Innovative iteration technique for large deflection problem of annular plate

- Journal title : Steel and Composite Structures
- Volume 14, Issue 6, 2013, pp.605-620
- Publisher : Techno-Press
- DOI : 10.12989/scs.2013.14.6.605

Title & Authors

Innovative iteration technique for large deflection problem of annular plate

Chen, Y.Z.;

Chen, Y.Z.;

Abstract

This paper provides an innovative iteration technique for the large deflection problem of annular plate. After some manipulation, the problem is reduced to a couple of ODEs (ordinary differential equation). Among them, one is derived from the plane stress problem for plate, and other is derived from the bending of plate. Since the large deflection for plate is assumed in the problem, the relevant non-linear terms appear in the resulting ODEs. The pseudo-linearization procedure is suggested to solve the problem and the nonlinear ODEs can be solved in the way for the solution of linear ODE. To obtain the final solution, it is necessary to use the iteration. Several numerical examples are provided. In the study, the assumed value for non-dimensional loading is larger than those in the available references.

Keywords

large deflection bending;pseudo-linearization of ODE;nonlinear analysis;iteration technique;annular plate;

Language

English

Cited by

References

1.

Al-Gahtani, H.J. and Naffa, M. (2009), "RBF meshless method for large deflection of thin plates with immovable edges", Eng. Anal. Boun. Elem., 33(2), 176-183.

2.

Arefi, M. and Rahimi, G.H. (2012), "Studying the nonlinear behavior of the functionally graded annular plates with piezoelectric layers as a sensor and actuator under normal pressure", Smart Structures and Systems, Int. J., 9(2), 127-143.

3.

Cao, J. (1996), "Computer extended perturbation solution of the large deflection of a circular plate. Part I Uniform loading with clamped edge", Quar. J. Mech. Appl. Math., 49(2), 163-178.

4.

Cao, J. (1997), "Computer extended perturbation solution of the large deflection of a circular plate. Part II Control loading with clamped edge", Quar. J. Mech. Appl. Math., 50(3), 333-347.

5.

Chen, Y.Z. and Lee, K.Y. (2003), "Pseudo-linearization procedure of nonlinear ordinary differential equations for large deflection problem of circular plates", Thin-walled Struct., 41(4), 375-388.

6.

Chia, C.Y. (1980), Nonlinear Analysis of Plates, McGraw-Hill, New York.

7.

He, J. H. (2003), "A Lagrangian for von Kármán equations of large deflection problem of thin circular plate", App. Math. Comp., 143(2-3), 543-549.

8.

Hildebland, F.B. (1974), Introduction to Numerical Analysis, McGraw-Hill, New York.

9.

Kármán, T.H. (1940), "The engineering grapples with non-linear problems", Bill. Amer. Math. Soc., 46, 615-683.

10.

Lia, Q.S., Liu, J. and Xiao, H.B. (2004), "A new approach for bending analysis of thin circular plates with large deflection", Int. J. Mech. Sci., 46(2), 173-180.

11.

Naffa, M. and Al-Gahtani, H.J. (2007), "RBF-based meshless method for large deflection of thin plates", Eng. Anal. Boun. Elem., 31(4), 311-317.

12.

Shufrin, I., Rabinovitch, O. and Eisenberger, M. (2010), "A semi-analytical approach for the geometrically nonlinear analysis of trapezoidal plates", Inter. J. of Mech. Sci., 52(12), 1588-1596.

13.

Timoshenko, S.P. and Woinowsky-Krieger, S. (1959), Theory of Plates and Shells, McGraw-Hill, London.

14.

Turvey, G.J. and Salehi, M. (1998), "Large deflection analysis of eccentrically stiffened sector plates", Comput. Struct., 68(1-3), 191-205.

15.

Van Gorder, R.A. (2012), "Analytical method for the construction of solutions to the Foppl von Karman equations governing deflections of a thin flat plate", Inter. J. of Non-Linear Mech., 47(3), 1-6.

16.

Volmir, A.C. (1963), Large Deflection problem for Plates and Shells, Science Press, Beijing. (Chinese translation from Russian)

17.

Way, S. (1934), "Bending of circular plate with large deflection", Trans. ASME, 56, 627-636.