High‐Order Theory for Sandwich‐Beam Behavior with Transversely Flexible Core

Abstract

A general, high‐order theory based on variational principles is presented for the bending behavior of a sandwich beam with a core that is vertically flexible. The theory embodies a rigorous and systematic approach to the analysis of such structurs, which have high‐order effects caused by the nonlinearity of the longitudinal and the transverse deformations of the core through the height. As such, it improves on the available classical and superposition theories. Beam construction consists of the upper and lower skin, metallic or composite laminated symmetric, with nonidentical mechanical and geometrical properties, and a soft core made of foam or honeycomb. The formulation uses a beam theory for the skins and a two‐dimensional elasticity theory for the core. The behavior is presented in terms of internal resultants and displacements in skins, peeling and shear stresses in skin‐core interfaces, and stress and displacement fields in the core, even in the vicinity of concentrated loads. The method is applicable to any type of loading exerted on the skins and to any type of boundary or continuity conditions, including cases in which at the same section the conditions at the upper skin are different from those at the lower. Some typical cases are studied numerically.