Modeling of Moving Heat Sources Using Meshless Element Free Galerkin Method

Many processes such as fusion welding, heat treatment or line heating forming involve the use of moving heat sources. The studies of Rosenthal on the heat distribution during arc welding and cutting process are considered as the earliest work to solve analytically the problem of moving heat sources. Based on the equation system for the heat conduction of solids, he introduced the moving coordinate system to develop solutions with some assumptions for moving heat sources which were successfully applied for different welding and metal heat treatment processes. The works of Rosenthal established the foundation for the way to solve this type of problem in many researches in this field later by both the analytical and numerical methods. The modeling of moving heat sources and deformation of the workpieces using the finite element method has been studied by many authors. To have a precise prediction this method requires a fine mesh for the heat sources as well as when the deformation is critical. Particularly when elements distorted, remeshing is required to avoid the problem of singularity. Adaptive mesh refinement is generally the solution for these problems. However this method takes a lot of time for remeshing and projecting results on new meshes. Meshless methods are new trends recently developed to avoid these difficulties thanks to node-based approximation rather than element-based approximation. In this paper, the modeling of moving heat sources using Meshless Element Free Galerkin method (MEFG) was studied. The moving least square approximant (MLS) is used in this study. Numerical results of temperature distribution are compared with the Rosenthal solution and experimental results of line heating performed with a laser moving heat source. Figure 1 shows the distribution of temperatures of the Rosenthal problem obtained from the MEFG code.

Figure 1. Distribution of temperatures with MEFG method.