Free vibration and buckling study of doubly curved laminated shell panels using higher order shear deformation theory based on Sander's approximation

Abstract

The free vibration and static stability analyses of higher order shear deformable doubly curved laminated shell panels have been carried out in this paper. The proposed shear deformation theory takes care of the parabolic variation of the transverse shear strains through the thickness of the shell and assumes rigid body motion. An eight-noded isoparametric finite shell elements with nine degrees–of-freedom per node is used for the analysis based of Kant and Khares' higher order shear deformation theory. Full geometric nonlinearity in the Green–Lagrange sense is considered for the buckling analysis, whereas for free vibration study only linear strains are taken into account. A generic code is developed in the MATLAB platform to solve the vibration and buckling eigenvalue problems. The effect of various parameters such as thickness ratio, curvature ratio, orthotropic ratio, lamination scheme, number of plies, boundary conditions, and shell geometries on the natural frequencies and critical buckling loads of shell panels are investigated. The efficacy and accuracy of the present formulation has been validated by comparing the results with those available in literature. The fundamental frequencies and critical buckling loads are found to increase with an increase in thickness ratio, ratio of principal radii of curvatures, and orthotropic ratio, but exhibit a decreasing trend with an increase in aspect ratio and radii of curvatures.