Chapter 6 - Strain Energy and Related Principles

Abstract

Before proceeding to the solution of specific elasticity problems we wish to explore the associated concepts of work and energy. Boundary tractions and body forces will do work on an elastic solid and this work will be stored inside the material in the form of strain energy. For the elastic case, removal of these loadings will result in complete recovery of the stored energy within the body. Development of strain energy concepts will yield new and useful information not found by other methods. This study will also lead to some new energy methods or principles that provide additional techniques to solve elasticity problems. In some sense these methods may be thought of as replacements of particular field equations that have been derived previously. For problems in structural mechanics involving rods, beams, plates, and shells, energy methods have proven to be very useful in developing the governing equations and associated boundary conditions. These schemes have also provided a method to generate approximate solutions to elasticity problems. More recently, particular energy and variational techniques have been used extensively in the development of finite and boundary element analysis. Our presentation here will only be a brief study on this extensive subject.