Advanced polymeric materials : structure property by Suresh G Advani; Gabriel O Shonaike

By Suresh G Advani; Gabriel O Shonaike

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55) The optimal values of θk depend on the anti-optimal values of (Nx, Ny) and vice versa. The solution of this problem produces the best values of the ply angles for the maximum reserve factor under the least favorable loading condition. 56) where F11 = (Xt Xc)–1, F22 = (Yt Yc) –1, F66 = S–2, F12 = (1/2) (F11 F22)–1/2, F1 = Xt–1 – Xc–1, F2 = Yt–1 – Yc–1, with (Xt, Xc) and (Yt, Yc) denoting the tensile and compressive strengths in the fiber and transverse directions, respectively, and S the shear strength.

12) Vanucci and Verchery (2001) used the polar method to obtain laminates with required stiffnesses. The studies aimed at increasing the stiffness of composite laminates by design optimization include Fukunaga and Vanderplaats (1991), Kam and Chang (1992), Avalle and Belingardi (1995), and Todoroki et al. (1996). 2 Optimization for Maximum Strength Design of laminates to maximize their load-carrying capacity is achieved by using a suitable strength (failure) theory to characterize the failure. Several failure criteria were developed over the years to describe the failure state that could be stress- or strain-based.

4 Optimization under Material, Load, and Geometric Uncertainties Optimal design in structures, and in particular composite structures, under deterministic conditions has the drawback that the design becomes unreliable if these conditions change even slightly under service conditions. The optimization of composites using deterministic material and load data leads to designs that are optimal under those specific conditions. Such designs do not take structural variabilities and load uncertainties into account and as such may be sensitive to changes in the material properties, load directions, etc.

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