中文摘要：

当不确定性信息量不足以精确确定概率模型时，基于凸模型的非概率可靠性理论为工程结构安全性提供一种有效的评估方法．论文基于材料、几何及荷载大小等不确定性因素扰动界限的多椭球模型描述，运用标准化变换和标准空间广义无穷范数度量，给出定义非概率可靠性指标的极小极大优化数学模型．该非概率可靠性指标可理解为结构所能容许的参数不确定范围与实际不确定范围的相对“长度”比值．通过对极限状态方程的线性化近似，推导优化问题的显式迭代公式，实现非概率可靠性指标的简便求解．数值算例验证了论文迭代算法的正确性和有效性．

英文摘要：

In the circumstances of hardly defining precise probability distributions of uncertainties when only a limited number of sample information is available, the non-probabilistic reliability based on convex models serves as an effective approach for structural safety assessment. Based on the multi-ellipsoid model description for bounds of uncertainties in material properties, geometric dimensions and loading conditions,a min-max mathematical definition of the non-probabilistic reliability index is presented by using the normalized transformation and the generalized infinity norm measurement. The presented non-probabilistic reliability index can be regarded as the relative ＂length＂ ratio of the structural allowable variation range to the reference variation range. By approximating the limit-state function with linear expansion, an explicit iterative algorithm is presented for solving the non-probabilistic reliability index conveniently. Numerical examples are given to illustrate the validity and efficiency of the present iterative approach.