Multi-objective design optimization of reentrant auxetic model using Lichtenberg algorithm based on metamodel

Abstract

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.

Citation

Francisco, M., Pereira, J., Oliveira, L., Simões Cunha, S. and Gomes, G.F. (2023), "Multi-objective design optimization of reentrant auxetic model using Lichtenberg algorithm based on metamodel", Engineering Computations, Vol. 40 No. 9/10, pp. 3009-3035. https://doi.org/10.1108/EC-07-2022-0448