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.

我们提出了一种采用局部网格细化的Bernstein–Bézier有限元方法，以模拟焊接过程中的传热问题。提出了一种新颖的约束方法来处理在局部四叉树/八叉树细化过程中与过渡元素相关的不兼容自由度。提出了具有局部L _2的动态优化策略投影方法可以在不同网格之间传递控制变量，从而可以减小模型尺寸，前提是要获得热源周围溶液的良好精度。焊接过程中的熔覆过程通过元素添加技术进行模拟。通过使用基本函数的有理形式，可以保持几何图形的精确性，从而避免了在局部细化网格时CAD与仿真之间的频繁交流。通过实例对提出的方法进行了研究，包括收敛性研究和工业应用。比较了使用该方法和偶然性有限元获得的数值结果的准确性和效率，揭示了该方法在焊接分析中的潜力。