Wave packet enriched finite element for generalized thermoelasticity theories for thermal shock wave problems

Abstract

A unified enriched finite element (FE) formulation for two generalized thermoelsaticity theories is developed for the transient thermal shock problems in one and two dimensional domains. Both the displacement and temperature field interpolations are enriched with harmonic functions defined in the local element coordinates. The coupled field finite element equations are derived using the generalized Hamilton’s principle and solved directly in time domain using the standard Newmark-β time integration technique as opposed to the transform techniques usually adopted for thermal shock problems. The method is assessed in comparison with the Laplace transform based analytical solutions and FE solutions with dynamic meshing available in the literature. It is shown that the present solution with a static uniform mesh captures the sharp discontinuities in the temperature and displacement fields and the wave properties of heat conduction very accurately, practically eliminating the severe drawbacks of the conventional FE solutions such as the spurious undulations and flattening out, while maintaining better computational efficiency.