Analysis of Rectangular Plate with Opening by Finite Difference Method

Md. Roknuzzaman^1, , Md. Belal Hossain¹, Md. Rashedul Haque¹ and Dr. Tarif Uddin Ahmed²

¹Department of Civil Engineering, Hajee Mohammad Danesh Science and Technology University, Dinajpur, Bangladesh

²Department of Civil Engineering, Rajshahi University of Engineering & Technology, Rajshahi, Bangladesh

Cite this paper:
Md. Roknuzzaman, Md. Belal Hossain, Md. Rashedul Haque and Dr. Tarif Uddin Ahmed. Analysis of Rectangular Plate with Opening by Finite Difference Method. American Journal of Civil Engineering and Architecture. 2015; 3(5):165-173. doi: 10.12691/ajcea-3-5-3

Abstract

Steel plates are commonly used to support lateral or vertical loads. Before the design of such a plate, analysis is performed to check the stability of plate for the proposed load. There are several methods for this analysis. In this research, a finite difference method (FDM) is proposed to analyze a rectangular steel plate. The plate is considered to be subjected to an arbitrary transverse uniformly distributed loading and is considered to be clamped at the two opposite edges and free at the other two edges. At first the plate is analyzed considering it to be completely solid and then it was re-analyzed considering a rectangular opening at its centre. The ordinary finite difference method is used to solve the governing differential equation of the plate deflection. The proposed method can be easily programmed to readily apply on a plate problem. The work covers the determination of displacement components at different points of the plate and checking the result by software (STAAD.Pro) analysis.

Keywords:
finite difference method plate analysis numerical analysis of hollow plate FDM

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References:

[1]	Cheung M.S., Chan M.Y.T. , Static and dynamic analysis of thin and thick sectorial plates by the finite strip method., Computers and Structures , 14, pp. 79-88, 1981.
[2]	Fernandes G.R., Venturini W.S. , Stiffened plate bending analysis by the boundary element method., Computational Mechanics, 28, pp. 275-281, 2002.
[3]	Baltacioglu A.K., Akgoz, B., Civalek, O., Nonlinear static response of laminated composite plates by discrete singular convolution method., Composite Structures, 93, pp. 153-161, 2010.
[4]	Leissa, A. W. and Niedenfuhr, F. W., Bending of a square plate with two adjacent Edges Free and the others Clamped or simply supported, AIAA Journal, V-1, pp. 116-120, 1962.
[5]	Aksu G., Ali R., Free vibration analysis of stiffened plates using finite-difference method., Journal of Sound and Vibration, 48, pp. 15-25, 1976.
[6]	Reddy, J. N., and Gera, R., An Improved Finite-Difference Analysis of Bending of Thin Rectangular Elastic Plates, Comp. Struct., v-10 , pp. 431-438, 1979
[7]	Vitor M. A. Leitão, A meshless method for Kirchhoff plate bending problems, International Journal for Numerical Methods in Engineering, V-52, I-10, 2001.
[8]	Yusof Bin Salleh, Mohd., A Finite Difference Simulation of a Flexible Rectangular Plate Structure, thesis submitted to the Faculty of Mechanical Engineering, University Technical Malayasia Malacca., 2007.
[9]	Ali Ergün and Nahit Kumbasar, A New Approach of Improved Finite Difference Scheme on Plate Bending Analysis, Scientific Research and Essays, Vol. 6(1), pp. 6-17, 4 January, 2011.
[10]	Szilard, R., Theory and Analysis of Plates, Classical and Numerical Methods, Prentice-Hall, Englewood Cliffs, New Jersey, 1974.
[11]	Szilard, R., Theories and Applications of Plate Analysis: Classical, Numerical and Engineering Methods, John Wiley & Sons, Inc., United States edition, 2004.
[12]	Levy, H. and Lessman, F., Finite Difference Equations, Dover Publications, New York., 1992.