Introduction

In Ritz method, an approximate solution of a boundary value problem is obtained by using the corresponding integral formulation. An approximate form for the solution is assumed in terms of a series containing known functions and unknown coefficients. When this form is substituted in the integral formulation, we get a set of algebraic equations in terms of the unknown coefficients. Solution of the algebraic equations determines the coefficients. To get the exact solution, usually, an infinite series is needed. A finite series, normally, gives an approximate solution. However, when sufficiently large number of terms is chosen, the accuracy is reasonable for most engineering applications. In this lecture, Ritz method is developed for the problem of an axial extension of bar, which is described in section 2.1. The bar is shown in fig. 2.1 and equations (2.1a), (2.1b), and (2.1c) describe the DE and BC of the corresponding boundary value problem.