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中文摘要：
考虑非概率可靠性的拓扑优化对于非确定参数和荷载条件下结构的概念设计具有重要意义，有关研究国内外少见报道。本文利用凸模型理论，考虑优化迭代过程的需要，提出改进的非概率可靠性指标的定义，并针对桁架结构拓扑优化设计问题建立了以杆件截面积为设计变量、结构重量极小化为目标、具有非概率可靠性指标约束的广义尺寸优化数学模型。本文指出，考虑桁架结构参数的不确定性的条件下所得到的最优杆件布局与确定性优化所得到的结果可能有显著不同。对文中提出的数学模型，采用数学规划算法求解，数值算例结果令人满意。本文工作表明了桁架结构非概率可靠性拓扑优化设计的可行性和所提出算法的有效性。
英文摘要：
The non-probabilistic reliability-based topology optimization is of great importance for conceptual design of structures under system uncertainties. This subject, however, has been rarely addressed in the literatures. This paper proposes a modified definition of non-probabilistic reliability based on the convex model theory. Such a definition facilitates the seeking of the optima in the design space. Furthermore, the topology optimization of truss structures under constraints on non-probabilistic reliability is mathematically stated as a generalized sizing problem, where the member cross-sectional areas are taken as design variables and the structural weight is considered as the objective function. The present paper reveals that, the optimal structural layout incorporating system uncertainties may differ significantly from those obtained with deterministic formulations. The optimization problem is solved with a mathematical programming method. Numerical results illustrate the applicability and the validity of the present problem settings as well as numerical techniques developed in this study.
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