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Topology optimization of load-bearing capacity

Abstract : The present work addresses the problem of maximizing a structure load-bearing capacity subject to given material strength properties and a material volume constraint. This problem can be viewed as an extension to limit analysis problems which consist in finding the maximum load capacity for a fixed geometry. We show that it is also closely linked to the problem of minimizing the total volume under the constraint of carrying a fixed loading. Formulating these topology optimization problems using a continuous field representing a fictitious material density yields convex optimization problems which can be solved efficiently using stateof-the-art solvers used for limit analysis problems. We further analyze these problems by discussing the choice of the material strength criterion, especially when considering materials with asymmetric tensile/compressive strengths. In particular, we advocate the use of a L 1-Rankine criterion which tends to promote uniaxial stress fields as in truss-like structures. We show that the considered problem is equivalent to a constrained Michell truss problem. Finally, following the idea of the SIMP method, the obtained continuous topology is post-processed by an iterative procedure penalizing intermediate densities. Benchmark examples are first considered to illustrate the method overall efficiency while final examples focus more particularly on no-tension materials, illustrating how the method is able to reproduce known structural patterns of masonry-like structures. This paper is accompanied by a Python package based on the FEniCS finite-element software library.
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https://hal-enpc.archives-ouvertes.fr/hal-03270638
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Soumis le : vendredi 25 juin 2021 - 09:07:35
Dernière modification le : mardi 7 septembre 2021 - 13:36:29
Archivage à long terme le : : dimanche 26 septembre 2021 - 18:15:37

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Leyla Mourad, Jeremy Bleyer, Romain Mesnil, Joanna Nseir, Karam Sab, et al.. Topology optimization of load-bearing capacity. Structural and Multidisciplinary Optimization, Springer Verlag (Germany), 2021, 64 (3), pp.1367-1383. ⟨10.1007/s00158-021-02923-1⟩. ⟨hal-03270638⟩

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