基于变密度法的飞行器升力面结构多目标拓扑优化设计

摘要

为研究权衡结构刚度与低阶振动频率的飞行器升力面最优结构设计，提出两种多目标拓扑优化方案（约束法、结合约束法与评价函数法）。基于变密度方法，在约束法方案中将多目标优化转化为设定参考点位移约束和低阶振动频率约束下，求解结构质量最小化的优化问题。在结合约束法与评价函数法方案中，定义组合柔度指数为评价函数（结构柔度与振动频率的函数），将多目标优化转化为设定低阶振动频率约束和体积分数约束下，求解结构最小组合柔度指数的优化问题。结果表明两种方案的优化结果具有一定的相似性，各有所长。优化设计不仅减轻了升力面结构重量，而且提高了结构的一、二阶振动频率。%Taking account of the structural stiffness and the low order vibration frequencies,two schemes of multi-objective topology optimization were proposed to obtain the best aircraft lifting-surface structural design. Based on penalized density theory,the scheme one (named as constrain method)is to convert the multi-objective optimization to single-objective optimization by considering the minimum structural mass as the objective with con-straints of reference points displacements and the low order vibration frequencies.The scheme two (named as the combination of constrain method and criterion function method)settles the multi-objective optimization by defi-ning combined compliance index (CCI)as the objective,with the constraints of volume fraction and the low order vibration frequencies.The CCI is the function of structural compliance and low order vibration frequencies.Nu-merical results demonstrate the proposed schemes not only realize reducing the structural mass but also raise the first and second order frequencies.