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Bending Analysis of Thick Orthotropic Sector Plates Using the Extended Kantorovich Method

Author(s): A. Rastgoo | H. Amirshaghaghi

Journal: Selçuk Journal of Applied Mathematics
ISSN 1302-7980

Volume: 8;
Issue: 2;
Start page: 13;
Date: 2007;
Original page

Keywords: Extended Kantorovich Method | Bending analysis | Shear deformation | Thick orthotropic sector plates.

This study aims to demonstrate the applicability of the Extended Kantorovich Method (EKM) to obtain solution for two dimensional elasticity problems in cylindrical coordinate system. Bending of shear deformable thick orthotropic sector plates with clamped edges is considered for this purpose. Based on the first order shear deformation theory of Reissner, the governing equations of the plate in terms of deflection and rotations of the mid-plane include a system of three second-order partial differential equations (PDEs). Application of the EKM reduces the governing equation to a double set of ordinary differential equations (ODEs) in terms of r and θ. The resulting systems of ODEs are then solved iteratively until convergence is achieved. It is shown that the presented procedure can also be applied to the bending of rectangular plates by choosing sufficiently large values for inner and outer radii and small value for total angle of the sector. It is also demonstrated that the method provides suitably accurate results with very fast convergence for both sector and rectangular plates. Normally, four or five iterations are enough to get the final results with desired accuracy. The obtained results show good agreement with those of the commercial finite element code, ABAQUS and other published data.
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