Keywords: annular sector plates, large deflections, elasto-plasticity, yield criteria.

Balcony floors in theatres and cinemas, circular curved bridge decks and plating between radially and circumferentially stiffened flat end closures of cylindrical pressure vessels are practical examples of annular sector plates used as load-bearing structural elements. Structures with circular geometry are generally more difficult to fabricate and, therefore, are much less common than those with rectangular geometry. These facts may explain why, compared to rectangular plates, far less effort has been directed towards developing knowledge and understanding of the structural response of annular sector plates. Indeed, during the course of the past sixty years, research on the structural analysis of annular sector plates has been sporadic. One of the earliest elastic small deflection annular sector plate analyses was carried out by Carrier [1] for the case of uniform transverse pressure and clamped edges. More recent studies for other edge support conditions and loading arrangements have been reported by Cheung and Chen [2], Rubin [3], Harik [4] and Azad [5]. These authors used a variety of formulations and analysis techniques, some of which also included polar material orthotropy and variable plate thickness.

Chisyaki and Takahashi [6] appear to be the first to have investigated the elastic large deflection, static and dynamic response of annular sector plates. They used Berger's approximation in a strain energy analysis and presented results for uniformly loaded plates with simply supported radial edges and clamped or simply supported curved edges. Further large deflection solutions for uniformly loaded plates with clamped in-plane fixed and free edge conditions were reported by Srinivasan and Thiruvenkatachari [7,8]. Der Avanessian [9] also obtained large deflection solutions for uniformly loaded annular sector plates with various boundary conditions using the Finite Element (FE) method. More recently, the authors [10] reported elastic large deflection results for uniformly loaded annular sector plates, which were computed using finite differences in conjunction with the Dynamic Relaxation (DR) method [11]. However, it appears that no results have been reported for the elasto-plastic large deflection response of annular sector plates.

Hence, the main objective of the present paper is to make a contribution towards closing this knowledge gap. The governing equilibrium, incremental strain/ curvature, incremental constititive and boundary condition equations are outlined first. Their numerical solution, using the DR algorithm and finite differences is then explained. Thereafter, numerical results are verified by comparison with exact first yield solutions. New results, which quantify the effects of: plate edge support conditions and the Ilyushin/Von Mises yield criteria on the centre deflection, radial stress resultant and radial stress couple, are presented for uniformly loaded stocky and slender annular sector plates.

1

G.F. Carrier, "Bending of a Clamped Sectorial Plate", Transactions of the American Society of Mechanical Engineers, Journal of Applied Mechanics, 11(33), A134-A139, 1944.

2

M.S. Cheung and M.Y.T. Chan, "Static and Dynamic Analysis of Thin and Thick Sectorial Plates by the Finite Strip Method", Computers & Structures, 14(1-2), 79-88, 1981. doi:10.1016/0045-7949(81)90086-9

3

C. Rubin, "General Solution to Bending of Orthotropic Sectors", Proceedings of the American Society of Civil Engineers, Journal of Engineering Mechanics, 109(1), 168-174, 1983. doi:10.1061/(ASCE)0733-9399(1983)109:1(168)

4

I.E. Harik and S. Pashanasangi, "Curved Bridge Decks: Analytical Strip Solution", Proceedings of the American Society of Civil Engineers, Journal of Structural Engineering, 111(7), 1517-1532, 1985. doi:10.1061/(ASCE)0733-9445(1985)111:7(1517)

5

A.K. Azad, M.K. Abdullah and M.H. Baluch, "Analysis of Radically Tapered Circular Plate Sectors by Finite Difference", Proceedings of the Fourth International Conference on Civil and Structural Engineering Computing, 2, 103-109, 1989.

6

T. Chisyaki and K. Takahashi, "Non-Linear Vibration of Ring Sector Plates", Proceedings of the Japanese Society of Civil Engineers, 204, 1-13, 1972.

7

R.S. Srinivasan and V. Thiruvenkatachari, "Non-Linear Bending of Annular Sector Plates Using a Matrix Method", Computers & Structures, 18(5), 803-812, 1984. doi:10.1016/0045-7949(84)90027-0

8

R.S. Srinivasan and V. Thiruvenkatachari, "Large Deflection Analysis of Clamped Annular Sector Plates", Journal of Strain Analysis, 19(1), 1-8, 1984. doi:10.1243/03093247V191001

9

H.G.V. Der Avanessian, "Finite Element Analysis of Curved Box Girder Bridges", PhD Thesis University College Cardiff, Cardiff, 1983.

10

G.J. Turvey and M. Salehi, "Elastic Large Deflection Response of Annular Sector Plates - A Comparison of DR Finite-Difference, Finite Element and Other Numerical Solutions", Computers and Structures, 40(5), 1267-1278, 1991. doi:10.1016/0045-7949(91)90397-5

11

J.R.H. Otter, A.C. Cassell and R.E. Hobbs, "Dynamic Relaxation", Proceedings of the Institution of Civil Engineers (Research and Theory), 3(2), 633-656, 1966. doi:10.1680/iicep.1966.8604

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