考虑重叠过滤及稳定性约束的桁架拓扑优化方法  

TOPOLOGY OPTIMIZATION OF TRUSS STRUCTURE BASED ON OVERLAPPING-FILTER AND STABILITY CONSTRAINTS

作　　者：冷国俊[1] 张卓[1] 保宏[1] 杨东武[1] 

机构地区：[1]f西安电子科技大学电子装备结构设计教育部重点实验室,西安710071

出　　处：《工程力学》2013年第2期8-13,共6页Engineering Mechanics

基　　金：973项目(61358);国家自然科学基金重点项目(51035006),国家自然科学基金项目(50775170);中央高校基本科研业务费专项资金项目(JY10000904008)

摘　　要：从工程实际的角度来说,一般不允许结构形式中包含重叠单元。目前桁架拓扑优化的基结构法在选定基节点的情况下一般不建重叠单元,这导致可行域缩小,使优化不能找到更优解,人为增删杆件缺乏科学依据。针对该问题,该文对重叠给出准确的数学描述,建立包含重叠杆的基结构,利用Heaviside函数将拓扑变量连续化处理,使之在优化过程中可以获取目标函数、约束函数的敏度信息,同时考虑在拓扑优化中加入基频约束以避免出现机构,并加入稳定性约束防止出现压杆失稳,通过优化模型实现重叠过滤。最后通过两个案例计算证明可以找到更优解,验证了该方法的有效性。Considering the manufacture and assemble techniques, overlap elements should be avoided in structure design in practical engineering. In truss topology optimization using the ground structure method, overlap elements are abandoned under a given set of chosen nodal points, which may lead to un-optimum designs. Adding or deleting element in the topology result is of no warranty; meanwhile, it＇s unreasonable if the overlap elements are reserved. This paper presents an accurate mathematical description of overlapping with more elements included in the initial ground structure. The Heaviside function is used to map the element cross-sectional area with the property of intersection to get the sensitivity information. Overlapping-filter constraints and fundamental eigenvalue constraint are imposed in the optimization model. Local stability constraints are imposed in order to prevent unstable result. Overlapping-phenomenon is avoided by the formulation of the topology optimization. Finally the method was applied to two examples to testify the validity of the proposed method and obtain a more reasonable result for actual projects.

关 键 词：拓扑优化 基结构法 重叠过滤 基频约束 稳定性约束 

分 类 号：TH122[机械工程—机械设计及理论]