中文摘要：

研究具有随机-区间-模糊混合变量的平面连续体结构在刚度约束下的拓扑优化设计问题。考虑结构的材料物理参数、外部载荷及结构许用柔度分别同时为随机、区间或模糊三种不同类型的变量，首先利用信息熵转化法将模糊变量转换为等价的正态随机变量，然后基于概率可靠性分析方法获得随机变量和区间变量共存时的混合可靠性指标。在此基础上建立了以结构单元有无为设计变量，结构体积极小化为目标函数，满足结构柔度混合可靠性约束的平面连续体结构拓扑优化数学模型，并利用渐进结构优化法求解。通过两个算例验证文中所建模型的合理性及求解策略、方法的有效性。

英文摘要：

Topology optimization design of planar continuum structures with random-interval-fuzzy hybrid variables under constraint of total stiffness was studied. The structural physical parameters, applied loads and allowed flexibility were considered as random variables, interval variables or fuzzy variables. Based on information entropy, the fuzzy variables were transformed into equivalent random variables with normal distribution. According to the probabilistic reliability analysis method, the hybrid reliability index containing random variables and interval variables was obtained. On this basis, the topology optimization model of planar continuum structures was constructed, in which the presence or absence of elements was regarded as the design variables, the total volume of the structures was minimized, and the hybrid reliability index with structural flexibility was taken as the constraint condition. The evolutionary structural optimization method was used in the optimization. The two examples were presented to demonstrate the feasibility and effectiveness of the optimal model and solving approach.