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考虑到结构系统参数的不确定性,基于提出的非概率凸模型可靠性指标的新定义,研究了在非概率凸模型可靠性约束下,结构优化设计的数学模型和求解方法.该方法通过超椭球域界定不确定参量,将结构基本不确定变量安全域的超体积与其可行域的超椭球总体积之比作为结构非概率可靠性的度量.并赋值可靠度作为约束条件,利用乘子法和阻尼牛顿法对结构的优化问题进行迭代求解,算法稳定,迭代速度快.数值算例验证了所提出方法的正确性.
Considering the uncertainty of structural system parameters, based on the new definition of the reliability index of non-probabilistic convex model, the mathematical model and solving method of structural optimization design under the constraints of non-probabilistic convex model reliability are studied. The uncertainty of the ellipsoid domain is defined, and the ratio of the hyperspherical volume of the structure’s basic uncertain security to the total volume of the hyperellipsoid of its feasible domain is taken as the measure of the non-probabilistic reliability of the structure, and the reliability of the assignment is taken as the constraint. The method and damping Newton method are used to solve the optimization problem of structure iteratively, and the algorithm is stable and the iteration speed is fast. Numerical examples verify the correctness of the proposed method.