Response of Orthotropic Sandwich Plates to Concentrated Loading

Abstract

Sandwich plates are often analyzed with either classical or first order shear deformation theory. However experiments have shown that for lower stiffness cores and with concentrated loadings, these theories omit important features of the response. Recently a higher order theory for sandwich beams and plates has appeared in the literature that appears to better predict the response of sandwich structures. This theory treats the faces of the sandwich as independent orthotropic plates, coupled together by means of a simplified elasticity solution for the core that includes shear deformation and through-the-thickness strains. Analytical solutions for transverse static loading of plates can be obtained for simply-supported boundary conditions, analogous to the Navier solution. However the accuracy of this theory has not been sufficiently examined. In this paper the exact elasticity solution available for this problem is used to compare with the higher order sandwich theory. The results show that classical and first order shear deformation theory under-predict stresses and strains in the sandwich faces by more than an order of magnitude, while the higher order shear deformation theory is much more accurate. Although the higher order theory gives reasonable agreement with the elasticity solution, and is believed to be useful in practical application, it still gives errors on the order of 10 to 25% in face strains and interface shear stresses. The elasticity solution shows that the shear stress varies through the core thickness in the vicinity of localized loads, contrary to the assumptions of the higher order sandwich theory.