Instability problem of multiple penny-shape interlaminar delaminations in circular axisymmetric plates subjected to a transverse concentrated loading is theoretically studied. The authors consider a case that all the delaminations located at the same intervals have a same size and propagate simultaneously. Then, they consider two cases that one of the delaminations is larger or smaller than the rest. The energy release rates are obtained in closed forms and the results are compared with those obtained numerically via a finite element analysis. The present solutions agree excellently with the finite element results. When the load is constant, the energy release rate is constant regardless of the size of the delaminations and increases linearly with the number of the delaminations. When one of the delamination is larger or smaller than the others, the energy release rate of the shorter delamination or delaminations become much larger than that of the longer delamination(s), that is, only the smaller delamination(s) tends to propagate until it grows up to the size of the larger delamination(s). Multiple delaminations, if they exist, have a tendency to grow self-similar way.

Instability problem of multiple penny-shape interlaminar delaminations in circular nonlinear axisymmetric plates subjected to a transverse loading is theoretically studied. It is an idealized problem of damage accumulation in composite laminates due to low velocity impact loading. All the delaminations having a same size are located at a same interval. Nonlinear behaviors of the plates are approximately solved through Rayleigh-Ritz method considering only two mode functions, that is, global and local mode functions which are based upon a linear exact solution. Energy release rate due to a simultaneous propagation of all the delaminations is obtained approximately and the results are compared with those obtained via a finite element analysis. The present solutions agree excellently with the finite element results except when the nonlinear effect is extremely large. The energy release rate significantly decreases with the propagation of the delaminations due to the nonlinear effects, particularly when the number of the delaminations is large. The load must be increased to keep the delaminations to propagate. The conclusions from the results obtained based on the linear assumption that the more delaminations exist, the easier delaminations propagate, may not be true when the nonlinear effect is considered.

The effect of localized damage due to impact on compressive buckling as well as postbuckling behaviors of blade stiffened composite plates was numerically studied. A partial debonding between a skin panel and a flange and multiple delaminations in the skin panel were chosen as the localized damage. The three-dimensional composite elements used to analyze the compressive behavior of the stiffened panel with multiple delaminations was found to be suitable for this kind of complex composite structure. The contact problem between the skin and flange panels was approximated by a spring element with no restraint of the positive relative displacement and a strong restraint of the negative displacement. At the delaminations in the skin panel, which tended to close during compression, the normal relative displacement was constrained to prevent the delaminated portions from overlapping; this constraint made the convergence of the solution quite smooth compared to the case where the contact problem was exactly considered. When a debonded area only was located at the edge of the flange, no notable reduction of compressive buckling load was found until the size of the debonding reached a half wavelength of the buckling mode. The compressive buckling load dropped significantly when multiple delaminations, which were small in comparison to the half wavelength of the buckling mode, accompanied the skin-flange debonding. The energy release rate distributions at the damage edges, calculated using the virtual crack closure technique, increased quite rapidly, particularly in the transverse direction after buckling became sufficient to increase the delamination.

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