On the surface elastic-based shear buckling characteristics of functionally graded composite skew nanoplates

Abstract

Abstract The prime objective of the present investigation is to predict the shear buckling characteristics of skew nanoplates made of a functionally graded material (FGM) in the presence of surface stress effect. For this purpose, the Gurtin-Murdoch surface theory of elasticity is applied to the higher-order shear deformation plate theory within the framework of the oblique coordinate system. Different types of the homogenization scheme including Reuss model, Voigt model, Mori-Tanaka model, and Hashin-Shtrikman bounds model are taken into consideration in order to extract the effective mechanical properties of FGM skew nanoplates. The Ritz method using Gram-Schmidt shape functions is utilized to obtain the surface elastic-based shear buckling loads of FGM skew nanoplates. It is indicated that by increasing the value of the index associated with the material property gradient, the significance of the surface stress type of size effect on the shear buckling behavior of a FGM skew nanoplate improves. Moreover, by changing the boundary conditions from simply supported ones to clamped ones, the influence of the skew angle on the surface elastic-based shear buckling load of a FGM skew nanoplate increases. Also, it is illustrated that by increasing the width to thickness ratio of a skew nanoplate, the free surface area increases which results in to enhance the effect of surface residual stress on its shear buckling characteristics.