The virtual node polygonal element method for nonlinear thermal analysis with application to hybrid laser welding

Abstract

The nonlinear heat transfer process occurring during hybrid laser welding was simulated using the Virtual-node Polygonal Element (VPE) method within the framework of the Finite Element Method (FEM). To achieve robustness in large-scale welding simulations, a dynamic mesh refinement with quadtree and octree data structures was used in the welding region. Accuracy, convergence and efficiency were verified by solving two and three dimensional problems. It is found that the present VPE can successfully simulate the hybrid laser welding process with good accuracy and convergence. The adaptive refined mesh box can synchronously move with the welding heat source, which dramatically reduces the number of field nodes. Compared with the standard FEM,the VPEM requires only approximately 42% of the total degrees of freedom used in standard FEM for the same accuracy. Furthermore, we compare the computational cost and accuracy of the method to that of the finite element method, the edge based virtual node polygonal element/virtual node method, the edge-based Smoothed Point Interpolation Meshless Method (ES-PIM), the edge-based Element (ES-PIM) the Element Free Galerkin (EFG) method and the Meshless Local Petrove-Galerkin Petrov–Galerkin (MLPG) method. Compared to all those methods, the proposed scheme is found competitive in terms of computational cost versus accuracy, and benefit from a simple implementation.