 An Object Oriented Finite Element Library

Line3 Class Reference

To describe a 3-Node quadratic planar line finite element. More...

`#include <Line3.h>` Inheritance diagram for Line3:

## Public Member Functions

Line3 ()
Default Constructor.

Line3 (const Element *el)
Constructor for an element.

Line3 (const Side *sd)
Constructor for a side.

~Line3 ()
Destructor.

void setLocal (real_t s)
Initialize local point coordinates in element.

LocalVect< Point< real_t >, 3 > DSh () const
Return partial derivatives of shape functions of element nodes. More...

Point< real_tgetLocalPoint () const
Return actual coordinates of localized point. Public Member Functions inherited from FEShape
FEShape ()
Default Constructor.

FEShape (const Element *el)
Constructor for an element. More...

FEShape (const Side *sd)
Constructor for a side. More...

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`. More...

real_t getDet () const
Return determinant of jacobian. More...

Point< real_tgetCenter () const
Return coordinates of center of element.

Point< real_tgetLocalPoint () const
Localize a point in the element. More...

Point< real_tgetLocalPoint (const Point< real_t > &s) const
Localize a point in the element. More...

## Detailed Description

To describe a 3-Node quadratic planar line finite element.

Defines geometric quantities associated to 3-node quadratic element `P2` in the space. The reference element is the segment `[-1,1]`. The user must take care to the fact that determinant of jacobian and other quantities depend on the point in the reference element where they are calculated. For this, before any utilization of shape functions or jacobian, function setLocal() must be invoked.
Element nodes are ordered as the following: the left one, the central one and the right one.

## ◆ DSh()

 LocalVect< Point< real_t >, 3 > 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