ABSTRACT
In the theory of elasticity, there is a class of problems in which an elastic state depends on two space variables only. For example, such a situation ariseswhen a homogeneous isotropic infinitely long elastic cylinder is subject to a constant normal pressure on its lateral surface. In this chapter, the two-dimensional elastic states as well as the two-dimensional elastodynamic processes are discussed. In particular, a plane strain state and a generalized plane stress state of homogeneous isotropic elastostatics are defined and the associated field equations are obtained. Also, a plane strain process and a generalized plane stress process of homogeneous isotropic elastodynamics are defined, and the associated field equations in terms of the displacements and stresses are obtained. The governing field equations of a nonisothermal two-dimensional elastodynamics are also discussed. The chapter contains a number of worked examples, as well as end-of-chapter problems that cover the general complete solutions of homogeneous isotropic two-dimensional elastostatics and elastodynamics, including a general solution to the stress equation of two-dimensional elastodynamics. The solutions to problems are provided in the Solutions Manual.
