Verification and validation of methods of numerical simulation of thermoelastic deformation of a solid

Abstract

Related non-stationary formulations of thermoelasticity problems arise in many fields of science and engineering. Analytical solutions are obtained only under significant assumptions, including reduction in the dimensionality of the problem, so numerical methods are required for applied problems, along with those software packages that check reliability procedures of verification and
validation. Verification is understood as checking the correctness of hypotheses and the formulation of the mathematical formulation, setting correct initial and boundary conditions, choosing a discrete analog and a numerical solution method, taking into account sources of errors and faults. The verification is confirmed by a sufficiently accurate correspondence of the numerical solution to the reference model. The relevance lies in the choice of a suitable reference model. In the present work, the reference model for the thermoelasticity problem is the classical Thompson formula, which describes the temperature change during elastic deformation of a solid body. The error of the numerical solution for the reference problem was of the order of 1% for five characteristic strain values from 0.01 to 0.05. Validation complements the verification procedure and is based on comparison with reliable experimental data or, in their absence, with known analytical solutions. The aim of the work is to carry out verification and validation procedures for the numerical solution of the unsteady problem of thermoelasticity of a deformable solid. The finite element method in the Comsol Multiphysics application package was used. A satisfactory correspondence between the numerical solution and the known analytical solution for the nonlinear heat conduction equation was obtained.