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Simultaneous optimization of elastic constants of laminated composites using artificial bee colony algorithm

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Abstract

Multifunctional application of laminated composites requires multi-objective optimization of their characteristics. In this paper, the ply angles of laminated composites are determined in order to maximize the effective in-plane elastic constants simultaneously. These constants are determined by considering a representative small element of the laminated composite and imposing the conditions of uniformity of out-of-plane stresses and in-plane strains at orthotropic layer interfaces. Then, by combining the artificial bee colony algorithm and various multi-objective optimization methods, the optimal ply angles and the corresponding co-optimized constants are determined. The correctness and accuracy of the method is verified not only by providing a comparison with the existing results but also by solving a known problem. The results are presented and discussed, considering different multi-objective optimization problems. The results show that the increasing number of layers in the problem of simultaneous optimization of Young’s moduli not only does result in finding more Pareto optimal solutions in the feasible objective region but also shifts the Pareto frontier toward the utopia point. However, when the shear modulus optimization is engaged in the problem, using more than two layers only leads to obtaining more Pareto optimal answers.

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Data availability

All data required to reproduce these findings exists in the text. It should be noted that the replication of these findings with enough number of cycles would result in the same objective values and similar variable values. However, the order of variables may change. A sample set of Matlab codes for determining the Pareto frontier in the problem of simultaneous optimization of Ex and Ey is available to download from [https://doi.org/10.17632/pkgty346y7.1].

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Authors and Affiliations

  1. School of Mechanical Engineering, Shiraz University, Shiraz, 7193616548, Iran

    Meysam Esmaeeli, Behzad Kazemianfar & Mohammad Rahim Nami

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  1. Meysam Esmaeeli
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  2. Behzad Kazemianfar
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  3. Mohammad Rahim Nami
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Highlights

• A combination of ABC algorithm and multi-objective optimization methods was used to maximize the laminate elastic constants simultaneously.

• The method was validated by using benchmark data, solving a problem that its answer was known, and finding the Pareto optimal frontier.

• Obtained angles in simultaneous optimization of Ex, Ey, and Gxy can be paired in a way that the absolute value of their difference becomes 90°.

• A stair shape Pareto optimal frontier was observed in the optimization of Ex and Ey. The stair shape approached to a straight line as the number of layers increased excessively.

• More layers in Young’s modulus optimization problem not only does result in finding more Pareto optimal solutions, but also shifts the Pareto frontier toward the utopia point.

• Current method is quick in determining the best ply angles and the Pareto optimal frontier regardless of the problem dimension.

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Esmaeeli, M., Kazemianfar, B. & Nami, M.R. Simultaneous optimization of elastic constants of laminated composites using artificial bee colony algorithm. Adv Compos Hybrid Mater 2, 431–443 (2019). https://doi.org/10.1007/s42114-019-00106-7

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  • DOI: https://doi.org/10.1007/s42114-019-00106-7

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