应力约束下多相材料结构非概率可靠性拓扑优化方法研究

Topology optimization considering uncertainties is an important approach for searching the optimal structure with comprehensive benefits like structural safety, performance and cost. Nowadays, the widely used method is based on the compliance topology optimization frame. However, for the multi-phase material structures which may suffer from strength failure in some real-world engineering design problems, it is essential to take into account stress reliability constraints of different materials. By using the relative density penalization model and the convex model-based non-probabilistic reliability definition, a non-probabilistic reliability based topology optimization theory for the design of multi-phase material structures considering stress constraints on different materials is proposed. In order to solve the proposed topology optimization model of multi-phase material structures, a series of challenge difficulties, such as the stress singularity phenomenon (in which the feasible sub-domain is degenerate and disconnected), the zigzag movement phenomenon in searching concerned points, and a large number of stress constraints, are mainly investigated. Then, numerical algorithms are fully studied to conquer these difficulties in this project. The proposed algorithms include the decreasing strategy of target reliability index, trust region-based iterative method and the selecting strategy of active constraints. At last, the abovementioned theory and methods are applied to the united material layout design of typical multi-phase material structures. This project will greatly enrich the theory and method of non-probabilistic reliability based optimization design, develop the application proceedings of topology optimization, and provide a reasonable and practical approach for the novel layout design of multi-phase composite structures.

不确定性拓扑优化设计是实现结构安全性、性能、成本等综合效益最优目标的重要途径，目前广泛采用基于柔顺性的拓扑优化方法。然而，对于工程中可能遭受强度失效的多相材料结构，考虑不同材料应力水平的可靠性约束显得至关重要。本项目基于相对密度惩罚模型，结合多椭球凸模型描述下的非概率可靠性定义及关心性能方法，建立多种材料应力准则并存下的多相材料结构非概率可靠性拓扑优化模型。重点针对其求解过程中存在的应力奇异解现象（可行子域退化且不连通）、关心点迂回振荡迭代现象及大规模应力约束这一系列挑战性问题，研究目标可靠性指标降低策略、关心点信赖域直接迭代方法、最优点紧约束选择机制等关键算法，以实现多相材料结构拓扑优化问题的顺利求解。最后将上述理论方法应用于典型多相材料结构的联合布局设计。项目研究将丰富和发展非概率可靠性优化理论，推动拓扑优化的工程实用化，为组合结构的新型布局优化问题提供切实可行的设计方案。

不确定性拓扑优化设计是实现结构安全性、性能、成本等综合效益最优目标的重要途径，目前广泛采用基于柔顺性的拓扑优化方法。然而，对于工程中可能遭受强度失效的多相材料结构，考虑不同材料应力水平的可靠性约束显得至关重要。本项目基于相对密度惩罚模型，结合多椭球凸模型描述下的非概率可靠性定义及关心性能方法，建立了多种材料应力准则并存下的多相材料结构非概率可靠性拓扑优化模型。重点针对其求解过程中存在的应力奇异解现象、关心点迂回振荡迭代现象及大规模应力约束这一系列难点问题，研究目标可靠性指标降低策略、关心点信赖域直接迭代方法、增强凝聚方法等关键算法，实现了多相材料结构拓扑优化问题的顺利求解。并进一步将上述理论方法应用于钢混凝土组合结构、超弹性组合结构、柔性薄膜结构等典型多相材料结构的联合材料布局设计。在本项目资助下，课题组在本领域权威SCI期刊上共发表与本项目研究内容相关的学术论文11篇（已标注），均为本人第一作者或通讯作者，包括固体力学顶级期刊JMPS 1篇，计算力学顶级期刊CMAME 2篇，中科院二区论文5篇。申请PCT国际专利2项。

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