基于子集模拟的连续体结构可靠性拓扑优化全局方法研究

In order to effectively improve the computational efficiency and engineering applicability of the reliability based topology optimization, the project aims to develop the global reliability based topology optimization algorithm with both high efficiency and precision and to construct the general reliability based topology optimization software platform for engineering structure design. On the basis of the structural parameterized model, considering the uncertainties of engineering structure, directly integrating probability analysis and optimization design as single loop optimization strategy, combining with the variable density method of continuum topological optimization, the global reliability based topology optimization algorithm utilizing subset simulation is established to search the global topology optimal solution with a higher probability in the degradation low-dimensional feasible region of design variables and to raise the optimization efficiency. Based on the reliability techniques and topology optimization methods, integrating the proposed reliability based topology optimization based on subset simulation method, a general reliability based topology optimization software system should be constructed for general engineering structure. The design of aircraft wing can be used to validate the effectiveness and versatility of the reliability based topology optimization software system. The proposed method and software system have broad application in the field of aerospace, mechanical and many other structural systems. The project has important signification for improving the theory and arithmetic of reliability based topology optimization and obtaining the reasonable and feasible engineering implementation.

为了有效提高可靠性拓扑优化的计算效率及其在工程中的适用性，本项目旨在发展高效高精度的可靠性拓扑优化全局方法，并建立适合一般工程结构的可靠性拓扑优化软件平台。在结构参数化建模的基础上，考虑工程结构的不确定性因素，通过解除可靠性约束与拓扑优化设计的耦合性，结合连续体结构拓扑优化的变密度法，建立基于子集模拟的可靠性拓扑优化的全局求解方法，使其能以较高的概率在设计变量的维数退化成的低维可行域内搜索全局最优拓扑解，并且在一定程度上克服全局优化效率低的问题。基于传统的可靠性技术和拓扑优化设计方法，融合所提出的基于子集模拟的可靠性拓扑优化方法，编制通用性较好的可靠性拓扑优化软件，并采用所编制的通用软件系统对某型飞机机翼结构进行可靠性拓扑优化设计，以考核软件的有效性和通用性，使其能适用于宇航、机械等领域的结构设计中。本项目对完善可靠性拓扑优化的理论方法并得到合理可行的工程实现方案具有重要意义。

考虑在可靠性拓扑优化中的高维设计变量问题，采用多种全局灵敏度指标来有效确定重要变量，进而降低变量的维数。并在此基础上考虑了基于泛函的上下限分析以及适用于混合变量情况的重要测度指标。针对复杂连续体结构力学性能分析过程中的隐式、非线性函数问题，先进的模型替代技术可用于高效地求解输入与输出响应之间的函数关系，并进行模型确认。研究的重点体现在基于GMDH方法的模型替代，包括GMDH-NN和GMDH-HDMR。飞机机翼的气动弹性可靠性优化设计与常规确定性优化设计的对比分析，证实了对结构进行可靠性优化的必要性。在结构参数化建模的基础上，考虑工程结构的不确定性因素，通过解除可靠性约束与拓扑优化设计的耦合性，结合连续体结构拓扑优化的变密度法，建立基于子集模拟的可靠性拓扑优化的全局求解方法，以较高的概率在设计变量的维数退化成的低维可行域内搜索全局最优拓扑解，并且在一定程度上克服全局优化效率低的问题。基于传统的可靠性技术和拓扑优化设计方法，融合基于子集模拟的可靠性拓扑优化方法，编制适合一般工程结构的可靠性拓扑优化系统，以桁架结构、板壳结构、复杂连续体结构为例，验证方法及其程序的可行性及正确性，并对某型飞机机翼结构进行可靠性拓扑优化设计，以考核程序的有效性和通用性，使其能适用于宇航、机械等领域的结构设计中。本项目对完善可靠性拓扑优化的理论方法并得到合理可行的工程实现方案具有重要意义。