ABSTRACT
This chapter discusses the finite element method. It presents the general steps followed in developing element equations for a given physical problem. The development of finite element equations involves the following basic steps: Selection of primary dependent variables; Definition of gradient, and constitutive relations; Identification of the approximate element equations; Selection of element interpolation functions; and Specialization of approximate element equations. Before proceeding to the actual derivation of element equations, one needs to explicitly define certain quantities and relations that enter into the equations. The quantities are the secondary dependent variables, which are related to the primary dependent variables through suitable relations involving derivatives of the primary dependent variables. The constitutive relations represent one of the most vital parts of a finite element formulation, for unless they are defined to correctly reflect the behavior of the material under consideration. The chapter concludes with extended examples that illustrate the formulation of the equations for several different elements.
