基于非概率凸模型可靠性的结构优化设计

摘要

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.%Taking into account the uncertainty of structural system parameters and based on the proposed new definition of the non-probabilistic reliability index based on convex models,a new mathematical model and solution method of structural optimization design was proposed under the non-probabilistic reliability constraint.The super-ellipsoidal convex sets were taken to describe the uncertain parameters.The ratio between the volume of safe region and the total volume of the super-ellipsoidal set for the basic uncertain variables was defined as the measurement of structural non-probabilistic reliability.By taking the reliability index as constraint condition,the structural optimization problem was iteratively solved through the multiplier method and the damping Newton’s method,which was a stable,efficient algorithm.Numerical examples verify the correctness of the proposed method.