Triang6S Class Reference

Defines a 6-Node straight triangular finite element using P2 interpolation. More...

#include <Triang6S.h>

Inheritance diagram for Triang6S:

Public Member Functions
	Triang6S ()
	Default Constructor.
	Triang6S (const Element *el)
	Constructor for an element.
	~Triang6S ()
	Destructor.
void	Sh (real_t s, real_t t, real_t *sh) const
	Calculate shape functions.
Point< real_t >	getCenter () const
	Return coordinates of center of element.
real_t	getMaxEdgeLength () const
	Return maximal edge length of triangle.
real_t	getMinEdgeLength () const
	Return minimal edge length of triangle.
void	setLocal (real_t s, real_t t)
	Initialize local point coordinates in element.
void	atMidEdges (std::vector< Point< real_t > > &dsh, std::vector< real_t > &w)
	Compute partial derivatives of shape functions at mid edges of triangles.
std::vector< Point< real_t > >	DSh () const
	Return partial derivatives of shape functions of element nodes.
Public Member Functions inherited from triangle
	triangle ()
	Default Constructor.
	triangle (const Element *el)
	Constructor for an element.
	triangle (const Side *sd)
	Constructor for a side.
virtual	~triangle ()
	Destructor.
real_t	getArea ()
	Return element area.
Point< real_t >	getCenter () const
	Return coordinates of center of element.
Point< real_t >	getCircumcenter () const
	Return coordinates of circumcenter of element.
real_t	getCircumRadius () const
	Return radius of circumscribed circle of triangle.
real_t	getInRadius () const
	Return radius of inscribed circle of triangle.
Point< real_t >	getRefCoord (const Point< real_t > &x) const
	Return reference coordinates of a point x in element.
real_t	getMaxEdgeLength () const
	Return maximal edge length of triangle.
real_t	getMinEdgeLength () const
	Return minimal edge length of triangle.
bool	isIn (const Point< real_t > &x) const
	Check whether point x is in current triangle or not.
bool	isStrictlyIn (const Point< real_t > &x) const
	Check whether point x is strictly in current triangle (not on the boundary) or not.
Public Member Functions inherited from FEShape
	FEShape ()
	Default Constructor.
	FEShape (const Element *el)
	Constructor for an element.
	FEShape (const Side *sd)
	Constructor for a side.
virtual	~FEShape ()
	Destructor.
real_t	Sh (size_t i) const
	Return shape function of node i at given point.
real_t	Sh (size_t i, Point< real_t > s) const
	Calculate shape function of node i at a given point s.
real_t	getDet () const
	Return determinant of jacobian.
Point< real_t >	getCenter () const
	Return coordinates of center of element.
Point< real_t >	getLocalPoint () const
	Localize a point in the element.
Point< real_t >	getLocalPoint (const Point< real_t > &s) const
	Localize a point in the element.

Detailed Description

Defines a 6-Node straight triangular finite element using P2 interpolation.

The reference element is the rectangle triangle with two unit edges.

Author

Rachid Touzani

Copyright

GNU Lesser Public License

Constructor & Destructor Documentation

Triang6S()

Triang6S

(

const Element *

el

)

Constructor for an element.

The constructed triangle is an element in a 2-D mesh.

Parameters

[in]

el

Pointer to Element instance

Member Function Documentation

atMidEdges()

void atMidEdges	(	std::vector< Point< real_t > > &	dsh,
		std::vector< real_t > &	w
	)

Compute partial derivatives of shape functions at mid edges of triangles.

This member function can be called for integrations using partial derivatives of shape functions and approximated by midedge integration formula

Parameters

[out]	dsh	Vector containing partial derivatives of shape functions
[out]	w	Vector containing weights for the integration formula

DSh()

std::vector< Point< real_t > > DSh

(

)

const

Return partial derivatives of shape functions of element nodes.

Returns

LocalVect instance of partial derivatives of shape functions e.g. dsh(i).x, dsh(i).y, are partial derivatives of the i-th shape function.

Note

The local point at which the derivatives are computed must be chosen before by using the member function setLocal

setLocal()

void setLocal	(	real_t	s,
		real_t	t
	)

Initialize local point coordinates in element.

Parameters

[in]	s	Local first coordinate of the point where the gradient of the shape functions are evaluated
[in]	t	Local second coordinate of the point where the gradient of the shape functions are evaluated

Sh()

void Sh	(	real_t	s,
		real_t	t,
		real_t *	sh
	)		const

Calculate shape functions.

Parameters

[in]	s	Local first coordinate of the point where the gradient of the shape functions are evaluated
[in]	t	Local second coordinate of the point where the gradient of the shape functions are evaluated
[out]	sh	Array of of shape functions at (s,t)