Abstract
It is well established that for a compliance constraint, the optimal topology of perforated plates under plane stress tends to that for least-weight trusses (Michell structures) as the “volume fraction” (i.e. the ratio material volume/available volume) approaches zero. It is shown in this note that for two loading conditions the optimal bar orientations for Michell structures are in general non-orthogonal and hence the assumption of orthogonal microstructures in multi-load plate topology optimization must lead to erroneous results.
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Rozvany, G.I.N., Zhou, M. & Birker, T. Why multi-load topology designs based on orthogonal microstructures are in general non-optimal. Structural Optimization 6, 200–204 (1993). https://doi.org/10.1007/BF01743514
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DOI: https://doi.org/10.1007/BF01743514