A Unified Generalized Thermoelasticity Formulation; Application to Thick Functionally Graded Cylinders

Abstract

In this article a new unified formulation for the generalized coupled thermoelasticity theories is presented. The generalized coupled thermoelasticity theories proposed by Lord–Shulman, Green–Lindsay, and Green–Naghdi are combined into a unified formulation introducing the unified parameters. The formulation is given for the general anisotropic heterogeneous linear thermoelastic materials and then is reduced to the system of equations for the isotropic heterogeneous materials. As an example, a functionally graded cylinder is considered and the thermoelastic waves based on the new unified formulation, using the generalized theories, are obtained and discussed. Utilizing the transfinite element method, the equations for a long thick circular cylinder are solved in the Laplace domain and the results are inverted to the real time domain using a numerical inversion technique of the Laplace transform. The results for the propagation of thermoelastic waves based on the Lord–Shulman, Green–Lindsay, and Green–Naghdi models are derived and compared.