S-shaped mode in the lower and upper bounds of the buckling of composite beams with two equal delaminations

In this paper, lower and upper bounds of the buckling load of a composite beam with two equal delaminations are obtained by developing analytical models. The characteristic equations governing the delamination buckling are derived by using Euler–Bernoulli beam theory, performing proper linearization and by imposing the appropriate continuity and boundary conditions. The effects of the differential stretching and the bending-extension coupling are considered. The accuracy of the models is verified by comparing results with previously published data and a separately carried out finite element analysis. The effects of the dimensions and locations of the two equal delaminations on the lower and upper bounds of the buckling load are investigated in detail. The lower and upper bounds of the buckling load strongly depend on the sizes and locations of the two equal delaminations. For certain lengths and thicknesswise locations of the two equal delaminations, S-shaped buckling mode strongly influences the buckling behavior for both the upper and lower bounds of the buckling load. The lower and upper bounds of the buckling load will be useful to gauge the working range of the bridging and give guidelines for practical applications.