European Journal of Mechanics A/Solids 27 (2008) 378–388 Application of the extended Kantorovich method to the bending of clamped cylindrical panels Farbod Alijani, Mohammad Mohammadi Aghdam ∗ , Morteza Abouhamze Department of Mechanical Engineering, Amirkabir University of Technology, Hafez Ave, Tehran 15914, Iran Received 22 August 2006; accepted 30 May 2007 Available online 31 July 2007 Abstract Applicability and performance of the extended Kantorovich method (EKM) to obtain highly accurate approximate closed form solution for bending analysis of a cylindrical panel is studied. Fully clamped panel subjected to both uniform and non-uniform loadings is considered. Based on the Love–Kirchhoff first approximation for thin shallow cylindrical panels, the governing equa- tions of the problem in terms of three displacement components include a system of two second order and one forth order partial differential equations. The governing PDE system is converted to a double set of ODE systems by assuming separable functions for displacements together with utilization of the extended Kantorovich method. The resulted ODE systems are solved iteratively. In each iteration, exact closed form solutions are presented for both ODE systems. Rapid convergence and high accuracy of the method is shown for various examples. Both displacement and stress predictions show close agreement with other analytical and finite element analysis.  2007 Elsevier Masson SAS. All rights reserved. Keywords: Extended Kantorovich method; Cylindrical panel; Bending analysis 1. Introduction Since its first introduction (Kerr, 1968), EKM has been extensively used to obtain solutions for various two- dimensional problems in elasticity. The method employs the novel idea of Kantorovich (Kantorovich and Krylov, 1958) to reduce the governing partial differential equation of a 2-D elasticity problem to a double set of ordinary differential equations. Some applications of the EKM in the literature include eigenvalue problem (Kerr, 1969), free vibration (Jones and Milne, 1976), buckling (Yuan and Jin, 1998) and stress analysis (Kerr and Alexander, 1968) of thin rectangular plates, bending of variable thickness thin plates (Fariborz and Pourbohloul, 1989), bending of thick rectangular isotropic (Aghdam et al., 1996) and orthotropic (Aghdam and Falahatgar, 2003) plates and free- edge stress analysis (Cho and Kim, 2000). Most recent EKM articles include stability (Jana and Bhaskar, 2006) and buckling (Ungbhakorn and Singhatanadgid, 2006) of rectangular plates. The EKM, in comparison with other numerical techniques, has various advantages among which one can refer to rapid convergence, excellent accuracy, less computational efforts, any type of distributed loading condition and * Corresponding author. Tel.: +98 21 6454 3429; fax: +98 21 6641 9736. E-mail address: aghdam@aut.ac.ir (M.M. Aghdam). 0997-7538/$ – see front matter  2007 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.euromechsol.2007.05.011