基于响应面法的负泊松比蜂窝芯结构多目标优化∗

摘要

以负泊松比六边形蜂窝芯结构为研究对象，以提高蜂窝芯结构抗振能力和尽可能减小其结构质量为研究目标，运用响应面理论模型，建立了蜂窝芯结构的低阶模态固有频率的近似显式表达式；采用加权系数法，将固有频率和结构质量的多目标优化问题转化为单目标优化，结合遗传算法进行目标优化。具体算例表明，参数优化后的蜂窝芯结构固有频率提高了25%，结构质量减小了10%，这为超弹性蜂窝蒙皮结构设计提供了很好的依据。%The honeycomb core structure with negative Poisson′s ratio is studied. We aim to improve its resistance to vibration and reduce its mass. An explicit expression of the lower order modal’ s natural frequencies is established using the response surface method. The multi-objective optimization problem is transferred to a single-objective optimization using weighting coefficient meth-od,and the genetic algorithm is adopted to carry out optimization. Experimental results show that the natural frequency of the hon-eycomb core structure is increased by 25%,while the total mass of the structure is reduced by 10%,which provides a good basis for hyper elastic cellular skin structure design.