连续体结构的模糊多目标拓扑优化设计方法研究  

Fuzzy Multi-objective Topology Optimization of Continuum Structures

作　　者：刘加光[1] 陈义保[1] 罗震[2] 

机构地区：[1]烟台大学机电汽车工程学院,烟台264005 [2]华中科技大学机械科学与工程学院,武汉430074

出　　处：《系统仿真学报》2007年第5期1095-1099,共5页Journal of System Simulation

基　　金：国家自然科学基金(50465001);国家"973"重点基础研究发展规划项目(2003CB716207)

摘　　要：提出了连续体结构静力学和动力学多目标拓扑优化设计的模糊-目标规划方法。该方法利用目标规划方法将多目标优化问题转化为等效的单目标问题,并用模糊集理论中的非线性隶属函数来体现目标规划方法中目标函数期望值所具有的模糊性和不确定性。以结构静力学的刚度和动力学的特征值作为优化的两个目标函数,提出并建立了连续体结构拓扑优化设计的多目标优化模型。用移动渐进线方法(MMA)求解单目标优化问题,用序列线性规划方法(SLP)求解模糊-目标混合规划问题。通过典型的求解算例验证了所研究方法的有效性。A hybrid fuzzy-goal programming scheme for continuum topology optimization with static and dynamic objectives was proposed. The original multi-objective optimization problem can be converted to a single objective problem using the goal programming scheme, and the nonlinear membership function is applied to embody uncertain and stochastic characteristics of the aspiration levels in the goal programming model. The multi-objective computational model involving static and dynamic objectives was worked out where minimizing compliance and maximizing mean eigenfrequencies were both concerned. The mathematical programming methods, both the method of moving asymptotes （MMA） belonging to convex programming methods and the sequential linear programming method （SLP）, were used to solving optimization problems. The validation for the presented methodology is demonstrated by a typical numerical application.

关 键 词：结构拓扑优化 多目标 目标规划 模糊集 数学规划 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]