中文摘要：

采用区间模型描述不确定参数,在考虑传统约束条件基础上,增加了可靠性指标作为约束条件,研究结构的稳健性优化设计.从非概率可靠性指标的几何意义出发,寻找非概率可靠性指标目标值与不确定参数的波动范围的关系,将非概率的稳健优化设计转化为两层优化模型.对于非线性功能函数,内层优化根据非概率可靠性指标的波动范围最小化功能函数,从而避免了内层优化直接计算非概率可靠性指标难的问题.对于线性功能函数,不确定性参数可以表示为非概率可靠性指标目标值的显示表达式,两层稳健优化转化为确定性的单层优化.该方法优化描述明确清晰,计算公式简便,计算效率高.算例验证了本文所提方法的可行性和正确性.

英文摘要：

The structural robust optimization with uncertain parameters which are described by inter- val models was investigated. Compared with the traditional optimization design, the robust optimization model involves the non-probabilistic reliability index as an constraint condition. In this contribution, the re- lationship between the target of non-probabilistic reliability index and the fluctuation range of uncertain pa- rameters was depicted by the geometric meaning of the reliability index. The non probabilistic robust opti- mization design model was converted into a two-level optimization model. The minimization for non-linear performance function was carried out according to the fluctuant range of the non-probabilistic reliability in- dex within the inner-lever optimization, so as to avoid the calculation of reliability index directly. For the linear performance function,the uncertain parameters could be described as the target value of non-probabi- listic reliability index with explicit expression, and therefore the two-level robust optimization was easily converted into a single level deterministic optimization. The advantages of the proposed method lie in clear geometric characterization, computing convenience and high calculation efficiency. Several numerical exam- ples are calculated, which show the proposed method is efficient.