Buckling Analysis of Tri-layer Beams with Overlapped Delaminations

Abstract

An exact solution to the buckling behavior of tri-layer beams with two overlapped delaminations is presented for the first time. In addition, new nondimensionalized parameters, axial and bending stiffnesses and effective slenderness ratio, are introduced. The characteristic equation governing buckling is derived by using the Euler-Bernoulli beam theory, performing proper linearization and by imposing appropriate equilibrium, kinematical continuity, and boundary conditions. Results of the present method are compared with those of homogeneous beams having single and double equal delaminations reported previously, and showed an excellent agreement. A parametric study has been carried out. The buckling load varies monotonically with the normalized axial stiffness whereas it does not with the normalized bending stiffness, where a transition region is observed. The effect of spanwise delamination location on critical buckling load is discussed for a tri-layer beam of carbon/epoxy, glass/epoxy, and carbon/epoxy. The accurate solution can serve as a benchmark solution for other numerical schemes.