| Buckling loads and postbuckling of clamped anisotropic laminated thin elliptical plates are obtained and used to investigate the buckling and growth behavior of elliptical thin-film delaminations in a general laminate. A symbolic algorithm is developed to generate the algebraic equations governing the expansion coefficients in the Rayleigh-Ritz procedure. Approximate postbuckling solutions based on polynomial expansions of the various orders for the displacement functions are calculated and compared in order to determine the lowest order expansion that can yield reasonably accurate results for the displacements, force and moment resultants, and the global and pointwise energy release rates. Numerical results for cross-ply and angle-ply delamination models with various aspect ratios are systematically evaluated to assess the effects of geometrical and material parameters, stacking sequence and the level of loading upon the buckling, postbuckling, and delamination growth behavior.;Furthermore, in the case of general model of strip delamination, we investigate the small vibration of the delaminated beam-plate with respect to a referential buckled state in chapter eight. The natural frequency of vibration depends on the geometry and material of the models as well as the loading in the referential state. The vibration solution of the differential equations governing the transverse motion is based on the perturbation of the static solution. The frequency and the fundamental mode of vibration of the delaminated beam-plate are solved numerically to determine the effects of delamination geometry on the frequencies and the mode shapes of vibration. The symmetrical and antisymmetrical mode shapes are shown to be uncoupled. In addition to familiar vibration modes where the split segments move generally in-phase, there are new out-of-phase vibration modes whose presence and frequencies are useful indications of delamination damage. |
