International Journal of Mathematics and Computational Science
Articles Information
International Journal of Mathematics and Computational Science, Vol.2, No.1, Feb. 2016, Pub. Date: Jan. 21, 2016
Application of the GDQ Method to Structural Analysis
Pages: 8-19 Views: 661 Downloads: 895
Authors
[01] Ramzy M. Abumandour, Basic Engineering Science Department, Faculty of Engineering, Menofia University, Shebin El-Kom, Egypt.
[02] M. H. Kamel, Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, Cairo, Egypt.
[03] S. Bichir, Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, Cairo, Egypt.
Abstract
This paper presents a generalized differential quadrature method as an accurate, efficient and simple numerical technique for structural analysis of uniform and non-uniform beams resting on fluid layer under axial force and distributed load under three sets of boundary conditions, that is, simply–simply supported (S–S), clamped–clamped supported (C–C) and clamped–simply supported (C–S) and studied the buckling of uniform and non-uniform bar resting on fluid layer under axial force and distributed load under the same three sets of boundary conditions. These problems were studied using the GDQ method. Firstly, drawbacks existing in the method of differential quadrature (DQ) are evaluated and discussed. Numerical examples have shown the super accuracy, efficiency, convenience and the great potential of this method.
Keywords
Uniform and Non-Uniform Beam and Bar, Deflection, Buckling, GDQM
References
[01] Bellman, R. E., Casti, J., 1971. Differential quadrature and long-term integration. Journal of Mathematical Analysis and Applications 34: 235–238.
[02] Bellman, R. E., B. G. Kashef and Casti, J., 1972. Differential quadrature: A technique for the rapid solution of non-linear partial differential equations. Journal of computational Physics 10: 40–52.
[03] Shu, C., 2000. Differential Quadrature and its Application in Engineering. Springer-Verlag London Berlin Heidelberg.
[04] Zong, Z. and Zhang, Y.Y. (2009) Advanced Differential Quadrature Methods. Chapman & Hall/CRC Applied Mathematics and Nonlinear Science Series.
[05] Shu, C. and Richards, B.E., 1990. High Resolution of Natural Convection in a Square Cavity by Generalized Differential Quadrature. Proceedings of 3rd International Conference on Advanced in numerical Methods in Engineering: Theory and Applications, Swansea, 2: 978-985.
[06] Shu, C., 1991. Generalized Differential-Integral Quadrature and Application to the Simulation of Incompressible Viscous Flows Including Parallel Computation. Ph.D. Thesis, University of Glasgow, Glasgow.
[07] Bert, C. W., Jang, S. K. and Striz A. G. 1988. Two new methods for analyzing free vibration of structure components. AIAA Journal, 26: 612–618.
[08] Jang, S. K., Bert, C. W. and Striz A. G., 1989. Application of differential quadrature to static analysis of Structural components. International Journal of Numerical Methods in Engineering 28: 561–577.
[09] Bert, C., Wang, X. and Striz, A. G. 1993. Differential quadrature for static and free vibration analysis of anisotropic plates. International Journal of Solids Structures 30: 1737–1744.
[10] Bert, C., Wang, X. and Striz, A. G. 1994. Static and free vibrational analysis of beams and plates by differential quadrature method. Acta Mechanica 102: 11–24.
[11] Du, H., Lim, M. K. and Lin, R. M., 1994. Application of Generalized Differential Quadrature to Structural problems. Journal of Sound and Vibrations 181: 279–293.
[12] Du, H., Lim, M. K. and Lin, R. M., 1995. Application of Generalized Differential Quadrature to Vibration Analysis. Journal of Sound and Vibrations 181: 279–293.
[13] Qiang Guo and Zhong, H., 2004. Non-linear Vibration Analysis of Beams by a Spline-based differential quadrature. Journal of Sound and Vibration 269: 405–432.
[14] Pu, J.-P. and Zheng, J.-J. 2006. Structural Dynamic Responses Analysis Applying Differential Quadrature Method. Journal of Zhejiang University Science 7: 1831-1838.
[15] Krowiak, A., 2008. Methods Based on the Differential Quadrature in Vibration Analysis of Plates. Journal of Theoretical and Applied Mechanics 46: 123-139.
[16] Ramzy M. Abumandour, Kamel, M. H. and Nassar, M. M., 2015. Application of the GDQ Method to Vibration Analysis. International Journal of Mathematics and Computational Science 1: 242-249.
[17] Shu, C., 1991. Generalized differential-integral quadrature and application to the simulation of incompressible viscous flows including parallel computation. PhD thesis, University of Glasgow.
[18] Shu, C. and Richards, B., 1992. Application of Generalized Differential Quadrature to Solve Two-Dimensional Incompressible Navier-Stokes Equations. International Journal for Numerical Methods in Fluids 15: 791-798.
[19] Al-Saif, A.S.J. and Zhu, Z.Y., 2003. Application of Mixed Differential Quadrature Method for Solving the Coupled Two-Dimensional Incompressible Navier-Stokes Equation and Heat Equation. Journal of Shanghai University 7: 343-351.
[20] Al-Saif, A.S.J. and Zhu, Z.Y., 2006. Differential Quadrature Method for Steady Flow of an Incompressible Second-Order Viscoelastic Fluid and Heat Transfer Model. Journal of Shanghai University 9: 298-306.
[21] Eldesoky, I. M., Kamel, M. H., Reda M. Hussien and Ramzy M. Abumandour, 2013. Numerical study of Unsteady MHD Pulsatile Flow through Porous Medium in an Artery using Generalized Differential Quadrature Method (GDQM). International Journal of Materials, Mechanics and Manufacturing 1: 200-206.
[22] Eldesoky, I. M., Kamel, M. H. and Abumandour, R. M., 2014. Numerical Study of Slip Effect of Unsteady MHD Pulsatile Flow through Porous Medium in an Artery Using Generalized Differential Quadrature Method (Comparative Study). World Journal of Engineering and Technology 2: 117-134.
[23] Eldesoky, I. M., Kamel, M. H., EL-Zahar, E. R. and Abumandour, R. M., 2015. Numerical Solution of Unsteady MHD Pulsating Flow of Couple Stress Fluid through Porous Medium between Permeable Beds using Differentia Quadrature Method (DQM). Asian Journal of Mathematics and Computer Research 9: 8-28.
[24] Chajes, A., 1974: "Principles of Structural Stability Theory." Prentice-Hall.
[25] Newbrry, A. L., Bert, C. W. and Striz, A. G., 1987. Non-integer-polynomial finite element analysis of column buckling. Journal of Engineering Structures 113: 873-878.
[26] Bert, C. W., 1984: "Improved technique for estimating buckling loads" Journal of Engineering Mechanics Vol. 110: pp. 1655-1665.
[27] Wen, D., and Yu, Y., 1993a: "Calculation and analysis of weighting coefficient matrices in differential quadrature method." In computational Engineering (Edited by Kwak, B. M. and Tanaka, M.): pp. 157–162. Elsevier Oxford.
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