ABSTRACT
In order to demonstrate the mathematical concepts behind the finite element method, this chapter begins by applying the method to solve second-order, ordinary differential equations with constant coefficients. There are different classes of trial functions that are used in the finite element method having varying degrees of continuity. A connectivity list is a matrix containing the same number of rows as there are elements in the finite element mesh. The element number is typically stored in the first column. The remaining columns contain the global node numbers that are associated with each local node number attached to the element. The finite element matrices and vectors for the one-dimensional elasticity problem are obtained by writing down the weak form of equation over a single element and then substituting the finite element approximations into this expression. The chapter presents some finite element results for the case where the composite bar is modeled with linear-u elements.
