Computer simulation of the plane thermoelasticity problems: comparative analysis of coupled and uncoupled statements

A computer simulation of a plane problem of linear thermoelasticity was carried out in coupled and uncoupled statements for an inhomogeneous medium with a hole. In the case of uncoupled statement at first we solve an independent part of the thermoelasticity problem, the nonstationary heat conduction equation without taking into account the term responsible for the mechanical power of internal forces with the Dirichlet boundary conditions, and determine the distribution of temperature. Then we proceed to the static problem of thermoelastic stresses based on the equilibrium equations and the Duhamel-Neumann law with the Neumann boundary condition and a given temperature distribution. For the discretization of differential equations, we use the finite element method which is based on the construction of a vector-matrix system of equations formed on the weak form of thermomechanical equations under the condition of quasistatic deformation. The finite element method is implemented in the specially designed home-made code PIONER. As a test problem, we considered a problem of cooling a hollow cylinder with prescribed temperatures and stresses on the inner and outer surfaces. The problem was solved using eight-node finite elements with a reduced biquadratic approximation of geometry and displacements within a plane strain model. Numerical experiments have shown that under certain restrictions that simplify the problem: the absence of mass forces, initial stresses, heat sources and convection on a part of the surface, for the given class of problems, the distribution of displacements, stresses, and temperature in coupled problems is close to that in uncoupled formulation. The obtained results are consistent with the fact that in the linear thermoelasticity the term in the heat conduction equation, responsible for the mechanical power of internal forces, has no significant effect on the solution of the thermoelastic system.