SOLVING DYNAMIC COUPLED THERMOELASTICITY PROBLEMS

Abstract

This paper presents a numerical method for solving a coupled dynamic thermoelasticity problem based on the finite element method. The formulation combines the implicit Newmark scheme for the mechanical part with the Crank-Nicolson scheme for the thermal field.

The study is restricted to a one-dimensional model describing the thermomechanical behavior of a homogeneous elastic rod. The rod is subjected to non-stationary temperature effects that generate transient thermal stresses and deformations. The governing equations of motion and heat conduction are written in coupled form and reduced to their integral representation. Spatial discretization is carried out using the finite element method with linear elements. For time integration, the Newmark and Crank–Nicolson schemes are employed to ensure stability and accuracy. Special attention is given to the consistent treatment of thermomechanical coupling terms during discretization. Numerical modeling is performed for a rod clamped at one end and subjected to exponential cooling at the free end. The computed distributions of displacement, strain, stress, and temperature are analyzed in detail. The obtained results demonstrate agreement with the theoretical principles of classical dynamic thermoelasticity. This confirms the reliability of the proposed algorithm for solving coupled transient thermomechanical problems.