Purpose

The present paper aims at the multi-objective optimization of a reentrant hexagonal cell auxetic structure. In addition, a parametric analysis will be carried out to verify how each of the design factors impact each of the responses.

Design/methodology/approach

The multi-objective optimization of five different responses of an auxetic model was considered: mass, critical buckling load under compression effort, natural frequency, Poisson's ratio and failure load. The response surface methodology was applied, and a new meta-heuristic of optimization called the multi-objective Lichtenberg algorithm was applied to find the optimized configuration of the model. It was possible to increase the failure load by 26.75% in compression performance optimization. Furthermore, in the optimization of modal performance, it was possible to increase the natural frequency by 37.43%. Finally, all 5 responses analyzed simultaneously were optimized. In this case, it was possible to increase the critical buckling load by 42.55%, the failure load by 28.70% and reduce the mass and Poisson's ratio by 15.97 and 11%, respectively. This paper addresses something new in the scientific world to date when evaluating in a multi-objective optimization problem, the compression and modal performance of an auxetic reentrant model.

Findings

It was possible to find multi-objective optimized structures. It was possible to increase the critical buckling load by 42.82%, and the failure load in compression performance by 26.75%. Furthermore, in the optimization of modal performance, it was possible to increase the natural frequency by 37.43%, and decrease the mass by 15.97%. Finally, all 5 responses analyzed simultaneously were optimized. In this case, it was possible to increase the critical buckling load by 42.55%, increase the failure load by 28.70% and reduce the mass and Poisson's ratio by 15.97 and 11%, respectively.

Originality/value

There is no work in the literature to date that performed the optimization of 5 responses simultaneously of a reentrant hexagonal cell auxetic structure. This paper also presents an unprecedented statistical analysis in the literature that verifies how the design factors impact each of the responses.

中文翻译：

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基于元模型的Lichtenberg算法可重入拉胀模型多目标设计优化

目的

本文旨在对可重入六边形细胞拉胀结构进行多目标优化。此外，还将进行参数分析，以验证每个设计因素如何影响每个响应。

设计/方法论/途径

考虑了拉胀模型的五种不同响应的多目标优化：质量、压缩作用下的临界屈曲载荷、固有频率、泊松比和失效载荷。应用响应面方法，并应用一种称为多目标 Lichtenberg 算法的新元启发式优化来找到模型的优化配置。压缩性能优化可将故障负载提高26.75%。此外，在模态性能的优化中，固有频率可以提高37.43%。最后，同时分析的所有 5 个响应均得到优化。在这种情况下，可以将临界屈曲载荷增加 42.55%，破坏载荷增加 28.70%，质量和泊松比分别减少 15.97 和 11%。本文在评估多目标优化问题、拉胀可重入模型的压缩和模态性能时，解决了迄今为止科学界的一些新问题。

发现

可以找到多目标优化结构。临界屈曲载荷可提高42.82%，压缩破坏载荷可提高26.75%。此外，在模态性能优化中，固有频率提高了37.43%，质量降低了15.97%。最后，同时分析的所有 5 个响应均得到优化。在这种情况下，可以将临界屈曲载荷增加 42.55%，破坏载荷增加 28.70%，质量和泊松比分别减少 15.97 和 11%。

原创性/价值

迄今为止，文献中还没有同时对可重入六边形细胞拉胀结构的 5 个响应进行优化的工作。本文还提出了文献中前所未有的统计分析，验证了设计因素如何影响每个响应。