Finite Difference Solutions of Reissner's Plate Equations
Publication: Journal of Engineering Mechanics
Volume 113, Issue 1
Abstract
A finite difference approach to the Reissner's theory of plate bending is presented. The theory for the numerical analysis of rectangular plates is presented. The results of an example of a plate with simply supported edges are compared with other forms of solution, i.e., finite element, etc., for the uniformly loaded and concentrated load situations. The numerical analysis procedure for simply supported, fixed, free, and combinations of the three type rectangular plates is presented along with methods of solution.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Anderkeggen, E., “Finite Element Plate Bending Equilibrium Analysis,” Journal of the Engineering Mechanics Division, ASCE, Vol. 95, No. EM4, Proc. Paper 6715, Aug., 1969, pp. 841–857.
2.
Carley, T. G., and Langhaar, H. L., “Transverse Shearing Stress in Rectangular Plaes,” Journal of the Engineering Mechanics Division, ASCE, Vol. 94, No. EM1, Feb., 1968, pp. 137–152.
3.
Clough, R. W., and Felyipa, C. A., “A Refined Quadrilateral Element for Analysis of Plate Bending,” Proceedings, 2nd Conference on Matrix Methods in Structural Mechanics, Wright‐Patterson AFB, Ohio, 1968.
4.
Donnell, D. H., Drucker, D. C., and Goodier, J. N., discussion of “On the Theory of Bending of Elastic Plates,” by E. Reissner, Journal of Applied Mechanics, Vol. 13, 1946.
5.
Green, A. E., “On Reissner's Theory of Bending Elastic Plates,” Quarterly of Applied Mathematics, Vol. 7, 1949.
6.
Greimann, L. F., and Lynn, P. O. “Finite Element Analysis of Plate Bending with Transverse Shear Deformation,” Nuclear Engineering Design, Vol. 11, 1970, pp. 223–230.
7.
Herrmann, L. R., “A Bending Analysis for Plates,” Proceedings I, Conference on Matrix Methods in Structural Mechanics, Wright‐Patterson AFB, Ohio, 1965.
8.
Pryor, C. W., Jr., “Finite Element Analysis of Laminated Anisotropic Plates including Transverse Shear Deformations,” thesis presented to the Virginia Polytechnic Institute, at Blacksburg, Va., in 1969, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
9.
Pryor, C. W., and Barker, R. M. “A Finite Element Analysis Including Transverse Shear Effects for Laminated Plates,” AIAA Journal, Vol. 9, No. 5, 1971, pp. 912–917.
10.
Pryor, C. W., Jr., Barber, R. M., and Frederick, D., “Finite Element Bending Analysis of Reissner Plates,” Journal of the Engineering Mechanics Division, ASCE, Vol. 96, No. EM6, Proc. Paper 7760, Dec., 1970, pp. 967–983.
11.
Reissner, E., “On Bending of Elastic Plates,” Journal of Mathematics and Physics, Vol. V, No. 1, 1947, pp. 55–68.
12.
Reissner, E., “The Effects of Transverse Shear Deformation on the Bending of Elastic Plates,” Journal of Applied Mechanics, Vol. 12, 1945, pp. 69–77.
13.
Salerno, V. L., and Goldberg, M. A., “Effect of Shear Deformation on the Bending and Rectangular Plates,” Journal of Applied Mechanics, Vol. 27, 1960, pp. 54–58.
14.
Schafer Von, M., “Uber eine Verfeinerung der klassischen Theorie dunner schwach gebogener Platten,” Z. Angew, Match Mech. Bd. 32NR 6, June, 1952, pp. 161–171.
15.
Smith, I. M., discussion of “Finite Element Bending Analysis of Reissner Plates,” by C. W. Pryor, Journal of the Engineering Mechanics Division, ASCE, Vol. 97, No. EM4, Aug., 1971, pp. 1302–1304.
16.
Smith, I. M., “A Finite Element Analysis for Moderately Thick Rectangular Plates in Bending,” International Journal of the Mechanical Sciences, Vol. 10, 1968, p. 563.
Information & Authors
Information
Published In
Copyright
Copyright © 1987 ASCE.
History
Published online: Jan 1, 1987
Published in print: Jan 1987
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.