Analytical solution to flexural responses of annular sector thin-plates

• Published in: Thin-walled structures Vol. 48; no. 12; pp. 879 - 887
• Main Authors: Kim, Kyungsik, Yoo, Chai H.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.12.2010; Elsevier
• Subjects: A closed-form solution; Analytical solution; Annular; Annular sector plate; Convergence; Deflection; Elastic deflection; Exact sciences and technology; Exact solutions; Finite element analysis; Finite element method; Fundamental areas of phenomenology (including applications); Mathematical analysis; Mathematical models; Physics; Plates; Polar coordinates; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); A closed-form solution; Annular sector plate; Finite element analysis; Analytical solution; Elastic deflection; Annular plate; Polar coordinate; Thin plate; Coordinate system; Modeling; Trigonometric series; Exact solution; Finite element method; Sector structure; Bending vibration
• ISSN: 0263-8231; 1879-3223
• DOI: 10.1016/j.tws.2010.05.002

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.