Analytical solution to flexural responses of annular sector thin-plates

Abstract

A novel analytical solution is presented for the flexural response of annular sector thin-plates. An exact solution has been developed in the series form including trigonometric and exponential functions in the polar coordinate system for annular sector plates subjected to uniform loading. The salient feature of the solution development includes the derivation of a closed-form solution for the fourth-order partial differential equation governing plate deflections in the polar coordinate system. The series solution developed in this study is not only very stable but also exhibits rapid convergence. To demonstrate the convergence and accuracy of the present method, several examples with various sector angles are selected and analyzed. Deflections and moments of example sector plates by the proposed solution are compared with those obtained by other analytical studies and then verified by numerical values evaluated by a commercial finite element analysis program, ABAQUS. Excellent agreements have been found between the results from the proposed analytical closed-form solution and numerical runs, thereby confirming the superior nature of the proposed method over other classical analytical techniques.