆ getIntegrationWeights()

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

override

Parameters

[out]	w	Integration weights at quadrature points
[in]	c	Node coordinates matrix

◆ getPi() [1/2]

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

Parameters

[out]	Pi	Pi(.,.,i) where i are the integration points
[out]	Ri	Ri(.,.,i) rotation at the integration points
[in]	Rn	rotations at the nodes.

◆ getPi() [2/2]

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

Parameters

[out]	Pi	Pi(.,.,i) where i are the integration points
[in]	Rn	rotations at the nodes.

◆ getPsi()

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

Parameters

[out]	Psi	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() [1/2]

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

Parameters

[out]	LambdaP	curvature at the integration points
[out]	w	integration weights
[in]	Rn	initial rotations at the integration points. Rn(.,.,i) initial rotation at the integration points
[in]	c	coordinates of the nodes, c(i,j) is the i-th coordinate of the j-th node
[in]	theta	rotation at the nodes. theta(.,i) rotational displacement at the nodes

◆ getRotationGradients() [2/2]

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

Parameters

[out]	LambdaP	curvature at the integration points
[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	rotation at the nodes.

◆ getRotations()

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

Parameters

[out]	Ri	Ri(.,.,i) rotational matrix at the integration points
[in]	Rn	rotation at the nodes. Rn(.,i) rotational displacement at the nodes

◆ getShapeFunctions()

Matrix Line3D::getShapeFunctions ( ) const

inlineoverride

◆ 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

◆ getVertexFunctions()

Matrix Line3D::getVertexFunctions ( ) const

inlineoverride

◆ getXi()

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

Parameters

[out]	Xi	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, c(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)

◆ ipointCount()

idx_t Line3D::ipointCount ( ) const

inlineoverride

◆ localRank()

idx_t Line3D::localRank ( ) const

inlineoverride

◆ nodeCount()

idx_t Line3D::nodeCount ( ) const

inlineoverride

◆ shapeFuncCount()

idx_t Line3D::shapeFuncCount ( ) const

inlineoverride

◆ vertexCount()

idx_t Line3D::vertexCount ( ) const

inlineoverride

Member Data Documentation

◆ GLOB_RANK

const idx_t Line3D::GLOB_RANK = 3

static

◆ intLine_

jem::Ref<ParametricLine> Line3D::intLine_

protected

◆ PROP_INT

const String Line3D::PROP_INT = "intScheme"

static

◆ PROP_LOCAL

const String Line3D::PROP_LOCAL

static

◆ PROP_NODES

const String Line3D::PROP_NODES = "numPoints"

static

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() [1/2]

◆ getRotationGradients() [2/2]

◆ getRotations()

◆ getShapeFunctions()

◆ getShapeGradients()

◆ getVertexCoords()

◆ getVertexFunctions()

◆ getXi()

◆ globalRank()

◆ ipointCount()

◆ localRank()

◆ nodeCount()

◆ shapeFuncCount()

◆ vertexCount()

Member Data Documentation

◆ GLOB_RANK

◆ intLine_

◆ PROP_INT

◆ PROP_LOCAL

◆ PROP_NODES