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By Suresh G Advani; Gabriel O Shonaike

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These results were obtained by considering a tetrahedron of ply angle percentages corresponding to 0°(p%), 90°(q%), 45(r%) with –45(s = 1 – p – q – r%). The vertices, edges, and surfaces of the tetrahedron make up a 14-ply angle. Combinations and the optimal percentages of each ply angle can be determined by considering these combinations individually. Applying this procedure, the optimum percentages p, q, r, and s can be computed for any stress combination. Strength optimization of laminates under transverse loading was studied by Song et al.

Several failure criteria were developed over the years to describe the failure state that could be stress- or strain-based. A criterion itself could be in the form of a single inequality based on energy considerations such as Tsai–Hill or Tsai–Wu criteria, which reduce to von Mises’ criterion in the case of isotropic materials. Alternatively, it could be in the form of several inequalities based on maximum stress or strain in the material directions. For further study of failure criteria, refer to one of the books on the mechanics of composite materials (Gibson, 1994; Daniel and Ishai, 1994; Hyer, 1998; Berthelot, 1999; Jones, 1999).

3 Buckling and Postbuckling Optimization: Complicating Effects An extensive review of the state of the art in the buckling optimization of laminated plates has been given in Adali (1995). In the present section, emphasis is placed on complicating effects such as thermal loads, stiffened laminates, thickness tailoring, cost, and optimization in the postbuckling range. fm Page 21 Monday, June 21, 2004 10:51 PM designs. In this section, the optimization of composites including these effects is illustrated by means of specific examples in which these effects can be observed.

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