摘要
针对工程中存在多个随机不确定工况载荷作用的情况,将鲁棒性设计思想引入到连续体结构拓扑优化设计,发展和完善不确定性优化理论和计算方法.基于概率模型和SIMP方法,提出以结构柔顺度标准差最小化为目标、具有体积约束的连续体鲁棒性拓扑优化数学模型.通过对目标函数及其灵敏度计算公式的推导,采用数学规划法实现优化问题的求解.数值算例验证了所提优化模型的正确性及算法的有效性,并通过与确定性优化结果的比较,证明鲁棒性拓扑优化能够给出结构柔顺性变异更小的材料分布.
In practical engineering,the structural performance always exhibit some degree of variations due to the fact that the applied loads fluctuate dramatically throughout its service life-cycle.Thus,the need is highlighted to account for uncertainties in topology optimization stage of the structural design.Conventional deterministic topology optimization searches for minimum compliance without considering the uncertainties in operating processes.Recently,the robust structural design has attracted intensive attentions because it can reduce the variability of structural performance.However,existing robust design methods are confined to the size and shape optimization problems.This paper aims to incorporate the robust design strategy into the continuum topology optimization problem under multiple uncertain load cases by minimizing variation of the objective performance.Following the SIMP approach,an artificial isotropic material model with penalization for elastic constants is assumed and elemental relative density variables are used for describing the structural layout.The considered robust topology optimization problem is thus formulated as to find the optimal structural topology that minimizes the standard deviation of structural total compliance under the constraint on material volume.To avoid the difficulties associated with directly evaluating the standard deviation of the structural compliance,a convenient computing formula of the objective function is presented based on the stochastic finite element method.In addition,an adjoint variable method is employed for the efficient sensitivity analysis of the objective function.Then,the gradient based optimization algorithm（Method of Moving Asymptotes,MMA） is used to update the design variables in the optimization loop.Finally,three numerical examples for topology optimization of 2D and 3D structures illustrate the applicability and the validity of the present model as well as the proposed numerical techniques.The computational results reveal that the robust topology optimization could yield a material layout with less variation of structural compliance than the conventional deterministic approach.The novelty of the proposed robust topology optimization approach lies in that it introduces the conception of robustness into earlier stage of the structural design,which may be considered as especial useful in some circumstances.
出处
《力学学报》
EI
CSCD
北大核心
2011年第1期227-234,共8页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金(51008248)
陕西省自然科学基金(2010JQ1008)
西北工业大学基础研究基金(JC200936)资助项目~~
关键词
鲁棒性
拓扑优化
多工况
标准差
灵敏度分析
robustness
topology optimization
multiple load cases
standard deviation
sensitivity analysis
