The Finite Element Method

Abstract

In the numerical solution of engineering problems, it is often convenient to assume the physical domain to consist of an assemblage of a finite number of subdomains, called finite elements, which are connected with one another along their interfaces. The distribution of a governing physical parameter within each element is approximated by a suitable continuous function, which is uniquely defined in terms of its values at a specified number of nodal points that are usually located along the boundary of the element. The solution to the original boundary value problem is often reduced to that of a variational problem involving the nodal point values of the unknown parameter. In this chapter, we shall be concerned with a rigid/plastic formulation of the finite element method, a complete elastic/plastic formulation of the problem being available elsewhere (Chakrabarty, 2006).