ABSTRACT
When the data of an initial-boundary value problem of elastodynamics depend on a single space variable and on time t, a solution to the problem satisfies the one-dimensional field equations subject to suitable initial and boundary conditions. In this chapter, a number of typical one-dimensional solutions of homogeneous isotropic isothermal and nonisothermal elastodynamics are obtained in a closed-form using the Laplace transform technique. The isothermal solutions include (a) one-dimensional stress waves in an infinite or semiinfinite elastic solid subject to the initial stress and stress-rate fields, and (b) one-dimensional stress waves in a semispace subject to a uniform dynamic boundary pressure. The nonisothermal solutions cover (1) dynamic thermal stresses in an infinite or semi-infinite elastic solid subject to a plane instantaneous heat source, and (2) dynamic thermal stresses in a semispace subject to a sudden heating of the boundary plane. Also, the solution (1) is applied to obtain the integral representation of a dynamic thermoelastic response of a semispace to a laser pulse. The chapter ends with problems, and their solutions are provided in the Solutions Manual.
