Forbidden Shapes in the Finite Element Method

Publisher Website
Google Scholar
Abstract
In two dimensional finite element analysis, increased accuracy is obtained by the addition of a number of nodal points along the sides of the elements. Curvilinear coordinates (p, q) were introduced to enable the interpolating functions to be obtained in these complicated situations. Unfortunately as was pointed out by Jordan (1970) and is further outlined here, many useful element shapes with side nodes are “forbidden” by this procedure due to the vanishing of the Jacobian of the transformation from the (p, q) system to the fixed (x, y) system. A new technique is introduced in the present paper, based on geometrical considerations, whereby interpolating functions are obtained directly in terms of x and y for the triangle and quadrilateral with arbitrarily placed side points. These local functions can be used to construct piecewise smooth global interpolating functions with C° continuity over regions possessing curved boundaries and composed of elements which are triangles and parallelograms with arbitrarily positioned side points.

This publication has 0 references indexed in Scilit: