中文摘要：

针对结构的多目标拓扑优化设计,提出一种基于折衷规划法归一化子目标建立综合目标函数、以灰色综合关联分析确定综合目标函数中子目标权重系数的方法。以某商用车悬架控制臂为例,运用动力学分析、静力学分析和模态分析,得到控制臂在典型工况下的刚度性能、强度性能和固有频率。用板结构进行拓扑优化和形貌优化确定控制臂外轮廓形状,再分别采用单目标拓扑优化降低典型工况下的柔顺度和提高前三阶固有频率,并采用多频率加权方式来抑制频率单目标优化时的振荡现象。将单目标拓扑优化形成的子序列与各个目标最优值形成的最优序列进行灰色综合关联分析,得到子目标的权重系数。用折衷规划法进行多目标拓扑优化,根据优化结果对控制臂进行改进设计。改进后结构分析表明：优化后的控制臂质量减轻9.3%,整体刚度性能和强度性能明显增强,各阶固有频率均有不同程度提高。

英文摘要：

Aiming at the multi-objective topology optimization design of structure, a method is presented based on compromise programming to normalize each sub objective to establish comprehensive objective function, with grey comprehensive relational analysis to determine the weight factors of the sub objective of the comprehensive objective function. Focusing on the suspension control arm of a commercial vehicle, the dynamic analysis, static analysis, and model analysis are used to obtain the stiffness and strength performance under typical operations and natural frequency. The shape of the outer contour is determined by topology and topography optimization of a plate. Using single objective topology optimization to reduce static compliances and improve the first three natural frequency, and the oscillation of the single objective optimization with frequency is suppressed by multi-frequency weighting method. The sub sequences and optimal sequence obtained by single objective topology are exerted comprehensive relational analysis to obtain the weight factors. The multi-objective topology optimization is carried out by compromise programming method, and the control arm is correspondingly optimized： The mass of modified structure is reduced by 9.3%; The stiffness and strength performance are improved and the natural frequency of each order are increased in different degree.