Numerical Solution of Coupled Thermo-Elastic-Plastic Dynamic Problems

Abstract

The article considers a numerical method for solving a two-dimensional coupled dynamic thermoplastic boundary value problem based on deformation theory of plasticity. Discrete equations are compiled by the finite-difference method in the form of explicit and implicit schemes. The solution of the explicit schemes is reduced to the recurrence relations regarding the components of displacement and temperature. Implicit schemes are efficiently solved using the elimination method for systems with a three diagonal matrix along the appropriate directions. In this case, the diagonal predominance of the transition matrices ensures the convergence of implicit difference schemes. The problem of a thermoplastic rectangle clamped from all sides under the action of an internal thermal field is solved numerically. The stress-strain state of a thermoplastic rectangle and the distribution of displacement and temperature over various sections and points in time have been investigated.