6 - Strain Energy and Related Principles

Abstract

This chapter explores the associated concepts of work and energy. Boundary tractions and body forces do work on an elastic solid, and this work is stored inside the material in the form of strain energy. For the elastic case, the removal of these loadings results in a complete recovery of the stored energy within the body. The development of strain energy concepts can yield new and useful information that cannot be found by other methods. This study also leads to some new energy methods or principles that provide additional techniques to solve elasticity problems. These methods may be thought of as replacements of particular field equations that have been previously derived. For problems in structural mechanics involving rods, beams, plates, and shells, energy methods have proved to be very useful in developing the governing equations and associated boundary conditions. These schemes have also provided a method to generate approximate solutions for elasticity problems. More recently, particular energy and variational techniques have been used extensively in the development of finite and boundary element analysis.