ABSTRACT
In this chapter, both the displacement and stress languages are used to present a number of closed-form solutions of three-dimensional isothermal and nonisothermal elastodynamics. The solutions of isothermal elastodynamics include (a) the plane progressive elastic waves in E3, (b) the elastic waves produced by a moving point force in E3, (c) the stress waves due to the initial stress and stress-rate fields in E3, and (d) the elastic waves generated by a pressurization of a spherical cavity in E3. A decomposition formula for the stress energy density of a progressive wave [see (a)] is obtained here for the first time. Also, the solutions (b) and (c) are obtained here for the first time. The solutions of nonisothermal elastodynamics include (1) a radially symmetric thermoelastic process corresponding to an instantaneous concentrated heat source in an infinite body, and (2) a radially symmetric thermoelastic process corresponding to an instantaneous spherical temperature inclusion in an infinite body. In addition, Saint-Venant’s principle of isothermal elastodynamics for a semi-infinite inhomogeneous anisotropic elastic cylinder, in terms of stresses, is formulated here for the first time. Problems on radial symmetry with solutions are presented, and their solutions are provided in the Solutions Manual.
