基于设计空间调整的结构拓扑优化方法  

A NEW STRUCTURAL TOPOLOGICAL OPTIMIZATION METHOD BASED ON DESIGN SPACE ADJUSTMENTS

作　　者：荣见华[1] 张强[1] 葛森 牟让科 

机构地区：[1]长沙理工大学汽车与机械工程学院,长沙410076 [2]中国飞机结构强度研究所,西安710065

出　　处：《力学学报》2010年第2期256-267,共12页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(10472016;10872036);国家863计划(2008AA04Z118);航空科学基金(2007ZA23007)资助项目~~

摘　　要：提出了一种基于设计空间调整的结构拓扑优化方法,以求解有限元网格规模大的问题,且获得0/1拓扑解.首先,借鉴有理分式材料模型,建立了材料刚度性质与拓扑变量的关系.为了解决分析计算量大和需要解释得到的材料分布等问题,给出了一种不影响数学规划求解算法收敛特性的设计空间调整手段.其次,当优化迭代求解接近结构最佳拓扑邻域后,采用了加速收敛求解的策略,并给出了一种加速收敛的启发式算法.然后,结合基于倒设计变量的位移函数的非完整二阶近似式,建立了一种基于设计空间调整的结构拓扑优化算法.该方法能获得较好0-1分布特征的优化拓扑,能较好地处理多载荷和多约束的结构拓扑优化问题.给出的算例表明通过结构分析模型规模的减小和传统的位移迭代求解法的采用,方法效率明显提高.算例验证了该方法的正确性和有效性.Although a discrete solid and void structural topology is typically desired,a continuous material density design field is usually assigned to the material points within the design domain to spatially indicate regions of solid and void material.The solid isotropic microstructure with penalization material（SIMP） formulation is easy to implement in a finite element（FEM） framework.However,the material in those regions,where the values of density variables are between 0 and 1,is artificial.It is necessary to deal with those regions after the optimum topological configuration is obtained.Then a new constraint,labeled the sum of the reciprocal variables（SRV）,for 0/1 topological design was introduced to obtain 0/1 topology solutions.The structural design domain need be divided into some finite element mesh when structural topology optimization is made. Some optimization problems may need a large finite element mesh,the authors propose a new structural topological optimization method based on design space adjustments in order to solving this problem and obtaining 0/1 topology solutions.In topology optimization,a design space is specified by the number of design variables, and their layout or configuration.The proposed procedure has one efficient algorithm for adjusting design space. First,the rational approximation for material properties（RAMP） is adopted to design the topology structural stiffness matrix filter function,and the design space can be adjusted in terms of design space expansion and reduction.This capability is automatic when the design domain needs expansion or reduction,and it will not affect the property of mathematical programming method convergences.Second,to get a clearer topological configuration at each iteration step,by introducing the discrete condition of topological variables,integrating with the original objective and introducing varying displacement constraint limit measurements,optimal series models with multi-constraints is formulated to make the topological variables approach

关 键 词：拓扑优化 位移约束 连续体结构 设计空间调整 有理分式材料模型 

分 类 号：O39[理学—工程力学]