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Optimization of plate supports using a feature mapping approach with techniques to avoid local minima

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Abstract

In this paper, we present a methodology for optimizing the locations of supports in arbitrary plate structures. We adopt a feature mapping approach where the stiffness of the supports is projected onto the finite element mesh using smooth super-Gaussian radial functions. This effectively separates the design space from the analysis model and a compact optimization problem with a continuous design space is obtained. We develop three techniques that improve the obtained minima significantly, namely: continuation of the stiffness projection; control over the initial design; and numerical damping. These techniques make the optimization insensitive to the initial design and much more resilient to convergence to local minima. Furthermore, the proposed method is not sensitive to the finite element mesh density, so coarse meshes may be used to reduce the computational cost. Results show that the optimal locations of supports are not trivial, especially in complex plate geometries, and that asymmetric distributions of supports may be optimal even if the plate is symmetric.

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Funding

This research was funded by the Ministry of Construction and Housing, Israel. The financial support is gratefully acknowledged.

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Authors and Affiliations

  1. Faculty of Civil and Environmental Engineering, Technion – Israel Institute of Technology, Haifa, Israel

    Yakov Zelickman & Oded Amir

Authors
  1. Yakov Zelickman
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  2. Oded Amir
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Correspondence to Yakov Zelickman.

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The authors declare that they have no conflict of interest.

Replication of results

To preform replication of the results presented in this paper, all parameter settings and implementation aspects have been described in detail in the paper. In addition, upon request an executable code file and associated data will be provided for research and education purposes.

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Appendix: Optimization parameters

Appendix: Optimization parameters

In this annex, we will provide the values of all parameters as used in the current study. As mentioned, in this study we used the MMA algorithm with all parameters set to their default. However, we scaled the compliance functional (and derivatives) by \({1\times 10^{-4}}\) so that a reasonable number of inner MMA iterations will be required for convergence of the MMA iterations. Other parameters are listed in Table 3.

Table 3 Optimization method parameters
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Zelickman, Y., Amir, O. Optimization of plate supports using a feature mapping approach with techniques to avoid local minima. Struct Multidisc Optim 65, 31 (2022). https://doi.org/10.1007/s00158-021-03135-3

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  • DOI: https://doi.org/10.1007/s00158-021-03135-3

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