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Parallel 3D topology optimization with multiple constraints and objectives

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Abstract

This paper introduces a parallel Topology Optimization (TO) platform capable of optimizing designs for multiple objectives, whilst subject to multiple constraints, in the open source Fierro Finite Element code. The TO methodology uses a continuous material interpolation scheme, which avoids checkerboard designs without additional filters and constraints as seen with piece-wise constant material interpolation schemes. Additionally, analytic Hessian-vector products are used, with the relevant adjoint calculation shown. The code utilizes OpenMPI to make parallel the major computational segments of TO: global equation assembly, global equation solution, and the non-linear optimization of the design. The algorithm leverages several software packages: ELEMENTS (grants FE basis functions), MATAR (grants efficient multidimensional dense and sparse matrix storage), Zoltan2 (Mesh Decomposition Algorithm), MueLu (parallel multi-grid solver for the global equilibrium equations), and ROL (non-linear optimization). It is found that the Fierro TO platform optimizes problems with mechanical and thermal objectives subject to multiple constraints: mass, several moment of inertia targets, and constraints related to load bearing regions. Additionally, the performance of several ROL algorithms using analytic Hessian-vector products is compared with the Method of Moving Asymptotes, approximate Hessian, for topology optimization.

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Acknowledgements

The Los Alamos unlimited release number is LA-UR-22-32677. Los Alamos National Laboratory is operated by Triad National Security, LLC for the U.S. Department of Energy NNSA under Contract No. 89233218CNA000001. This work acknowledges Austin Sutton for providing the initial rabbit mesh used in Sect. 4.2.

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Author notes

  1. Nathaniel Morgan and John Bernardin equally contributed to this work.

Authors and Affiliations

  1. Computational Physics Division, Los Alamos National Laboratory, Bikini Atoll Rd SM 30, Los Alamos, NM, 87545, USA

    Adrian Diaz & Nathaniel Morgan

  2. Mechanical and Thermal Engineering, Los Alamos National Laboratory, Bikini Atoll Rd SM 30, Los Alamos, NM, 87545, USA

    John Bernardin

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  1. Adrian Diaz
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Correspondence to Adrian Diaz.

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Replication of results

All results presented in this work may be reproduced with the stated parameters using the Fierro codebase available at: https://github.com/lanl/Fierro. The rabbit mesh used in the work may be found in the following repo: https://github.com/Adrian-Diaz/My_Meshes.

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Appendix A: Verification

Appendix A: Verification

In order to verify the FEM solvers, several simple problems such as beam bending, tension/compression, and steady state heat flux were successfully matched to analytical results for beam geometries. Additionally, the optimization results were compared for the rabbit example seen in Sect. 4, subject to the same loading conditions, to the same optimization problem run using the Ansys Mechanical software. As seen in Fig. 9, the geometries are very similar; naturally results differ by a margin due to different optimization algorithms and material interpolation strategies.

Fig. 9
figure 9

Comparison of results from Fierro and Ansys software for compliance minimization under mass and yy moment of inertia constraints. Final objectives for the Fierro and Ansys results are 7.18 J and 7.17 J respectively. Relative errors in the mass constraint are 4.9% and 10% for Fierro and Ansys respectively. Relative errors in the Moment of Inertia constraint are 0.6% and 2.5% for Fierro and Ansys respectively. As demonstrated here, Fierro delivers a topology similar to the one from Ansys but the topology matches all design goals more accurately compared to the Ansys result

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Diaz, A., Morgan, N. & Bernardin, J. Parallel 3D topology optimization with multiple constraints and objectives. Optim Eng (2023). https://doi.org/10.1007/s11081-023-09852-6

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