A Note on a Non-Linear Theory on Bending of Orthotropic Sandwich Plates

Abstract

SummaryThe derivation of a non-linear theory on bending of orthotropic sandwich plates is carried out by the principle of complementary energy from elasticity. The governing differential equations and natural boundary conditions are obtained. The assumptions used are, namely, the facings are orthotropic thin elastic plates with negligible bending rigidities and are made of the same material; the orthotropic core can take the transverse shear only; and the transverse shortening of the core may be ignored. The geometrical non-linearities are equivalent to von Kármán’s theory for single-layered plates. Through the introduction of a “shear function”, the number of differential equations is reduced to three and the equations are in rather simple form. It appears that the equations obtained here would require, comparatively, the least amount of work for analysing the finite deflection sandwich plate problems having a wide range of properties of practical interest.