中文摘要：

针对传统凸模型方法分析不确定性结构时仅给出结构响应边界的局限性，论文结合基于体积比的伪概率度量和一次二阶矩提出一种结构响应不确定性量化的新方法．该方法在准确求解不确定性结构响应上下界的同时，给出了结构响应在上下界内的伪概率分布．首先利用椭球凸模型对结构不确定性进行建模，结构响应关于不确定性参数的传播方程将椭球分割成两个区域，则分割区域体积与椭球域总体积之比可作为伪概率来度量结构响应的不确定性；其次，用一次二阶矩法序列求解结构响应不确定性传播方程，有效获取最可能展开点及相应分割区域的近似体积．最后，通过一个典型的六杆桁架结构算例与传统凸模型方法和蒙特卡洛法进行比较，验证了论文方法对不确定性结构响应量化的有效性和优越性．

英文摘要：

Uncertainty widely exists in practical engineering problems, which are commonly associated with material properties, loads, manufacturing errors, and boundary conditions. Non-probabilistic convex model has been adopted to quantify uncertainty when information of uncertain parameters is insufficient. However, only the upper-lower bounds can be obtained by the traditional response analysis method for uncertain structures based on non-probabilistic convex model. Therefore, it is necessary to develop some measurements for uncertainty of structural response based on non-probabilistic convex model. In this study, a new uncertainty propagation method combining volume ratio with first order second moment was proposed,by means o{ which, not only the upper-lower hounds but also the pseudo-probability distribution bewteen the bounds of the structural response were able to be accurately evaluated. First, the uncertainty of structure parameters were modeled by a multidimensional ellipsoid convex set. One part of the ellipsoid domain was separated from the original one based on the state function of structural response with respect to uncertain parameters. Then the volume ratio between the separated and the whole ellipsoid domain was used to quantify the uncertainty of structural response. Second,to smplify the calculation of the separated domain volume,the original ellipsoidal set was transformed into a regularized sphere of unit radi- us, and linear approximation of the state function was adopted using Taylor series around the most probable point （or desgin point） up to the first order. To effectively obtain the most probable expansion point and the approximate volume of the separated domain, the propagation equation of uncertain response was then sequentially solved using the First Order Second Moment Method. Finally, the uncertain response of a typi- cal six-bar-truss was analyzed using the proposed method,the Monte Carlo simulation,and the traditional method,respectively. The comparisons of the results demonstrated t