Complete Pascal Interpolation Scheme For Approximating The Geometry Of A Quadrilateral Element

Abstract This paper applies a complete parametric set for approximating the geometry of a quadrilateral element. The approximation basis used is a complete Pascal polynomial of second order with six free parameters. The interpolation procedure is a natural interpolation scheme. The six free parameters are determined using the natural coordinates of the four nodal points (vertices) of the quadrilateral element and the two intersections points of the lines crossing every two opposite edges (poles). The presented scheme recovers the well known Lagrangian interpolation scheme, when every two opposite edges are parallel. A third order Pascal interpolation scheme is also presented. The four midpoints of the four edges in addition to the six nodal point from the second order case are used as significant nodal points. It is expected to reflect the geometry properties better since the shape functions are complete.