ABSTRACT
In this chapter, a number of general solutions of the homogeneous isotropic elastostatics and elastodynamics are presented. The general solutions to the displacement equation of equilibrium include (i) Boussinesq-Papkovitch-Neuber representation in terms of the potentials satisfying Poisson’s equations, and (ii) Boussinesq-Somigliana-Galerkin representation in terms of the potential satisfying a biharmonic equation; and it is shown that both solutions (i) and (ii) are complete in the sense that the potentials exist for any displacement that satisfies the displacement equation of equilibrium. For the displacement equation of homogeneous isotropic elastodynamics, a complete Green-Lamé representation in terms of the potentials satisfying the wave equations, and a complete Cauchy-Kovalevski-Somigliana representation in terms of the vectorial potential satisfying a biwave equation, are discussed. The chapter also contains worked examples and end-of-chapter problems, including the one related to the stress equations of homogeneous isotropic elastodynamics for which a complete Galerkin-type tensor solution is to be obtained. As in the previous chapters, the solutions to problems are given in the Solutions Manual.
