Introduction

The theory of elasticity is the basis for several engineering theories which, in turn, are applied to mechanical and structural design. The basic components of the elasticity problem are often designated as equilibrium, compatibility, and a constitutive law. The equilibrium equations represent a statement of Newton’s laws, which are restricted here to the static case. The compatibility conditions express the kinematic relationships between strains and displacements, and the constitutive law embodies the stress-strain behavior of the material which is presumed here to be linear elastic. In general, this set of basic components may be collected as a set of differential equations or as an energy principle. The simultaneous satisfaction of each component of the elasticity problem often is foreboding from the mathematical standpoint; therefore, engineers have naturally looked to simplifications and approximations.