模糊-随机环境下连续体结构可靠性拓扑优化方法研究

Most of the existing reliability based topology optimization algorithms are tailored for structures with random uncertainty. However, a large number of fuzzy uncertainties exist in structural systems in engineering simultaneously. To study the reliability based topology optimization algorithm in presence of fuzzy-random uncertainties, this project is devoted to establishing reliability based topology optimization algorithm for the fuzzy-random structure based on maintaining the physical attributes of fuzzy and random parameters. By introducing probability transition model with a standard uniform distribution into the membership level of the fuzzy input parameter, a uniform reliability model is established. Meanwhile, through establishing the structural parameterized model based on the finite element analysis, decoupling reliability constraint and topological optimization by building the equivalence relation between fuzzy-random reliability constraint and performance function constraint, and combining with the variable density method of topological optimization, the global reliability based topology optimization algorithm is established. According to the reliability sensitivity and importance measure analysis of the uncertainties, the dimensions of designed variables can be decreased. This means that it is efficient to search the global topology optimal solution in the degradation low-dimensional feasible region of design variables. Based on the established topology optimization algorithm in presence of fuzzy-random uncertainties, a general reliability based topology optimization software system for fuzzy-random continuum structures is constructed. The software system is then applied to design the stiffened thin-walled structure. This can validate the effectiveness and versatility of the established reliability based topology optimization algorithm and software system. This project contributes significantly to the improvement of reliability based topology optimization theory and gives impetus to its further engineering application.

目前已有的结构可靠性拓扑优化方法绝大多数是针对随机不确定性的，而在实际工程中同时存在着大量的模糊不确定性。本项目旨在探索结构参数同时具有模糊-随机不确定性的可靠性拓扑优化方法。通过对模糊变量的隶属水平引入[0,1]区间均匀分布的概率转换模型，建立模糊-随机可靠性分析的统一模型。基于有限元分析建立结构参数化模型，通过建立模糊-随机可靠性约束与功能函数约束的等价关系，将模糊-随机可靠性分析与拓扑优化过程进行解耦，同时融合拓扑优化的变密度法，建立模糊-随机环境下的可靠性拓扑优化的全局求解方法。通过不确定性灵敏度和重要性测度分析，合理地降低设计变量的维数，进而高效地在可行域内搜索全局最优拓扑解。将所建立模糊-随机环境下的结构可靠性拓扑优化方法编制成通用软件，并针对加筋类薄壁结构进行可靠性拓扑优化分析，考核所建方法的有效性和通用性。本项目对完善可靠性拓扑优化的理论及推动其工程应用具有重要意义。

复杂结构系统的优化设计过程中，除了要面临广泛存在的随机不确定性外，还需要面临着由于数据缺乏、专家信息的存在以及结构自身物理特性决定的模糊不确定性。模糊-随机混合不确定性环境下的可靠性拓扑优化已成为学术界和工程界的难点问题。本项目首先通过对模糊变量的隶属水平引入概率转化模型，揭示了模糊不确定性的传播机理，建立了基于概率视角的模糊可靠性理论模型。基于上述模型进一步建立了模糊随机混合不确定性的传播模型，并给出了所建模型的物理意义，解决了复杂结构模糊环境可靠性分析理论不完备的问题，为传统经典可靠性评估分析模型重要补充，促进了可靠性理论体系完善与发展；在此基础上，构建了模糊、模糊-随机不确定性的重要性测度理论模型和高效求解算法，以识别混合不确定性对结构输出性能的影响程度，解决了混合不确定性不同空间无法横向比较的难题，补充了不确定性重要性测度的理论体系，同时为复杂系统的可靠性设计提供指导方向；针对随机不确定性环境下结构可靠性拓扑优化，建立了水平集-随机可靠性拓扑优化方法，该方避免在拓扑优化迭代时进行复杂的可靠性分析循环，提高了求解效率，并保证了拓扑结构的光滑性，避免出现拓扑优化中常见的数值问题，整体上提高了可靠性拓扑优化的计算效率及优化效果；针对非概率不确定性环境下结构可靠性拓扑优化，建立了水平集-区间可靠性拓扑优化方法，提出了QMU置信因子度量区间结构的可靠性拓扑优化的方法，避免了传统优化方法计算精度差和优化结果不稳定的问题，为可靠性拓扑优化问题的研究提供了新思路；在上述获得的理论模型和算法的基础上，编制了适用于XX装备的软件程序。已发表期刊论文7篇，其中SCI期刊论文4篇，参加国内外学术交流7人次，培养多名XX装备的科研骨干。本项目完成了项目申请时的预期目标。