Three-dimensional coupled dynamic thermoplastic boundary value issue for a transversely isotropic parallelepiped numerical solution

Abstract

This article is devoted to the numerical study of a three-dimensional coupled thermoplastic boundary value problem for a transversely isotropic parallelepiped. The coupled boundary value problem consists of an equation of motion, the thermoplastic constitutive relations for transversally isotropic bodies, the Cauchy relation, and the heat conduction equations with the corresponding initial and boundary conditions. For coupled dynamic boundary value problem, an explicit and implicit difference schemes are constructed. The finite-difference schemes are numerically solved, using the recurrent formulae and elimination method, corresponding to explicit and implicit schemes. The distribution of the displacement and temperature depending on time and coordinates are investigated. The propagation of the plastic zones also is considered. The coincidence of the numerical results obtained by the two methods is shown.