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By Suresh G Advani; Gabriel O Shonaike

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The uncertainty parameter for single-load cases, and the insert for multiple-load cases. (Reprinted from S. , 1997, ASME J. Appl. , 64:90–96. 8 Minimum thickness vs. the aspect ratio for single-load cases, and the insert for multiple-load cases. (Reprinted from S. , 1997, ASME J. Appl. , 64:90–96. 5, indicating that neglecting the effect of uncertainty leads to substantial design errors. 7. It is observed that loading case 3 is the critical one for all values of S for a/b = 1. 5, different loading cases become critical at different values of S.

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.

Miki et al. (1989, 1990a, 1990b, 1993, 1997), Yang and Ma (1989), Shao et al. (1991, 1992, 1993), Murotsu et al. (1994), Boyer et al. (1997), and Nozomu et al. (1998) applied reliability methods for the optimum design of laminated composites subject to load and material uncertainties. Nonprobabilistic techniques were also employed to study the behavior of structures subject to uncertain load conditions when there is no information available on statistical distributions and probability functions of relevant quantities.

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