基于改进自适应成长法的薄壁结构频率优化设计
收稿日期: 2022-12-08
修回日期: 2023-03-15
录用日期: 2023-04-20
网络出版日期: 2023-05-12
基金资助
国家自然科学基金(51975380)
Optimization design of natural frequencies for thin-walled structures based on improved adaptive growth method
Received date: 2022-12-08
Revised date: 2023-03-15
Accepted date: 2023-04-20
Online published: 2023-05-12
Supported by
National Natural Science Foundation of China(51975380)
自适应成长法是一种基于自然界分支系统形成机制的薄壁结构加筋拓扑优化设计方法。针对现有自适应成长法在结构自振频率拓扑优化设计中存在局部模态的问题，提出一种多项式材料插值模型；为了提高算法的收敛性，将基于仿生学的基因遗传特性引入灵敏度信息处理中，并运用敏度过滤技术解决数值不稳定问题。针对简支和固支的典型板壳结构算例进行加筋优化，设计结果表明，提出的方法可得到形态清晰的加强筋布局；进一步分析了简支约束方式和固支约束方式在结构自振频率拓扑优化问题中的影响，结果表明，虽然2种约束方式下结构的一阶振型相同，但由于约束点自由度的差异，得到的加强筋布局并不相同。分析2种约束方式下优化设计结果的自振性能，发现在固支约束方式下得到的加筋结构的第一阶频率比简支约束方式下的加筋结构高7%以上，因此在实际工程应用中，当结构边界约束条件不明确的情况下，可选择固支作为设计模型的约束方式。
张德慧 , 丁晓红 , 胡天男 , 张横 . 基于改进自适应成长法的薄壁结构频率优化设计[J]. 航空学报, 2023 , 44(19) : 228378 -228378 . DOI: 10.7527/S1000-6893.2023.28378
The adaptive growth method is a topology optimization design method for stiffened thin-walled structures based on the formation mechanism of natural branching systems. Aiming at the problem that the existing adaptive growth method has local modes in the topology optimization design of structural natural frequency， a polynomial material interpolation model is proposed. To improve the convergence of the algorithm， the genetic characteristics based on bionics are introduced into the sensitivity information processing， and the sensitivity filtering technique is used to solve numerical instability problems. The stiffeners layout optimization is carried out for the typical plate and shell structure examples of the simple supported and clamped. The design results show that the proposed method can obtain a clear stiffeners layout. The influence of simple-supported constraint and clamped-supported constraint on the topology optimization of structural natural frequency is further analyzed. The results show that although the first-order vibration modes of the structure are the same under the two constraint ways， the stiffener layout is different due to the difference in the degree of freedom of the constraint points. The natural vibration performance of the optimized design results under the two constraint ways is analyzed. It is found that the natural frequency of the stiffened structure obtained under the clamped-supported constraint way is about 7% higher than that under the simple-supported constraint way. Therefore， in practical engineering applications， when the structural boundary constraints are not clear， the clamped supported can be selected as the constraint way of the design model.
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