On the nonlinear post-critical responses of VAT sandwich beams with variable stiffness composite skins under axial compression

Abstract

In this article, the nonlinear post-critical problem of Variable Angle Tow (VAT) sandwich beams with variable stiffness composite skins under axial compression is studied for the first time. The present sandwich beam model is constructed from a modified version of extended high-order sandwich panel theory (EHSAPT), in which the first-order shear deformation theory with von Kármán’s strain–displacement relation is utilized for the skin layer, whereas the high-order theory with linear strain–displacement is applied to characterize the deformation of the core layer. Based on the principal of virtual work, a system of differential equations with variable coefficients is firstly formulated for the postbuckling problem of VAT sandwich beams with variable stiffness composite skins under plane-strain state. Meanwhile, a more efficient Rayleigh–Ritz approach combined with variational formulas is employed to derive the nonlinear algebraic equations in weak forms, and thereafter a sophisticated path-tracing technique is applied to determine the postbuckling equilibrium path. Both super-critical and sub-critical postbuckling states of VAT sandwich beams can be readily captured under the present analytical model framework. The accuracy and effectiveness of the developed Rayleigh–Ritz procedure are validated by comparing against the results available in literature. Effects of variation in skin stiffness on both the critical instability and post-critical behaviours of VAT sandwich beams are discussed in numerical examples. It is found that the change in skin stiffness plays a determinative role in the formation of nonperiodic wrinkling patterns of VAT sandwich beams. In addition, the change in skin stiffness may cause global and local instability loads to be close to each other, and accordingly, the possibility of encountering interactive buckling is increased. The results presented herein may be beneficial for the design of VAT sandwich structures under compression.