By Suresh G Advani; Gabriel O Shonaike
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Additional resources for Advanced polymeric materials : structure property relationships / [...] XA-GB
The solution of the anti-optimization problem yields the values of Nx and Ny, corresponding to the worst case of loading, which minimizes the reserve factor. Computing the optimal θk requires the solution of the coupled anti-optimization/optimization problem. The coupling of anti-optimization and optimization problems occurs because of the interdependence of uncertainty and design variables. 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.
13) where the maximum stresses satisfy the chosen failure criterion. The strength ratio provides quantitative information on the relation between the applied stresses and the maximum stresses that can be applied before failure. 14) gives the strength ratio for the laminate. 15) subject to σxk, σyk, and τxyk satisfying the failure criterion for all k = 1, 2, …, K, where K is the total number of layers. Susuki (1991) determined the optimal ply angles under various loading conditions using the discrete set of angles (0°, ±45°, 90°) for graphite/epoxy (T300-N5208) laminates subject to Tsai–Wu failure criterion.
Similarly, the initial postbuckling stiffness P* under biaxial loading is defined as P* = min( P x* , P y* ). Due to the specific nature of the problem involving conflicting design objectives, several laminate configurations with ply angles of θ, 0°, and 90° are considered as candidate designs. More specifically, the configurations of the candidate designs are taken in the form of (θ/–θ/ … /0°/ … /90°/ … /0°/ … )s. The best design gives the highest design index, DI, leading to the optimal laminate configuration.
Advanced polymeric materials : structure property relationships / [...] XA-GB by Suresh G Advani; Gabriel O Shonaike