A body-fitted adaptive mesh and Helmholtz-type filter based parameterized level-set method for structural topology optimization

IF 3.8 2区 工程技术 Q1 ENGINEERING, MECHANICAL Acta Mechanica Sinica Pub Date : 2024-09-21 DOI:10.1007/s10409-024-24119-x
Yijie Lu  (, ), Xueying Chang  (, ), Zhengwei Zhang  (, ), Hui Liu  (, ), Yanguo Zhou  (, ), Hao Li  (, )
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Abstract

Parameterized level-set method (PLSM) has been proposed and developed for many years, and is renowned for its efficacy in addressing topology optimization challenges associated with intricate boundaries and nucleation of new holes. However, most pertinent investigations in the field rely predominantly on fixed background mesh, which is never remeshed. Consequently, the mesh element partitioned by material interface during the optimization process necessitates approximation by using artificial interpolation models to obtain its element stiffness or other properties. This paper introduces a novel approach to topology optimization by integrating the PLSM with body-fitted adaptive mesh and Helmholtz-type filter. Primarily, combining the PLSM with body-fitted adaptive mesh enables the regeneration of mesh based on the zero level-set interface. This not only precludes the direct traversal of the material interface through the mesh element during the topology optimization process, but also improves the accuracy of calculation. Additionally, the incorporation of a Helmholtz-type partial differential equation filter, relying solely on mesh information essential for finite element discretization, serves to regulate the topological complexity and the minimum feature size of the optimized structure. Leveraging these advantages, the topology optimization program demonstrates its versatility by successfully addressing various design problems, encompassing the minimum mean compliance problem and minimum energy dissipation problem. Ultimately, the result of numerical example indicates that the optimized structure exhibits a distinct and smooth boundary, affirming the effective control over both topological complexity and the minimum feature size of the optimized structure.

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基于体拟合自适应网格和亥姆霍兹型滤波器的参数化水平集方法,用于结构拓扑优化
参数化水平集法(PLSM)已提出并发展多年,因其在解决与错综复杂的边界和新孔成核相关的拓扑优化难题方面的功效而闻名。然而,该领域的大多数相关研究都主要依赖于固定的背景网格,而这种网格是永远不会重修的。因此,在优化过程中,按材料界面划分的网格元素必须使用人工插值模型进行近似,以获得其元素刚度或其他属性。本文介绍了一种拓扑优化的新方法,它将 PLSM 与体拟自适应网格和 Helmholtz 型滤波器相结合。首先,将 PLSM 与体拟合自适应网格相结合,可实现基于零水平集界面的网格再生。这不仅避免了在拓扑优化过程中通过网格元素直接遍历材料界面,还提高了计算精度。此外,亥姆霍兹型偏微分方程滤波器的加入,仅仅依靠有限元离散化所必需的网格信息,就能调节拓扑复杂性和优化结构的最小特征尺寸。利用这些优势,拓扑优化程序成功解决了各种设计问题,包括最小平均顺应性问题和最小能量耗散问题,展示了其多功能性。最终,数值示例结果表明,优化后的结构呈现出明显而平滑的边界,证实了对拓扑复杂性和优化结构最小特征尺寸的有效控制。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Acta Mechanica Sinica
Acta Mechanica Sinica 物理-工程:机械
CiteScore
5.60
自引率
20.00%
发文量
1807
审稿时长
4 months
期刊介绍: Acta Mechanica Sinica, sponsored by the Chinese Society of Theoretical and Applied Mechanics, promotes scientific exchanges and collaboration among Chinese scientists in China and abroad. It features high quality, original papers in all aspects of mechanics and mechanical sciences. Not only does the journal explore the classical subdivisions of theoretical and applied mechanics such as solid and fluid mechanics, it also explores recently emerging areas such as biomechanics and nanomechanics. In addition, the journal investigates analytical, computational, and experimental progresses in all areas of mechanics. Lastly, it encourages research in interdisciplinary subjects, serving as a bridge between mechanics and other branches of engineering and the sciences. In addition to research papers, Acta Mechanica Sinica publishes reviews, notes, experimental techniques, scientific events, and other special topics of interest. Related subjects » Classical Continuum Physics - Computational Intelligence and Complexity - Mechanics
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