This paper presents an efficient solution for designing the topology of structures that can withstand dynamic loads. The method, called image/stereolithography (STL)-based adaptive scaled boundary finite element (SBFE), is a novel approach to topology optimization (TO) that is particularly effective for designing two/three-dimensional structures. The SBFE-based TO algorithm adopts a bi-evolutionary structural optimization (BESO) approach, which utilizes image/STL-based procedures to automatically adapt meshes and minimize mechanical compliance under varying volume fractions in the time domain. A key advantage of this approach is that it uses images of TO responses, rather than specific error functions, to guide the automatic adaptive mesh schemes. The method also incorporates a quadtree/octree mesh refinement to address the problem of hanging nodes, ensuring fast mesh convergence during the optimization process. Furthermore, a high-order implicit time integration technique provides a close approximation of equivalent static loads, allowing for the accurate mapping of displacement fields under actual dynamic responses at each time step. The effectiveness of this method is demonstrated through a variety of numerical examples and benchmarks.

中文翻译：

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基于动态响应的二维/三维结构拓扑优化的自适应尺度边界有限元方法

本文提出了一种有效的解决方案，用于设计可承受动态载荷的结构拓扑。该方法称为基于图像/立体光刻 (STL) 的自适应缩放边界有限元 (SBFE)，是一种新颖的拓扑优化 (TO) 方法，对于设计二维/三维结构特别有效。基于 SBFE 的 TO 算法采用双进化结构优化 (BESO) 方法，该方法利用基于图像/STL 的程序自动适应网格，并最大限度地减少时域中不同体积分数下的机械柔量。这种方法的一个关键优点是它使用 TO 响应图像而不是特定的误差函数来指导自动自适应网格方案。该方法还结合了四叉树/八叉树网格细化来解决悬挂节点问题，确保优化过程中网格快速收敛。此外，高阶隐式时间积分技术提供了等效静载荷的近似近似，从而可以在每个时间步长的实际动态响应下精确映射位移场。通过各种数值示例和基准证明了该方法的有效性。