The application of the meshless local Petrov-Galerkin method for the analysis of heat conduction and residual stress due to welding

The structural analysis of welding based on the thermal-elastic-plastic finite element method can lead to acceptable accuracy for the short time of welding. But if the welding time is long and the thermal source is moving, problems arise in the analysis due to the mesh re-generation. In this paper, in order to overcome the weak points of the finite element method, the meshless local Petrov-Galerkin (MLPG) method by using moving least square (MLS) has been used, based on the weak solution of equations governing the temperature field and the residual stress caused by welding. Without increasing the computational time, accuracy of the MLPG method has increased by developing this numerical method by taking into account the influence of MLPG parameters. To investigate the distance and density of nodal distribution, the relation between support domain size and quadrature domain size with distance between nodes is optimized. A good agreement is seen between the outputs of this numerical method to the hole-drilling strain-gauge method results. Therefore, it can be concluded that a new application based on thermoelastic-plastic equation for the MLPG method to numerical analysis of the residual stress due to welding is introduced.