Boundary discontinuous Fourier solution of thin Levy type flat and doubly curved shallow shells

Abstract

This study presents a static analysis of thin shallow cylindrical and spherical panels, as well as plates (which are a special case of shells), under Levy-type mixed boundary conditions and various loading conditions. The study utilizes the boundary discontinuous double Fourier series method, where displacements are expressed as trigonometric functions, to analyze the system of partial differential equations. The panels are subjected to a simply supported type 3 (SS3) boundary condition on two opposite edges, while the remaining two edges are subjected to clamped type 3 (C3) boundary conditions. The study presents comprehensive tabular and graphical results that demonstrate the effects of curvature on the deflections and moments of thin shallow shells made from symmetric and antisymmetric cross-ply laminated composites, as well as isotropic steel materials. The proposed model is validated through comparison with existing literature, and the convergence characteristics are demonstrated. The changing trends of displacements and moments are explained in detail by investigating the effect of various parameters, such as stacking lamination, material types, curvature, and loading conditions.