显式几何描述下考虑非概率不确定性的连续体结构拓扑优化研究

Structural topology optimization considering uncertainty has become a hot research topic due to the existence of scattering of material properties, manufacture error, load perturbation and the limitation of human knowledge. However, for topology optimization of continuum structures under non-probabilistic uncertainty description, which has immense potential in engineering application, some challenging problems such as fail-safe design and optimization, multi-scale optimization, the issue of the confidence of an optimal solution and the computability of the corresponding optimization formulations have not been well addressed yet. In this project, it is intended to resolve the aforementioned challenging problems from a new perspective through describing the structural geometry/topology in an explicit way, which is completely different from the geometry description schemes in traditional topology optimization frameworks. The theories and methods developed in this project can not only help advance the frontier of structural topology optimization but also provide efficient tools for the solution of practical engineering problems.

由于材料性能分散、制造误差、荷载波动、认知能力有限等因素的存在，近年来考虑不确定性的结构拓扑优化研究成为了一个前沿研究热点。但对于具有重要应用背景的、考虑非概率描述不确定性的连续体结构拓扑优化，仍有诸如失效-安全设计、多尺度优化设计、优化结果的可置信性以及优化模型的可计算性等挑战性问题没有得到很好的解决。在本项目中，我们拟突破传统的基于隐式几何/拓扑描述的拓扑优化框架，转而从结构几何/拓扑显式描述这一全新思路出发，对考虑不确定性的连续体结构拓扑优化开展系统研究，在此基础上发展优化理论和数值方法，以期为破解前述挑战性问题提供有效解决方案。本项目研究对于推进结构拓扑优化研究的前沿进展以及工程应用均具有重要意义。

针对具有重要应用背景的、考虑非概率描述不确定性的连续体结构拓扑优化问题，基于结构几何/拓扑显式描述这一全新思路开展了系统研究，通过发展相关的基础理论与关键算法，为解决了高鲁棒性多尺度点阵结构优化设计、结构失效-安全性能优化以及考虑不确定性的结构极值响应分析中的一些难点问题提供了新思路，推进了不确定性优化与结构拓扑优化交叉领域的前沿进展，为运用拓扑优化方法进行具有高鲁棒/可靠性的创新产品和高端装备设计提供了科学基础和方法支撑。相关研究工作已在计算力学顶级期刊《Computer Methods in Applied Mechanics and Engineering 》（CMAME）、《International Journal for Numerical Methods in Engineering》（IJNME）等上发表，代表性论文引用量位居所发表期刊的前列。项目成果还为国家重点发展装备研制提供了重要支撑。