Lurie (1994, 1995a, b) proved recently that variabletopology shape optimization of perforated plates in flexure for non-selfadjoint problems leads to rank-2 microstructures which are in general nonorthogonal. An extension of the same optimal microstructures to perforated plates in plane stress will be presented in Part II of this study. Using the above microstructure, the optimal solution is derived in this part for cantilever plates in plane stress, which are subject to two displacement constraints. For low volume fractions the above solutions are shown to converge to the known truss solutions of Birkeret al. (1994). The problem of homogenizing the stiffness of nonorthogonal rank-2 microstructures is also discussed.
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Károlyi, G., Rozvany, G.I.N. Exact analytical solutions for non-selfadjoint variable-topology shape optimization problems: perforated cantilever plates in plane stress subject to displacement constraints. Part I. Structural Optimization 13, 119–127 (1997). https://doi.org/10.1007/BF01199230