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本文研究了考虑材料性能空间分布不确定性的连续体结构可靠度拓扑优化问题。其中,材料的弹性模量视为具有给定概率分布特征的随机场,其离散采用级数最优线性估值法(EOLE)。随机结构的响应以及相应的灵敏度分析采用多项式混沌展开(PCE)近似表达,并采用Monte Carlo方法验证了该方法的精度。结构的可靠度分析采用一次可靠度方法(FORM),在优化问题的求解中,对双层嵌套方法和序列近似规划(SAP)方法进行了对比。数值算例中,该方法应用于二维和三维结构的拓扑优化问题,优化结果验证了方法的正确性和有效性。
In this paper, we study the topology optimization of continuum structural reliability considering the uncertainty of the spatial distribution of material properties. Among them, the material’s elastic modulus is considered as a random field with a given probability distribution characteristic, and its dispersion is based on the EOLE. The response of random structure and the corresponding sensitivity analysis are approximated by polynomial Chaos Expansion (PCE). The Monte Carlo method is used to verify the accuracy of the proposed method. The structural reliability analysis uses the first-order reliability method (FORM) to compare the two-level nesting method and the sequence approximation planning (SAP) method in solving the optimization problem. In numerical examples, the proposed method is applied to the topology optimization of two-dimensional and three-dimensional structures. The optimization results verify the correctness and validity of the proposed method.