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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。
The topologically optimal design of a planar continuum structure with stochastic-interval-fuzzy mixed variables is studied under stiffness constraints. Considering the material physical parameters of the structure, the external load and the permissible flexibility of the structure, they are at the same time random variables, intervals or fuzzy variables of three different types. Firstly, the fuzzy variables are transformed into equivalent normal random variables by the information entropy conversion method, Reliability analysis method to obtain mixed reliability index when random variables and interval variables coexist. On this basis, a topology optimization mathematical model of planar continuum structure with or without structural elements as design variables and minimization of structural volume as objective function is established, and the topology optimization of planar continuum structure is solved. The asymptotic structural optimization method is used to solve this problem. Two examples are used to verify the rationality of the model and the solution strategy, the validity of the method.