A parametric study of the MLPG method for thermo-mechanical solidification analysis

Based on the meshless local Petrov-Galerkin (MLPG) method, a thermo-elasto-plastic analysis of solidification problem is presented. The effect of significant parameters of the MLPG method, including the size and shape of sub-domain and support domain, nodal arrangement, nodal density and Gaussian points on the solution accuracy of the problems is investigated to determine their optimal values. The local weak forms are derived by considering a Heaviside step function as the test function. To interpolate the solution variables, the moving least-squares (MLS) approximation is applied. Using the effective heat capacity method, thermal analysis of the solidification process is performed. The von-Mises yield criterion and isotropic hardening model are employed for the elasto-plastic behavior, and material parameters are assumed to be temperature-dependent. To demonstrate the capability of the present method in solving solidification problems, the obtained results have been compared with the analytical and accurate finite element method solutions.