Quick and robust meshless analysis of cracked body with coupled generalized hyperbolic thermo-elasticity formulation

In this article, the MLPG method is applied to the generalized linear coupled thermoelectricity equations. Lord-Shulman modification with a relaxation time parameter is used in the hyperbolic heat conduction equations. A new linear test function which is zero on the boundaries of local test domains is introduced. The test function and its partial derivatives are determined by an exponential RBF approximation method. The approximation of test function and main variables are similar. For the construction of shape functions, neighbors of every point are determined based on the definition of the closest adjacent point pattern. Consequently, test function space becomes independent of trial function space. Direct interpolation method and penalty parameter are used to impose essential boundary conditions. The selection of appropriate parameters are demonstrated in two numerical examples. The small number of used points is the advantage of this method over the FEM that is shown in several examples. The accuracy of results is compared between the meshless method and different analytical and FE solutions. The effect of the relaxation time on SIF under thermal shock is discussed in a separate example. The comparison of meshless results with various examples shows that employed method is accurate and reliable.