The Evaluation of Theoretical Critical Compression in Sandwich Plates

Formulas for the critical compression of sandwich plates, which take into account everything that might influence the buckling load, are extremely complex. When simplicity is achieved by concessions in accuracy, the range of validity is not easily distinguished. The evaluations presented here use check points obtained from an "exact" analysis to test the accuracy of simpler formulas, with the result that one of the latter (proposed in reference 5) is found to be remarkably accurate over a wide range of geometrical and elastic parameters. (1) INTRODUCTION AND SUMMARY OF R E S U L T S THE COMPRESSIVE STRENGTH of thin sheets can be realized only if they are stabilized against buckling. In sandwich construction, two such sheets are bonded to a core slab of different (light) material. The core is sometimes isotropic, sometimes anisotropic. Only the isotropic case is considered here. Panels of this construction give rise to a set of problems of strength, stiffness, and stability analogous to, but by no means identical with, the well-known problems of the ordinary homogeneous and isotropic elastic plate. One of these is "cylindrical buckling," illustrated in Fig. 1. The panel is so wide tha t lines such as E F can be taken as uncurved. In the ordinary plate, a unit width is treated as a Euler column, but , since anticlastic curvature is prevented, the Young's modulus E is replaced by 12/(1 — v), v being Poisson's ratio.** If it could be assumed t h a t plane sections remained plane, the corresponding sandwich problem would require merely a straightforward modification to take account of the fact t ha t the section is composite ra ther than homogeneous, ff This assumption will be valid when the modulus of the core (Ec) and t h e modulus of the face sheets (Ef) are not too far apart . The sandwich constructions of interest to aeronautical engineers Received February 1, 1951. * The results reported herein were obtained in the course of research studies supported by the Office of Naval Research (Contract N6-ONR-251-TO-12 with Stanford University). f Professor of Engineering Mechanics. X Research Assistant. ** Actually a wide strip must begin to bend with anticlastic curvature, but this curvature does not develop as bending proceeds. There is a transition from E to E/(l — v). The critical load for infinitesimal buckling would appear, therefore, not to require the factor 1/(1 — v), f t See Eq. (11). have light cores with low moduli—not so low tha t they leave the sheets practically free to buckle as independent sheets and not so high tha t plane sections remain plane. The actual buckling is either like column buckling (quasi-Euler buckling) or a short wave "wrinkling" of the face sheets. In the former, the core m a y exhibit a substantial shearing deformation; in the latter, it acts like an elastic foundation, and the buckling deformation may be confined to the layers adjacent to the face sheets. These s tatements rest on the numerous investigations published during the past 10 years. (A few of these are cited in the list of references.) One group of these deals only with the quasi-Euler buckling, the procedure simplest in principle being the introduction of the "correction due to shear" in the elementary bending theory. Another group deals with both quasi-Euler buckling and with wrinkling,, treating the core deformation by the methods of the ordinary theory of elasticity. This involves the assumption tha t the (usually small) compressive load borne by the core does not influence its response to lateral forces. A third group goes further by taking this influence into account. The theory used for the core is an extension of the ordinary theory of elasticity developed in the past 20 years which can deal, in general, with elastic deformations in the presence of initial stress severe enough to exert a destabilizing effect; a simple and well-known instance is the lateral loading of an initially compressed bar. The solutions of the sandwich problem so obtained are necessarily complicated. Prior to their appearFIG. 1. Cylindrical buckling of a wide plate in compression.