连续体结构的模糊多目标拓扑优化设计方法研究

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。

Fuzzy Multi-objective Topology Optimization of Continuum Structures

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.