Formulation of Problems of Elasticity

Abstract

In this chapter both the basic boundary value problems of elastostatics and initial-boundary value problems of elastodynamics are recalled; in particular, the mixed boundary value problems of isothermal and nonisothermal elastostatics, as well as the pure displacement and the pure stress problems of classical elastodynamics are discussed. The Betti reciprocal theorem of elastostatics and Graffi’s reciprocal theorem of elastodynamics together with the uniqueness theorems are also presented. An emphasis is made on a pure stress initial-boundary value problem of incompatible elastodynamics in which a body possesses initially distributed defects.