Keywords: large deflection, circular plate, annular, bending, axisymmetric, nonlinear.

Large deflection analysis of an isotropic and homogeneous annular circular plate with uniform thickness is presented in this computational study. Axisymmetric lateral loading is considered in the paper. The analysis is made for several boundary conditions including a simply supported edge, a clamped edge, or a free edge. Geometrically nonlinear shallow spherical shell equations in which transverse shear deformation is not considered, are used in the paper. The formulation is obtained by reorganizing and rearranging the governing equations presented in Reference [1]. The set of equations used in this paper enables plate problems for various boundary conditions and for different loading types to be considered. The axisymmetric plate investigated is under rotational symmetric loading hence the system of partial differential equations is automatically transformed into a system of ordinary differential equations which are solved numerically by the finite difference and the Newton-Raphson methods, respectively. The total number of points to be used along the radial coordinate is determined by performing convergence studies. Six unknowns at each point are defined in the solution. The unknowns are chosen to be the deflection, the radial displacement, the rotation, the membrane force, the transverse shear force, and the bending moment. Firstly, the differential equations are transformed into algebraic equations using the finite difference method. Next, the Newton-Raphson method is used to find the unknowns. The boundary conditions along the inner and the outer edge of the plate are satisfied exactly. The present paper is a complementary study to the work done by Altekin and Yükseler [2]. The accuracy of the results is verified by checking the deflections with those available in the literature. The influence of the parameter of thickness and of the parameter of the hole on the displacements and the stress resultants is investigated using the sensitivity analysis. The numerical procedure employed in the paper is computationally efficient and produces results with acceptable accuracy. The main findings of the numerical results are highlighted as follows:

• As the parameter of thickness is increased, or as the parameter of hole is decreased, the maximum values of the deflection, the radial displacement, the membrane force, the transverse shear force, and the bending moment increase.
• The location of the grid point which maximizes the deflection, the radial displacement, the membrane force, the transverse shear force, and the bending moment is independent of the parameter of thickness.
• The thickness of the plate has a dominant influence on the deflection.
• The clamped inner edge - simply supported outer edge (C-S) plate produces larger deflection, radial displacement, and membrane force than (simply supported inner edge - clamped outer edge (S-C) plate does.
• Beyond a certain hole size the maximum transverse shear force develops at the outer edge for S-C plate.
• The maximum bending moment develops at the outer edge for S-C plate.

1

N.C. Huang, "Unsymmetrical buckling of thin shallow spherical shells", Journal of Applied Mechanics-ASME, 31(3), 447-457, 1964. doi:10.1115/1.3629662

2

M Altekin, R.F. Yükseler, "Large deflection analysis of clamped circular plates", WCE 2011 Proceedings, Volume III, 2210-2212, IAENG, London, UK, 6-8 July, 2011.

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