A semi-analytical solution on static analysis of circular plate exposed to non-uniform axisymmetric transverse loading resting on Winkler elastic foundation

• Autorzy: Abbasi S. , Farhatnia F. , Jazi S. R.

Identyfikatory

DOI

10.1016/j.acme.2013.09.007

• Języki publikacji: EN

Abstrakty

EN

This paper is concerned with static analysis of functionally graded (FG) circular plates resting on Winkler elastic foundation. The material properties vary across the thickness direction so the power-law distribution is used to describe the constituent components. The differential transforms method (DTM) is utilized to solve the governing differential equations of bending of the thin circular plate under various boundary conditions. By employing this solution method, governing differential equations are transformed into recurrence relations and boundary/regularity conditions are changed into algebraic equations. In this study, the plate is subjected to uniform/non-uniform transverse load in two cases of boundary conditions (clamped and simply-supported). Some numerical examples are presented to show the influence of functionally graded variation, different elastic foundation modulus, and variation of the symmetrical transverse loads on the stress and displacement fields. Based on the results, the obtained out-plane displacement coincide with the available solution for a homogenous circular plate. It can be concluded that the applied method provides accurate results and it is easily used for static analysis of circular plates on an elastic foundation.

Słowa kluczowe

EN

static analysis; circular plates; functionally graded material (FGM); Winkler elastic foundation; differential transform method; DTM

PL

analiza statyczna; podłoże sprężyste; pole naprężeń

• Wydawca: Springer ; Wrocław University of Science and Technology
• Czasopismo: Archives of Civil and Mechanical Engineering
• Rocznik: 2014
• Tom: Vol. 14, no. 3
• Strony: 476--488
• Opis fizyczny: Bibliogr. 27 poz., rys., tab., wykr.

Twórcy

autor

Abbasi S.

• Department of Mechanical Engineering, Islamic Azad University, Khomeinishahr branch, Boulevard Manzariye, Khomeinishahr, Esfahan, Iran

autor

Farhatnia F.

• Department of Mechanical Engineering, Islamic Azad University, Khomeinishahr branch, Boulevard Manzariye, Khomeinishahr, Esfahan, Iran

autor

Jazi S. R.

• Department of Mechanical Engineering, Islamic Azad University, Khomeinishahr branch, Boulevard Manzariye, Khomeinishahr, Esfahan, Iran

Bibliografia

• [1] M. Yamanouchi, M. Koizumi, M.T. Hirai, I. Shiota, Proceedings of the First International Symposium on Functionally Gradient Materials, Sendai, Japan, 1990.
• [2] J.N. Reddy, C.M. Wang, S. Kitipornchai, Axisymmetric bending of functionally graded circular and annular plate, European Journal of Mechanics-A/Solids 18 (2) (1999) 185–195.
• [3] Q.S. Li, J. Liu, H.B. Xiao, A new approach for bending analysis of thin circular plates with large deflection, International Journal of Mechanics Science 46 (2004) 173–180.
• [4] O. Civalek, Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns, Engineering Structure 26 (2) (2004) 171–186.
• [5] X.Y. Li, H.J. Ding, W.Q. Chen, Elasticity solutions for a transversely isotropic functionally graded circular plate subject to an axisymmetric transverse load qrk, International Journal of Solids Structure 45 (2008) 191–210.
• [6] L. Zheng, Zh. Zhong, Exact solution for axisymmetric bending of functionally graded circular plate, Tsinghua Science Technolgy 14 (Supple. 2) (2009) S64–S68.
• [7] Ö. Civalek, H. Ersoy, Free vibration and bending analysis of circular Mindlin plates using singular convolution method, Communications in Numerical Methods in Engineering 25 (2009) 907–922.
• [8] S. Sahraee, A.R. Saidi, Axisymmetric bending analysis of thick functionally graded circular plates using fourth-order shear deformation theory, European Journal of Mechanics-A/Solids 28 (2009) 974–984.
• [9] S. Sahraee, A.R. Saidi, A. Rasouli, Axisymmetric bending and buckling analysis of thick functionally graded circular plates using unconstrained third-order shear deformation plate theory, Composite Structures 89 (2009) 110–119.
• [10] W. Yun, X. Rongqiao, D. Haojiang, Three-dimensional solution of axisymmetric bending of functionally graded circular plates, Composite Structures 92 (7) (2010) 1683–1693.
• [11] Y.Z. Chen, Innovative iteration technique for nonlinear ordinary differential equations of large deflection problem of circular plates, Mechanics Research Communication 43 (2012) 75–79.
• [12] M.M. Alipour, M. Shariyat, An elasticity-equilibrium-based zigzag theory for axisymmetric bending and stress analysis of the functionally graded circular sandwich plates, using a Maclaurin-type series solution, European Journal of Mechanics-A/Solids 34 (2012) 78–101.
• [13] V. Birman, Plate Structures, first edition, Springer Science, New York, 2011.
• [14] J.K. Zhou, Differential Transformation and Its Applications for Electrical Circuits, Huarjung University Press, Wuuhahn, China, 1986.
• [15] F. Ayaz, On the two-dimensional differential transform method, Applied Mathematics and Computation 143 (2003) 361–374.
• [16] H.S. Yalcin, A. Arikoglu, I. Ozkol, Free vibration analysis of circular plates by differential transformation method, Computational and Applied Mathematics 212 (2009) 377–386.
• [17] Ö. Özdemir, M.O. Kaya, Flap wise bending vibration analysis of a rotating tapered cantilever Bernoulli–Euler beam by differential transform method, Journal of Sound and Vibration 289 (2006) 413–420.
• [18] M. Balkaya, M.O. Kaya, A. Sağlamer, Analysis of the vibration of an elastic beam supported on elastic soil using the differential transform method, Archive of Applied Mechanics 79 (2009) 135–146.
• [19] R. Attarnejad, Sh.J. Semnani, A. Shahba, Basic displacement functions for free vibration analysis of non-prismatic Timoshenko beams, Journal Finite Elements in Analysis and Design 46 (10) (2010) 916–929.
• [20] B. Soltanalizadeh, Differential transformation method for solving one-space-dimensional telegraph equation, Computational and Applied Mathematics 30 (3) (2011) 639–653.
• [21] D.G. Zhang, Y.H. Zhou, A theoretical analysis of FGM thin plates based on physical neutral surface, Computational Materials Science 44 (2008) 716–720.
• [22] M. Latifi, F. Farhatnia, M. Kadkhodaei, Buckling analysis of rectangular functionally graded plates under various edge conditions using Fourier series expansion, European Journal of Mechanics-A/Solids 41 (2013) 16–27.
• [23] Sh. Momani, M.A. Noor, Numerical comparison of methods for solving a special fourth-order boundary value problem, Applied Mathematics and computation 191 (1) (2007) 218– 224.
• [24] V.S. Erturk, Differential transformation method for solving differential equations of Lane–Emden type, Mathematical and Computational Applications 12 (3) (2007) 135–139. pp (2007) 135–139.
• [25] Z. Odibat, Sh. Momani, A generalized differential transform method for linear partial differential equations of fractional order, Applied Mathematics Letters 21 (2008) 194–199.
• [26] S. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells, second edition, McGraw-Hill, New York, 1959.
• [27] A. Arikoglu, I. Ozkol, Solution of boundary value problems for integro-differential equations by using differential transform method, Applied Mathematics and Computation 168 (2005) 1145–1158.