Large Deflection of Imperfect Plates by Iterative BE‐FE Method
Publication: Journal of Engineering Mechanics
Volume 120, Issue 3
Abstract
The nonlinear behavior of rectangular thin plates with initial imperfections is studied in this paper by using an iterative boundary element and finite element method. The transverse and the in‐plane deformations of the plates are analyzed, respectively, by the boundary element method and the finite element method. The coupling between these two deformations and the nonlinearity of the problem considered are taken into account by introducing initial strains and through an iterative procedure. Spline functions are used in both boundary element and finite element analysis. Imperfections, which are expressed by double Fourier series, are considered in the numerical examples, although the method is also applicable to other imperfections. Numerical results, dealing with large deflection of imperfect rectangular plates with either simply supported or clamped boundaries, are presented, discussed and compared with the results obtained by using alternative approaches. Upon assuming the absence of imperfections, the corresponding large deflection analysis of a perfect plate occurs as a particular case.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bezine, G. P., and Gamby, D. A. (1984). “A new integral equation formulation for plate bending problems.” Recent Advances in Boundary Element Method, C. A. Brebbia, ed., Pentech Press, London, England.
2.
Brebbia, C. A., Telles, J. C. F., and Wrobel, L. C. (1985). Boundary element techniques—Theory and application in engineering. Springer‐Verlag. New York, N.Y.
3.
Bushton, K. R. (1970). “Large deflection of plates with initial curvature.” Int. J. Mech. Sci., 12(12), 1037–1051.
4.
Domburian, E. M., Smith, C. V., and Carlson, R. L. (1976). “A perturbation solution to a plate postbuckling problem.” Int. J. Non‐linear Mech., 11(1), 49–58.
5.
Huang, Y. Y., Zhong, W. F., and Qin, Q. H. (1992). “Postbuckling analysis of plates on an elastic foundation by the boundary element method.” Comput. Methods Appl. Mech. Engrg., 100(3), 315–323.
6.
Prenter, P. M. (1975). Spline and variational method. John Wiley, New York, N.Y.
7.
Tanaka, M. (1984). “Large deflection analysis of thin elastic plate.” Development in Boundary Element Methods, Elsevier, London, England.
8.
Tillerson, J. R., Stricklin, J. A., and Haisler, W. C. (1973). “Numerical methods for the solution of nonlinear problems in structural analysis.” Numerical Solution of Nonlinear Structural Problems, R. F. Hartung, ed., American Society of Mech. Engrs., New York, N.Y.
9.
Timoshenko, S. (1959). Theory of plates and shells. McGraw‐Hill, New York, N.Y.
10.
Vlasov, V. Z. (1959). Theory of flexible plates and shells. Science Press, Beijing, China.
11.
Wang, Y. C., Ye, J. Q., and Wang, Z. H. (1986). “Spline boundary element method for shallow thin shells.” Boundary Elements, T. H. Du, ed., Pergamon Press, Oxford, England, 375–380.
12.
Ye, T. Q., and Liu, Y. Z. (1985). “Finite deflection analysis of elastic plates by the boundary element method.” Appl. Math. Modeling, 9(3), 181–188.
13.
Ye, J. Q. (1991). “Nonlinear bending analysis of plates and shells by using a mixed spline boundary element and finite element method.” Int. J. Numer. Meth. Engrg., 31(7), 1283–1294.
14.
Ye, J. Q. (1993a). “Postbuckling analysis of plates under combined loads by a mixed finite element and boundary element method.” J. Pressure Vessel Tech., 115(3), 262–267.
15.
Ye, J. Q. (1993b). “A unified approach for the linear and nonlinear analysis of plates and shallow shells.” Thin‐walled Struct., 17(3), 223–236.
16.
Yuan, S. (1984). “Rectangular spline elements.” Comput. Struct. Mech. Appl., 1(2), 41–47.
Information & Authors
Information
Published In
Copyright
Copyright © 1994 American Society of Civil Engineers.
History
Received: Feb 1, 1993
Published online: Mar 1, 1994
Published in print: Mar 1994
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.