A semianalytical solution for the bending of clamped laminated doubly curved or spherical panels

Abstract

A semianalytical solution is presented for bending of moderately thick fully clamped laminated doubly curved panels using the extended Kantorovich method (EKM). The panel is subjected to uniform and nonuniform distributed loading and cut from a rectangular platform. Based on the first-order shear deformation theory, five highly coupled second-order partial differential equations in terms of displacement components are derived. Assuming separable functions for panel displacements together with the EKM converts the governing equations into double sets of ordinary differential equations with constant coefficients in terms of x and y. The resulting ODE systems are then solved iteratively until a level of prescribed convergence is achieved. Closed-form solutions can be presented for ODE systems in each iteration. Efficiency and rapid convergence of the solution technique are examined using several examples. Predictions of both deflection and stress resultants show very good agreement with other available results in the literature. It is also shown that the same formulation and solution method can be used to obtain results for spherical and cylindrical panels and rectangular plates.