Rectangular and skew shear buckling of FG-CNT reinforced composite skew plates using Ritz method

Present research deals with the shear buckling behaviour of composite skew plates reinforced with aligned single walled carbon nanotubes (CNTs). Distribution of CNTs across the thickness of the skew plate are assumed to be uniform or functionally graded. Two different types of shear loads are considered. The case of rectangular shear which produces pure shear and the case of skew shear which results in a combined uniform shear and uniaxial tension/compression. Suitable for moderately thick plates, first order shear deformation plate theory is used to estimate the displacement field of the plate. The equivalent properties of the composite media are obtained by means of the refined rule of mixtures approach which contains efficiency parameters to capture the size dependent properties of the CNTs. With the aid of the Hamilton principle, transformation of the orthogonal coordinate system to an oblique one and the conventional Ritz method whose shape functions are constructed according to the Gram-Schmidt process, the stability equations of the plate are established and solved for two different types of loading, namely rectangular and skew shear loads. As shown, through introduction of a proper functionally graded pattern, i.e., FG-X pattern, the buckling load of the plate may be increased, significantly.