传统的结构拓扑优化分析和设计都是基于特定参数确定性的物理模型。然而，在实际的结构设计中存在着广泛的不确定性，这种不确定性严重影响结构的物理性能。文中基于多椭球凸模型的非概率可靠性来量化结构参数的变化，研究存在不确定但有界的参数的连续体结构的拓扑优化问题。首先，建立变量具区间不确定性的可靠性拓扑优化模型，以结构设计区域质量最小为目标函数; 然后，根据可靠性指标的几何意义，应用非概率模型寻求满足目标可靠性指标约束的设计点; 在此基础上，应用区间 Cheby-shev 零点多项式逼近归一化随机变量的真实极限状态函数，并利用单环可靠性算法计算相应目标可靠性指标下的最佳设计点值，从而使得非概率可靠性优化问题可以转化为确定性优化问题。两个数值例子说明了方法的有效性。结果表明，与确定性的结构拓扑优化设计相比，考虑变量随机性的可靠性拓扑优化能够获得更加可靠的拓扑结构。

Traditional structural topology optimization analysis and design is a deterministic physical model based on specific parameters． However，in the actual design process，there are a wide range of uncertainties，which extreme-ly affect the physical properties of the structure． In this study，the variation of structural parameters was quantified by the non-probabilistic reliability based on multi-ellipsoidal convex model，and the topology optimization problem with uncertain but bounded parameter continuum structure was studied． Firstly，the reliability topology optimization model with variable uncertainty was established，taking the structural design quality minimization as the objective function． Then，based on the geometric meaning of the reliability index，the non-probability model was used to find the design point that satisfies the target reliability index constraint． On this basis，the interval Chebyshev zero poly-nomial was applied to approximate the real limit state function of the normalized random variable，and the single-loop reliability algorithm was used to calculate the optimal design points value under the corresponding target relia-bility index，so that the optimization problem of non-probability reliability can be transformed into deterministic op-timization problem． The effectiveness of the method was illustrated by two numerical examples． The results show that，compared with the deterministic structural topology optimization design，the reliability topology optimization with random variables can obtain more reliable topology structure．