Boundary Condition Effects in Buckling of “Soft” Core Sandwich Panels

Abstract

The effects of boundary conditions on the critical load level and the corresponding deflection mode shape of sandwich panels with a “soft” core due to in-plane loads are presented. The study is conducted using a closed-form high-order linearized buckling analysis that includes the influence of the transverse flexibility of the core as well as of the localized effects on the overall sandwich panel behavior, and allows the use of different boundary conditions for the upper and lower skin at the same section. The panel construction is general and consists of two skins (not necessarily identical), metallic or composite-laminated symmetric, and a soft core made of foam or a low-strength honeycomb. The closed-form high-order analysis yields the general buckling behavior of the structure, which means that the solutions obtained allow for interaction between the skins and the core. The solutions are general and are not based on separation of the buckling response on several types of uncoupled buckling modes, such as overall buckling, skins wrinkling, etc., as commonly used in the literature. The numerical scheme consists of finite differences to approximate the governing equations of the closed-form high-order formulation and to transform the set of linearized governing differential equations into an eigenvalue problem that is solved using the deflated iterative Arnoldi procedure. The influence of a general type of boundary conditions, including different conditions throughout the height of the same section and nonidentical conditions at the upper and lower skin, as well as of the core properties, on the buckling behavior of the sandwich panels is considered. The discrepancy between the Timoshenko-Reissner model and the present formulation is discussed. In particular, a partial fixity phenomenon due to the existence of the pinned boundary conditions, i.e., simply supported conditions, at the upper and lower skins at the edge is demonstrated. It is shown that the core properties affect the buckling loads and the corresponding modes of the panel in such a way that the structures with identical boundary conditions but with different cores may undergo different types of buckling such as overall and local as well as interactive loss of stability. The effect of an edge concentrated moment, induced by a couple and exerted on the skins only is also studied.