中文摘要：

为了对网格结构进行鲁棒性定量分析及找出鲁棒构型,以系统传递函数的H2范数作为结构鲁棒性的定量评价指标和优化目标;以单元相对密度为设计变量,采用固体各向同性惩罚微结构（SIMP）模型描述材料的刚度,建立鲁棒设计的数学模型,将结构的鲁棒性设计转化成连续体拓扑优化;引入保留精英种群的思想,并将大爆炸算法扩展应用在质点系优化中,求得全局最优解.以四点支承双曲扁网壳为例,分析了不同荷载条件下拓扑优化得到的鲁棒构型.结果表明：大爆炸算法可以有效地应用于连续体拓扑优化的鲁棒性构型设计中;以鲁棒构型为准则的正交斜放双曲扁网壳结构优于正交正放双曲扁网壳结构;结构的鲁棒构型可以明确结构的传力路径,对结构的杆件布置和截面设计具有指导作用.

英文摘要：

In order to make quantitative robustness analysis of grid structures and find out the robust configurations,first,the H2 norm of system transfer function was treated as the quantitative evaluation index of structural robustness and the optimization objective.Then,by chossing the relative densities of each element as design variables,using the solid isotropic material with penalization（SIMP）model to describe the stiffness of material,the robustness based structural design was transformed into continuum topology optimization.Introducing the idea of reserving elite populations,the modified Big bang-Big crunch（BB-BC）was employed in the particles optimization to get the global optimum solution.Finally, taking hyperbolic latticed flat shell as an example,the robust configurations of hyperboloid latticed flat shell supported by four points under different load conditions were obtained by topology optimization.The results show that the BB-BC optimization can be effectively applied into the robust design of continuum topology optimization.The orthogonal-diagonal hyperbolic latticed flat shell structure which using robust configuration as criterion is better than the orthogonal-spatial hyperbolic latticed flat shell structure.The robust configuration of structure can give explicit path of force transfer,and also has guidance to the bar arrangement and section design of structure.