Asymptotic approach to transient thermal shock problem with variable material properties

In this paper, an asymptotic approach is proposed to solve the transient thermal shock problem with variable material properties. The governing equations of isotropic elastic medium with temperature-dependent properties are derived in the context of the Lord–Shulman generalized theory of thermoelasticity, where the higher-order expansion with respected to increment temperature of the Helmholtz free energy is used to describe the relation of each material parameter with real temperature. Then, the layer method is used to deal with the variation of material properties with real temperature, and a system with discrete linear equations is obtained by ignoring some higher-order quantities. This system is then solved analytically by the integral transform method, where the Laplace transform technique and its limit theorem is employed to deal with these linear partial differential equations. This asymptotic approach is applied to solve the thermoelastic response of a thin plate with variable material properties. The asymptotic solutions of the displacement, temperature and stresses, induced by a sudden temperature rise at the boundary of thin plate, are obtained. The corresponding results for each physical field are discussed, as well as the comparison with the results obtained from the case with constant properties is also conducted to evaluate the effect of temperature dependency of material properties.