Elastic Coupling Effects in Tapered Sandwich Panels with Laminated Anisotropic Composite Facings

Abstract

A newly developed theory for the analysis of tapered sandwich panels with laminated anisotropic facings is presented. Unlike sandwich panels of uniform depth, the response of tapered sandwich panels is counterintuitive. For example, prior studies have demonstrated that a tapered cantilever sandwich beam having constant dimensions at the clamped edge and subjected to a tip load has an optimum taper angle where the tip deflection is a minimum. The decrease in tip deflection with increasing taper angle, despite the reduction in core thickness, is due to the participation of the facings in resisting transverse shear loads. In the present work, we systematically develop a tapered sandwich theory that is simple to use, yet accurately predicts the stresses and deflection of both symmetric and nonsymmetric tapered sections. A novel feature of the analytical model is that the elastic rigidities of tapered sandwich composites are expressed in terms of the familiar A, B, and D matrices that are widely used to analyze the response of laminated plates and sandwich beams of uniform depth. It is shown that the stiffness matrix for a tapered sandwich member exhibits a total of 12 elastic couplings that are absent in sandwich beams of uniform depth. The analytical model predicts large interlaminar shear and normal stresses near the root of the tapered sandwich beam, which can cause delamination failure between the facings and the core. Numerical results obtained using the tapered sandwich theory and two-dimensional finite element models are in good agreement for several case studies.