Abstract In this paper, an adaptive refinement technique using the scaled boundary finite element method (SBFEM) is proposed. The salient feature of this technique is that it is not required to regenerate the mesh for the whole model during the iterations. To this end, a local mesh refinement strategy is implemented based on a polytree algorithm in three dimensions, which can be applied to polyhedral elements with arbitrary number of nodes, edges and faces. These elements constructed by the SBFEM can be used in analysis with their boundaries discretized only, which reduce the difficulty to connect elements with different sizes. An explicit residual based error indicator is developed using the discontinuity of the stress field to guide the adaptive mesh refinement. The accuracy and efficiency of the proposed method are demonstrated using five numerical examples, including complex geometry and stress singularity.

中文翻译：

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在 3D 中使用缩放边界有限元方法进行自适应分析

摘要 在本文中，提出了一种使用缩放边界有限元方法（SBFEM）的自适应细化技术。这种技术的显着特点是不需要在迭代过程中为整个模型重新生成网格。为此，基于三维多树算法实现了局部网格细化策略，该策略可应用于具有任意数量节点、边和面的多面体元素。这些由 SBFEM 构建的单元可用于分析，仅将其边界离散化，从而降低了连接不同尺寸单元的难度。使用应力场的不连续性来指导自适应网格细化，开发了基于显式残差的误差指标。