Abstract
In this paper, the differential quadrature method (DQM) was employed to study nonlinear analysis of annular isotropic membrane in which an attempt was made to explore the applicability and accuracy of DQM for nonlinear analysis of a structural membrane. For this purpose, the large deformation analyses of symmetric circular membranes were investigated. Relaxed strain energy function in conjunction with Green’s strain and perfectly flexible assumptions was utilized for modeling the nonlinear behavior of the membranes. The nonlinear governing equations were discretized at whole domain grid points, and boundary conditions were implemented exactly at boundary grid points. Comparative studies were made between approaches for different boundaries. Convergence of the methodology was demonstrated, and the results were compared with existing solutions of other methods, such as dynamic relaxation. It was shown that accurate results were obtained even when utilizing only a small number of grid points.
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References
F. Otto, Tensile structures. The MIT Press; (1973).
A. A. Atai and D. J. Steigmann, Coupled Deformation of elastic curves and surfaces. International Journal of Solids and Structures, (35) (1998) 1915–1952.
E. Haseganu and D. J. Steigmann, Equilibrium analysis of finitely deformed elastic networks. Computational Mechanics (17) (1996) 359–373.
N. J. Cook, Dynamic responses of single-ply membrane roofing systems, Journal of Wind Engineering and Industrial Aerodynamics, 41–44 (1992) 1525–1536.
M. Mozaffari, A. A. Atai and N. Mostafa, Large deformation and mechanics of flexible isotropic membrane ballooning in three dimensions by differential quadrature method, Journal of Mechanical Science and Techonology (23) (2009) 2921–2927.
A. Baskaran, Y. Chen and M. G. Savage, Development of a wind load cycle for testing commercial building envelopes. ASCE Structures Congress XV, Portland, Oregon, USA., (1997) 25–32.
C. W. Bert and M. Malik Differential Quadrature Method in computational mechanics: A review. Applied Mechanics Review, 49 (1996) 1–27.
G. Karami and P. Malekzadeh A new differential quadrature methodology for beam analysis and the associated DQEM. Computer Methods in Applied Mechanics and Engineering, 191 (2002) 3509–3026.
K. M. Liew and J. B. Han. A four-node differential quadrature method for straight-sided quadrilateral Reissner/Mindlin plates. Communication in Numerical Methods in Engineering, 13 (1997) 73–81.
Pipkin, The relaxed energy density for isotropic elastic membranes, IMA Journal of Applied Mathematics (36) (1986) 85–99.
Varga, Stress Strain Behavior of Elastic Materials. Wiley, New York, (1966).
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This paper was recommended for publication in revised form by Associate Editor Maenghyo Cho
Ali Asghar Atai received his B.Sc. in Mechanical Engineering from the University of Tehran, Iran, in 1990. He obtained his M.Sc. and Ph.D. from the University of Alberta, Canada, in 1994 and 1998, respectively. He is currently a professor at the Department of Mechanical Engineering, Islamic Azad University, Karaj Branch, Iran. His areas of research interest include flexible structural mechanics, continuous media, and dynamics of machines.
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Atai, A.A., Mozaffari, M. Large deformation and stress analysis of isotropic annular membranes by differential quadrature method. J Mech Sci Technol 24, 703–709 (2010). https://doi.org/10.1007/s12206-010-0116-y
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DOI: https://doi.org/10.1007/s12206-010-0116-y