Thermoelastic body model in nonlinear response environment, mathematical model and approximation, Chapter A17,

Abstract

Design and approximation of the mathematical model of the thermoelastic body?environment set within framework of the linearized theory of the coupled thermoelasticity has been discussed. Corresponding response function has included nonlinear terms. Analysis of the model correctness has been restricted only to the coercive cases and 1D bodies?beams, plates; bilateral and unilateral nonlinear one-parametric models have been used to represent response of subsoil parts, two-parametric models can represent response of supports. Generalized formulation of the problem has been introduced; semidiscrete and space approximation has been defined by Rothe method of discretization in time, and by FEM, generating computational model of the set. The statements on existence and uniqueness of the model problem solution, based on a-priory estimations, approximation, including convergence results are also introduced. Model generalization to semicoercive cases and multiparametric response functions is also mentioned.