Boundary Element Solution for Plates of Variable Thickness
Publication: Journal of Engineering Mechanics
Volume 117, Issue 6
Abstract
A boundary element method (BEM) is developed for the analysis of plates of variable thickness. The plate may have arbitrary shape, and its boundary may be subjected to any type of boundary conditions. The nonuniform thickness of the plate is an arbitrary function of the coordinates x, y. Since it is practically not possible to establish the fundamental solution of the governing equation, which is a differential equation with variable coefficients, the proposed method uses the fundamental solution of the plate with constant thickness and treats the unknown terms as domain forces. The boundary value problem is formulated in terms of two differential and three integral coupled equations. The differential equations are solved using the finite difference method, while the integral equations using the BEM. The domain integrals are treated by employing an effective Gaussian integration over domains of arbitrary shape. Numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bares, R. (1979). Tables for the analysis of plates, slabs and diaphragms. Third Ed., Bauverlag GmbH, Wiesbaden, Berlin, Germany.
2.
Bezine, G. P. (1978). “Boundary integral formulation for plate flexure with arbitrary boundary conditions.” Mech. Res. Commun., 5, 197–206.
3.
Chen, S. S. H. (1976). “Bending and vibration of plates of variable thickness.” J. Engrg. Ind. Trans. ASME, 2, 166–170.
4.
Duff, G., and Naylor, D. (1966). Differential equations of applied mathematics. John Wiley and Sons, Inc., New York, N.Y.
5.
Fertis, D., and Mijatov, M. (1989). “Equivalent systems for variable thickness plates.” J. Engrg. Mech., ASCE, 115(10), 2287–2300.
6.
Hartmann, F., and Zotemantel, R. (1986). “The direct boundary element method in plate bending.” Int. J. Numer. Methods Engrg., 23, 2049–2069.
7.
Jaswon, M. A., and Maiti, M. (1968). “An integral equation formulation of plate bending problems.” J. Engrg. Math., 11, 83–93.
8.
Jaswon, M. A., and Symm, G. T. (1977). Integral equation methods in potential theory and elastostatistics. Academic Press, London, U.K.
9.
Katsikadelis, J. T. (1982). “The analysis of plates on elastic foundation by the boundary element method,” thesis presented to the Polytechnic University of New York, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
10.
Katsikadelis, J. T., and Armenakas, A. E. (1989). “A new boundary equation solution to the plate problem.” J. Appl. Mech., 56, 364–374.
11.
Katsikadelis, J. T., and Kallivokas, L. F. (1986). “Clamped plates on Pasternaktype elastic foundation by the boundary element method.” J. Appl. Mech., 53, 909–917.
12.
Katsikadelis, J. T., and Sapountzakis, E. J. (1988). “An approach to the vibration problem of homogeneous, non‐homogeneous and composite membranes based on the boundary element method.” Int. J. Numer. Methods Engrg., 26, 2439–2455.
13.
Stern, M. (1979). “A general boundary integral formulation for the numerical solution of plate bending problems.” Int. J. Solids Struct., 15, 769–782.
14.
Timoshenko, S., and Woinowsky‐Krieger, S. (1959). Theory of plates and shells. Second Ed., McGraw‐Hill, New York, N.Y.
Information & Authors
Information
Published In
Copyright
Copyright © 1991 ASCE.
History
Published online: Jun 1, 1991
Published in print: Jun 1991
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.