An adaptive Bernstein-Bézier finite element method for heat transfer analysis in welding

Abstract

We present a Bernstein–Bézier finite element method with local mesh refinement to simulate the heat transfer problem in the welding process. A novel constraint method is formulated to handle the incompatible degrees of freedom associated with the transitional elements during the local quad-tree/oct-tree refinement. A dynamic refinement strategy is proposed with a local L2 projection approach to transfer the control variables between different meshes, which enables the reduction of the model size, on the premise that good accuracy of the solution around the heat source is obtained. The cladding process during welding is simulated by the element addition technique. Exactness of the geometry is preserved by use of the rational form of the basis functions, which avoids frequent communication between the CAD and simulation when refining the mesh locally. The proposed method is investigated through examples, including convergence studies and industrial applications. The numerical results obtained using the proposed method and serendipity finite elements are compared in terms of accuracy and efficiency, revealing the potential of the proposed method for welding analysis.