The meshless local Petrov-Galerkin method for the analysis of heat conduction due to a moving heat source, in welding

Abstract

Recently, the efficiency of computer modeling and simulations has been improving dramatically. Consequently, the structural analysis of welding phenomena based on thermal–elastic–plastic finite element method (FEM) can be performed with a good accuracy in a short time. However, if the model to be analyzed is large and it has a complex shape, problems might occur with preprocessing, such as the mesh generation process which is very time consuming. To overcome these problems, meshless methods such as the meshless local Petrov-Galerkin (MLPG) method have been developed. In this study, the MLPG method is applied to heat conduction analysis, in the problem of bead-on-plate welding (a moving heat source problem), and the fundamental properties (influence of MLPG parameters and nodal point density, etc.) of the method are investigated to verify the applicability of the proposed method. As a result, it is clearly shown that when the number of nodal points is sufficiently high, the influence of the MLPG parameters is small. In addition, an adaptive analytical method using the MLPG is proposed, which includes the addition and elimination of nodal points. From the results of the MLPG method using the adaptive method, it is found that a very high accuracy can be obtained. In this method, the nodal point distribution can be set relatively freely. Thus, the use of the MLPG method in welding analysis is expected to grow in the future.