Singularly Perturbed Solutions for a Class of Thermoelastic Weakly Coupled Problems

Abstract Based on the basic equation of Green Lindsay (G-L) theory, the thermoelastic weak coupling problem under the basic equation is discussed, that is, two thermal relaxation parameters are added to the constitutive equation, the influence of the coupling term on the temperature field and elastic field is considered, and the asymptotic solution of the governing equation is constructed. Firstly, in order to obtain the asymptotic solution, the singularly perturbed expansion method is used.Then,combined with the corresponding boundary conditions, the partial differential equation method is used to solve the external solution and the boundary layer correction term. Secondly, in the case of weak coupling, the uniformly efficient estimation of the remainder of the asymptotic solution is obtained by using Gronwall inequality, so as to obtain the uniformly efficient of the formal asymptotic solution. Finally, the first term of the asymptotic solution is numerically analyzed by using the singularly perturbed numerical method. The present work will be conducive to the analysis of thermoelastic processes and numerical simulation of different materials in the case of weak coupling.