Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T05:52:42.320Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear Dynamic Analysis for FGM Circular Plates

Published online by Cambridge University Press:  19 December 2012

H.-L. Dai ,
X. Yan  and
L. Yang
H.-L. Dai*
Affiliation:
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, China Department of Engineering Mechanics, College of Mechanical & Vehicle Engineering, Hunan UniversityChangsha, 410082, China
X. Yan
Affiliation:
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, China Department of Engineering Mechanics, College of Mechanical & Vehicle Engineering, Hunan UniversityChangsha, 410082, China
L. Yang
Affiliation:
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, China Department of Engineering Mechanics, College of Mechanical & Vehicle Engineering, Hunan UniversityChangsha, 410082, China
*
*Corresponding author (, [email protected])
Get access

Abstract

In the paper, nonlinear dynamic analysis of a circular plate composed of functionally graded material (FGM) is presented. Considering a transverse shear deformation and geometric nonlinearity, the von Karman geometric relation of the FGM circular plate is established. Based on the theory of the first-order shear deformation, a new set of equilibrium equations is developed by the principle of minimum total energy. Applying the finite difference method and Newmark scheme, the nonlinear transient problem is solved by the iterative method. To validate the presented method, the transient problem of the FGM circular plate is compared with those of the existed literature, and good agreement is observed. The effects of the volume fraction index, boundary conditions, mechanical load and the ratio of thickness to radius on the nonlinear transient problem of the FGM circular plate are investigated.

Keywords

NonlinearDynamic analysisFGM circular plate
Type
Articles
Information
Journal of Mechanics , Volume 29 , Issue 2 , June 2013 , pp. 287 - 296
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Ma, L. S. and Wang, T. J.,“Nonlinear Bending and Post-Buckling of a Functionally Graded Circular Plate Under Mechanical and Thermal Loadings,” International Journal of Solids and Structures, 40, pp. 3311–3330 (2003).CrossRefGoogle Scholar
2.Najafizadeh, M. M. and Eslami, M. R.,“Buckling Analysis of Circular Plates of Functionally Graded Materials Under Uniform Radial Compression,” International Journal of Mechanical Sciences, 44, pp. 2479–2493 (2002).Google Scholar
3.Najafizadeh, M. M. and Heydari, H. R.,“Thermal Buckling of Functionally Graded Circular Plates Based on Higher Order Shear Deformation Plate Theory,” European Journal of Mechanics-A/Solids, 23, pp. 1085–1100 (2004).Google Scholar
4.Ebrahimi, F. and Rastgo, A.,“An Analytical Study on the Free Vibration of Smart Circular Thin FGM Plate Based on Classical Plate Theory,” Thin-Walled Structures, 46, pp. 1402–1408 (2008).Google Scholar
5.Li, X. Y., Ding, H. J. and Chen, W. Q.,“Elasticity Solutions for a Transversely Isotropic Functionally Graded Circular Plate Subjected to an Axisymmetric Transverse Load,” International Journal of Solids and Structures, 45, pp. 191–210 (2008).Google Scholar
6.Saidi, A. R., Rasouli, A. and Sahraee, S.,“Axisymmetric Bending and Buckling Analysis of Thick Functionally Graded Circular Plates Using Unconstrained Third-Order Shear Deformation Plate Theory,” Composite Structures, 89, pp. 110–119 (2009).Google Scholar
7.Hosseini-Hashemi, S. H., Akhavan, H., Rokni Damavandi Taher, H., Daemi, N. and Alibeigloo, A.,“Differential Quadrature Analysis of Functionally Graded Circular Sector Plates on Elastic Foundation,” Materials & Design, 31, pp. 1871–1880 (2010).Google Scholar
8.Nie, G. J. and Zhong, Z.,“Dynamic Analysis of Multi-Directional Functionally Graded Annular Plates,” Applied Mathematical Modelling, 34, pp. 608–616 (2010).Google Scholar
9.Ebrahimi, F. and Rastgoo, A.,“Nonlinear Vibration Analysis of Piezothermoelectrically Actuated Functionally Graded Circular Plates,” Archive of Applied Mechanics, 81, pp. 361–383 (2011).Google Scholar
10.Shariyat, M. and Alipour, M. M.,“Differential Transform Vibration and Modal Stress Analyses of Circular Plates Made of Two-Directional Functionally Graded Materials Resting on Elastic Foundations,” Archive of Applied Mechanics, 81, pp. 1289–1306 (2011).CrossRefGoogle Scholar
11.Shariyat, M. and Jafari, R.,“Nonlinear Low-Velocity Impact Response Analysis of a Radially Preloaded Two- Directional-Functionally Graded Circular Plate: A Refined Contact Stiffness Approach,” Composites, Part B: Engineering, http://dx.doi.org/10.1016/j.compositesb.2012.05.014 (2012).Google Scholar
12.Khorshidvand, A. R., Jabbari, M. and Eslami, M. R.,“Thermoelastic Buckling Analysis of Functionally Graded Circular Plates Integrated with Piezoelectric Layers,” Journal of Thermal Stresses, 35, pp. 695–717 (2012).CrossRefGoogle Scholar
13.Li, X. Y., Li, P. D., Kang, G. Z. and Pan, D. Z., “Axisymmetric Thermoelasticity Field in a Functionally Graded Circular Plate of Transversely Isotropic Material,” Mathematics and Mechanics of Solids, DOI: 10.1177/1081286512442437 (2012).Google Scholar
14.Woo, J. and Meguid, S. A.,“Nonlinear Analysis of Functionally Graded Plates and Shallow Shells,” International Journal of Solids and Structures, 38, pp. 7409–7421 (2001).CrossRefGoogle Scholar
15.Reddy, J. N.,“Analysis of Functionally Graded Plates,” International Journal for Numerical Methods in Engineering, 47, pp. 663–684 (2000).Google Scholar
16.Reddy, J. N. and Huang, C. L.,“Nonlinear Axisymmetric Bending of Annular Plates with Varying Thickness,” International Journal of Solids and Structures, 17, pp. 811–825 (1981).CrossRefGoogle Scholar
17.Reddy, J. N., Wang, C. M. and Kitipornchai, S., “Axisymmetric Bending of Functionally Graded Circular and Annular Plates,” European Journal of Mechanics A/Solids, 18, pp. 185–199 (1999).Google Scholar
18.Bayat, M., Saleemb, M., Sahari, B. B., Hamoude, A. M. S. and Mahdi, E.,“Thermoelastic Analysis of a Functionally Graded Rotating Disk with Small and Large Deflections,” Thin-Walled Structures, 45, pp. 677–691 (2007).Google Scholar
19.Fu, Y. M., Li, P. E. and Zheng, Y. F.,“Creep Postbuckling of Viscoelastic Plates with Matrix Transverse Cracks,” Acta Mechanica Sinica. 37, pp. 32–39 (2005).Google Scholar