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| 基于可靠性指标法的连续体结构可靠性拓扑优化 |
| Reliability topology optimization of continuum structure based on reliability index method |
| 投稿时间：2023-09-04 修订日期：2023-10-12 |
| DOI： |
| 中文关键词: 可靠性指标法 移动渐进性法 变密度法 可靠性拓扑优化 |
| 英文关键词:Reliability index method Moving Progressive Method Variable density method Reliability based topology optimization |
| 基金项目:国家自然科学基金资助项目(11202116, 12072242, 12372200) |
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| 中文摘要: |
| 实际工程中，结构面临着来自多种复杂环境下不确定性因素的影响，导致结构性能的变化，传统拓扑优化未考虑这些因素的影响。因此，本文提出了一种可靠性指标法(RIA)的可靠性拓扑优化方法，用于连续体结构拓扑优化。旨在考虑结构可靠性的情况下，使得结构最终拓扑构型的体积分数最小。本文将载荷作为不确定量，通过可靠性指标法寻找极限状态点；然后基于双向渐进结构优化法(BESO)，以结构体积为目标函数，可靠性指标作为约束条件，采用移动渐近线法（MMA）进行优化。通过对不同的数值案例（如简支梁、悬臂梁、L型梁）进行分析，同时研究了目标可靠度和标准差对结构性能的影响，还考虑了多工况、载荷方向不确定性等情况。研究结果表明，本文方法能够高效地找到极限状态点，相较于传统拓扑优化方法所得的拓扑构型更加可靠。 |
| 英文摘要: |
| In practical engineering, the structure is faced with the influence of uncertain factors from a variety of complex environments, which leads to the change of structural performance. Traditional topology optimization does not consider the influence of these factors. Therefore, this paper proposes a reliability index method ( RIA ) reliability topology optimization method for continuum structure topology optimization. The aim is to minimize the volume fraction of the final topological configuration of the structure considering the structural reliability. In this paper, the load is taken as the uncertainty, and the limit state point is found by the reliability index method. Then, based on the bi-directional evolutionary structural optimization ( BESO ) method, the moving asymptote method ( MMA ) is used to optimize the structural volume as the objective function and the reliability index as the constraint condition. Through the analysis of different numerical cases ( such as simply supported beam, cantilever beam, L-shaped beam ), the influence of target reliability and standard deviation on structural performance is studied, and the uncertainty of multiple working conditions and load direction is also considered. The results show that the proposed method can efficiently find the limit state points, which is more reliable than the topological configuration obtained by the traditional topology optimization method. |
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