A Semi-Analytical Solution for Bending of Moderately Thick Doubly Curved Functionally Graded Panels

Abstract

A semi-analytical solution for static response of fully clamped shear-deformable functionally graded (FG) doubly curved panels is presented. Panels with rectangular platforms are considered. Based on the first shear deformation theory (FSDT), a system of five highly coupled second-order linear partial differential equations (PDE) in terms of displacement components is obtained. Using the Extended Kantorovich Method (EKM), the governing system of PDEs is separated into two distinct systems of five coupled second-order ordinary differential equations (ODE). A successive procedure using close-form solutions for the resulted ODE systems is presented until a predefined level of convergence is reached. The efficiency of the method in terms of stability and convergence rate is examined by various examples. Results revealed that the method is stable for various geometric parameters while providing very fast convergence. It is shown that the solution procedure is useful in the case of assuming infinite values for one or both curvature radii which represent cylindrical panel or rectangular plate, respectively. It is shown that predictions of the method for FG cylindrical panels show very good agreement with finite element and differential quadrature methods. Furthermore, extensive results for both deflections and stress resultants of clamped FG doubly curved panels are resented for future references.