Multi-cell tubal structures have widely been used in the automobile industry due to proven superior crashworthiness performance than single-cell and foam-filled tubes. This superior performance is attributed to the number of corners within the cross-sectional profile of the tube. In this paper, a two-stage optimization design of a multi-cell tubal structure is presented to address an important design problem by combining a discrete and continuous optimization process into a sequential optimization that generates an overall optimum. The first stage entails a configurational optimization which is realized by formulating a discrete topological optimization problem where the webs within the tube configuration are taken as the topological design variables. Each topological configuration is represented using a binary scheme that shows the presence or not of an edge to create different combinations of the corners. The constraints in the first stage are connectivity, mass ratio, and peak crushing force (PCF). The binary genetic algorithm (BGA) is utilized in searching for the optimal configuration in the first stage. The second stage entails parameter optimization where the cell sizes are the design variables. The objective functions in the second stage are defined using meta-models. Multi-objective particle swarm optimization (MOPSO) is employed for Pareto searching and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is used to find the optimal point for each of the mass ratios considered. Compared with the baseline configuration, the optimized tubal structures demonstrated superior crashworthiness performance. The two-stage discrete and continuous optimization approach has demonstrated that it not only provides a systematic approach to searching optimal structure but also creates a series of novel multi-cell topological configurations with enhanced crashworthiness.

由于多孔管状结构比单孔和泡沫填充管具有更好的耐撞性，因此已广泛应用于汽车工业。这种优异的性能归因于管子的横截面轮廓内的拐角数量。在本文中，提出了一种多细胞输卵管结构的两阶段优化设计，以解决一个重要的设计问题，方法是将离散的和连续的优化过程组合到产生总体优化的顺序优化中。第一阶段需要进行结构优化，这是通过制定离散的拓扑优化问题来实现的，其中，将管配置内的腹板作为拓扑设计变量。每个拓扑配置都使用二进制方案表示，该方案显示是否存在边缘以创建拐角的不同组合。第一阶段的约束条件是连通性，质量比和峰值破碎力（PCF）。在第一阶段中，利用二进制遗传算法（BGA）搜索最佳配置。第二阶段需要参数优化，其中像元大小是设计变量。第二阶段的目标函数是使用元模型定义的。多目标粒子群优化（MOPSO）用于帕累托搜索，并且通过类似于理想解的阶次偏好技术（TOPSIS）用于为所考虑的每个质量比找到最佳点。与基准配置相比，优化的输卵管结构显示出卓越的耐撞性能。两阶段离散和连续的优化方法表明，它不仅提供了一种搜索最佳结构的系统方法，而且还创建了一系列具有增强的耐撞性的新颖的多单元拓扑结构。