Introduction

The shape functions used for approximating the primary variable have been expressed as functions of the physical coordinate x . The evaluation of element stiffness matrix and the right side vector involves the integration of shape functions or their derivatives. For computer implementation of the finite element method, this integration needs to be done numerically. For the ease of numerical integration, we map each element onto a standard element of size two (which is called as Master Element ) . Further, the coordinate employed on the master element varies from minus one to plus one. This coordinate is called as the Natural Coordinate . To carry out the numerical integration, the shape functions need to be expressed in terms of the natural coordinate. This gives a generic definition of the shape functions. We first discuss the mapping function between the physical coordinate x and the natural coordinate.