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Application of explicit energy bounds in optimization of 3D elastic structures

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Abstract

We present a novel numerical method for calculating optimal design in topology optimization problems for 3D linear elastic structures. The algorithm is based on necessary conditions of optimality for problem which was obtained by relaxing the original one via the homogenization method in the sense of operators (G- or H-convergence), and can be implemented for self-adjoint problems. The method relies on recently obtained explicit expressions for the lower Hashin–Shtrikman bound on complementary energy and information on the microstructure that saturates the bound. We tested the algorithm on two benchmark examples, namely the cantilever and the bridge problem. The algorithm provides the solution in a first few iterations and the true composites appear in the optimal design. We also implement a penalization procedure to obtain classical design with slight increase of the cost functional.

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Acknowledgements

We would like to thank to Prof. Domagoj Matijević (School of Applied Mathematics and Computer Science, J. J. Strossmayer University of Osijek) who provided us with technical support for execution of parts of the algorithm.

Funding

This work has been supported in part by Croatian Science Foundation under the projects 8904 Homdirestroptcm.

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Authors and Affiliations

  1. School of Applied Mathematics and Computer Science, J.J. Strossmayer University of Osijek, trg Lj. Gaja 6, 31000, Osijek, Republic of Croatia

    Krešimir Burazin & Ivana Crnjac

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  1. Krešimir Burazin
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  2. Ivana Crnjac
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Correspondence to Ivana Crnjac.

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Burazin, K., Crnjac, I. Application of explicit energy bounds in optimization of 3D elastic structures. Optim Eng (2023). https://doi.org/10.1007/s11081-023-09840-w

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