ABSTRACT
The variational or energy methods of structural mechanics have been important tools for the development of basic equations for more than a century. In particular, they have been useful, and sometimes essential, for the derivation of governing differential equations of motion. It has long been recognized that the fundamental relationships of the previous chapter, e.g., the equations of equilibrium or the strain-displacement equations, have equivalent energy representations. Now, the variationally based integral forms of the basic equations are emerging as important foundations for computational techniques of structural mechanics. This chapter considers the classical variational principles of the theory of elasticity and then treats the generalized variational principles which are particularly helpful in achieving a better understanding of the interrelationships between the various methods of structural mechanics. The study of variational methods should begin with a brief look at the basics of the calculus of variations, a branch of mathematics dealing with the extremal values of integrals. Numerous sources covering the calculus of variations are available; a short summary is provided in Appendix I.
