基于概率和非概率混合模型的结构鲁棒设计方法

讨论了同时存在概率不确定性量和非概率不确定性量时可行鲁棒性和目标函数鲁棒性的实现策略，提出了基于概率和非概率混合模型的结构鲁棒设计方法。基本做法是首先视非概率型不确定性量为参变量，按照传统概率统计的方法计算约束函数和目标函数的均值和标准方差，然后再考虑非概率型不确定性量的波动变化对约束函数和目标函数统计特征量的影响，以修正常规可行鲁棒性和目标函数鲁棒性的数学模型。所提方法应用于一个10杆桁架结构的最轻质量设计和节点位移鲁棒设计，获得了对不确定性量波动变化不敏感的设计方案。

Structural robust design based on hybrid probabilistic and non-probabilistic models

The paper described the strategies for feasibility robustness and objective function robustness respectively subjected to both probabilistic and non-probabilistic uncertainties in detail and proposed hybrid probabilistic and non-probabilistic models for structural robust design. In the study, non-probabilistic variables were first taken as design parameters at their nominal values while the conventional statistical methods were employed to compute the means and standard deviations of constraint functions and the objective function. The effects on the means and standard deviations of constraint functions and the objective function due to variation of non-probabilistic variables were then taken into account by either an optimization procedure or a worst-case analysis with respect to the non-probabilistic uncertain variables. The mathematical models of conventional feasibility robustness and objective function robustness were consequently modified to achieve the robustness of constraint functions and the objective function under both probabilistic and non-probabilistic uncertainties. The proposed method was applied to the minimum weight design and the displacement robust design of a 10-bar truss structure subjected to bar cross-sectional areas with probabilistic properties and uncertain applied loads with non-probabilistic properties. The insensitive design schemes with respect to uncertain variables are obtained based on proposed method.