Hybrid Laplace transform-finite element method to a generalized electromagneto-thermoelastic problem

A finite element method based on the Laplace transform technique is developed for a two-dimensional problem in electromagneto-thermoelasticity. The problem is in the context of the following generalized thermoelasticity theories: Lord–Shulman’s, Green–Lindsay’s, the Chandrasekharaiah–Tzou, as well as the dynamic coupled theory. The Laplace transform method is applied to the time domain and the resulting equations are discretized using the finite element method. The inversion process is carried out using a numerical method based on a Fourier series expansions. Numerical results compared with those given in literature prove the good performance of the used method. It is demonstrated that the Chandrasekharaiah–Tzou theory can be considered as an extension of Lord–Shulman’s, and the generalized heat conduction mechanism is completely different from the classical Fourier’s in essence.