Introduction

So far, we have considered only one-dimensional problems in our discussion on finite element formulation. Now we shall discuss the finite element formulation of two dimensional (2-D) problems. This formulation differs from one-dimensional (1-D) formulation in certain respects. For 1-D problems, the elements being line segments have only the size. But, for 2-D problems, the elements have both the size and shape. The typical shapes are triangles, rectangles, quadrilaterals, curved triangles, curved quadrilaterals etc. Further, the shape functions are functions of two coordinates. Therefore, we need 2-D numerical integration scheme for the evaluation of element stiffness matrix. Another difference between the 1-D and 2-D formulations is that, now the boundary of the domain is a curve and not just a pair of points. Therefore, application of the Neumann boundary condition involves line integration along that boundary using the consistent 1-D shape functions.

In the present lecture, we shall discuss the integral formulations of a typical 2-D problem. Other aspects of the finite element formulation will be discussed in subsequent lectures.