Solution to Eigenvalue Problems of Antisymmetric Cross-Ply and Antisymmetric Angle-Ply Laminated Plates Using Affine Transformations.

摘要

Using affine transformations and suitably recasting the buckling vibration differential equations, the eigenvalue problem of anti-symmetric cross-ply and antisymmetric angle-ply laminated rectangular plates has been reduced to a function of two strong material constants, the generalized rigidity ratio, whose range is in the closed interval from 0 to 1, and the ratio of principal lamina stiffness. With the reduction in number of constants an exhaustive parameter study of buckling and vibration solution trends, is possible. The buckling coefficients decrease with decreasing value of generalized rigidity ratio for both antisymmetric cross-ply and antisymmetric angle-ply laminates. For a given aspect ratio, and ratio of principal lamina stiffnesses, the buckling and frequency coefficient for antisymmetric cross-ply laminates vary linearly with the value of the generalized rigidity ratio, so that one may accurately interpolate between the values of the generalized rigidity ratio. The buckling and frequency coefficients increase with increasing F for antisymmetric cross-ply laminates. No such trend could be established for antisymmetric angle-ply laminates. A simple and fairly accurate method has been established for estimating the buckling and vibration coefficients for anti-symmetric cross-ply laminates.