Shock-induced thermoelastic wave propagation analysisin a thick hollow cylinder without energy dissipation using mesh-free generalized finite difference (GFD) method

Abstract

The main objective of this article is the exploitation of the generalized finite difference method to study the thermoelastic wave propagation, that is, the dynamic behaviors of displacement and temperature field in a thick hollow cylinder. The thermoelasticity governing equations are derived based on Green–Naghdi coupled thermoelasticity theory (without energy dissipation). The generalized finite difference (GFD) method is used to approximate the space variables, and Newmark finite difference (NFD) is employed to obtain the behaviors of parameters in time domain. The time histories of displacement and temperature fields across the thickness of the cylinder are obtained and the propagations of thermal and elastic waves are illustrated at various times. Using the GFD method, the wave front in temperature and elastic domains can be tracked, and the comparison between results based on GFD and other numerical methods shows very good agreement. The application of GFD method in coupled thermoelasticity problems has a high capability because it does not require a mesh generation. A comparison between the presented mesh-free GFD method and meshless local Petrov–Galerkin (MLPG) method shows a good agreement of the results.