Abstract
In this paper we investigate optimization of laminates for maximal membrane stiffness under single in-plane loads. The design parameters are the relative ply thicknesses and fiber orientations of an arbitrary number of plies. The design is allowed to vary in a pointwise fashion throughout the structure.
From prior work on lamination parameters (Hammeret al. 1997), it is known that the optimal design is given by either some sort of two ply lay-up in special strain situations or otherwise by just a single rotated ply. This is exploited in the present analysis to derive analytically the unique parameters of the optimal design (cross-ply, angle-ply or single ply) as expressions of the membrane forces. Both high and low shear stiffness material are treated. Furthermore the analysis covers all possible local strain or membrane force situations.
Finally, it is shown how these expressions for the optimal configuration of the laminate also appear as bounds on the principal membrane forces in order to obtain alignment between the numerically largest principal membrane force and principal strain.
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Hammer, V.B. Optimal laminate design subject to single membrane loads. Structural Optimization 17, 65–73 (1999). https://doi.org/10.1007/BF01197714
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DOI: https://doi.org/10.1007/BF01197714