Semianalytical Solution of Rectangular Plates
Publication: Journal of Engineering Mechanics
Volume 123, Issue 7
Abstract
A general procedure is developed for the static analysis of a single transversely loaded rectangular plate. Boundary displacements are expressed as linear functions plus sine series, and boundary normal moments by sine series. Unknown coefficients are determined to make stationary a modified total potential energy principle, which is shown to be equivalent to a weighted integral method. The procedure enables any rectangular plate with uniform boundary conditions on each side, with or without corner displacements, to be analyzed. Equations obtained using the method are identical to those obtained for solving a number of well-known plate problems that have been treated in a range of ways, and in a sense the method unifies those procedures. The method also enables additional cases to be treated in a semianalytical manner. As an example, a cantilever plate is treated in some detail.
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References
1.
Banerjee, P. K., and Butterfield, R. (1981). Boundary element methods in engineering science. McGraw-Hill, London, England.
2.
Betti, E. (1872). Nuovo Cimento. Series 2, 7, and 8.
3.
Gorman, D. J. (1982). Free vibration analysis of rectangular plates. Elsevier, New York.
4.
Gorman, D. J.(1995). “Free vibration analysis of orthotropic cantilever plates with point supports.”J. Engrg. Mech., ASCE, 121(8), 851–857.
5.
Hearn, A. C. (1991). REDUCE user's manual 3.5. RAND, Santa Monica, Calif.
6.
Kreyszig, E. (1967). Advanced engineering mathematics, 2nd Ed., John Wiley and Sons, Inc., New York.
7.
Leissa, A. W. (1969). Vibration of plates. NASA SP-160. Scientific and Technical Information Division of NASA, Washington, D.C.
8.
Melzer, H., and Rannacher, R.(1980). “Spannungskonzentrationen in Eckpunkten der Kirchhoffschen Platte.”Bauingenieur, Springer-Verlag KG, Berlin, Germany, 55(2), 181–184.
9.
Nash, W. A.(1952). “Several approximate analyses of the bending of a rectangular cantilever plate by uniform normal pressure.”J. Appl. Mech., 19(1), 33–36.
10.
Timoshenko, S. P. (1938). “Bending of rectangular plates with clamped edges.”Proc., 5th Int. Congress Appl. Mech., Cambridge, Mass.
11.
Timoshenko, S., and Woinowsky-Krieger, S. (1959). Theory of plates and shells. McGraw-Hill Book Co., New York.
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Copyright © 1997 American Society of Civil Engineers.
History
Published online: Jul 1, 1997
Published in print: Jul 1997
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