High-order behavior of sandwich panels with a bilinear transversely flexible core

A closed-form high-order theory for the analysis of a sandwich panel with a core made of a material characterized by a nonlinear constitutive relation is presented. The material nonlinearities in the core are a result of bilinear constitutive relations of the shear and vertical normal stresses. The governing equations are nonlinear in the longitudinal and in the vertical coordinates in general. The solution procedure adopted is an iterative one along with convergence criteria. The numerical examples include three types of core material behaviors: the first one deals with a bilinear constitutive relations for the shear stress only; the second one with a bilinear constitutive relations for vertical normal stresses only, and the last case considers the behavior of a panel characterized by bilinear constitutive relations for the shear and the vertical normal stresses. The results demonstrate the relaxation of the stress concentration involved as the load level increase beyond the yielding level and as the secant modulus decrease. In the sequel, a summary and conclusions are presented.