ABSTRACT
This chapter focuses on the approximate solution of physical problems using variational methods. It considers the techniques for developing continuous approximate solutions based on variational methods. Similar to the solutions based on the method of weighted residuals, variational based approximations are continuous within the domain Ω and along its boundary Γ. As such, they also overcome the fundamental shortcoming of discrete approaches such as the finite difference method. In the analysis of continuous systems using variational methods, certain restrictions must be, placed on the primary dependent variables ϕ. The statement of a variational principle implicitly contains the rules for evaluating the functional I for an admissible function ϕ. To illustrate the application of the principle of minimum potential energy, it derives the equations governing the transverse displacement of a Bernoulli-Euler beam. The chapter considers a general approach for generating approximate solutions of physical problems by rendering the functional stationary.
