TECHNICAL NOTES
Apr 1, 1996

Static Analyses of Beams and Plates by Spline Collocation Method

Publication: Journal of Engineering Mechanics
Volume 122, Issue 4

Abstract

Analyses of beams and plates are conducted using the spline collocation (interpolation) method, which may not be well known to engineers. A brief literature review of the method is given and the method is explained. Then it is applied to example beam and plate problems. Results are compared with those obtained by the differential quadrature method (DQM) and available analytic results. Good results are obtained and some problems encountered in using DQM for such problems are resolved.

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References

1.
Bellman, R., Kashef, B., and Casti, J.(1972). “Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations.”J. Computational Phys., 10, 40–52.
2.
Chajes, A. (1974). Principles of structural stability theory . Prentice Hall, Englewood Cliffs, N.J., 114.
3.
Gu, D. G.(1991). “Calculation in the unsymmetric bending problems of thin plates by spline boundary layer method.”Comp. and Struct., 34(4), 663–668.
4.
Jang, S. K. (1987). “Application of differential quadrature to static analysis of structural components,” PhD dissertation, The Univ. of Oklahoma, Norman, Okla.
5.
Jang, S. K., Bert, C. W., and Striz, A. G.(1989). “Application of differential quadrature to static analysis of structural components.”Int. J. Numerical Methods in Engrg., 28, 561–577.
6.
Prenter, P. M. (1975). Splines and variational methods . John Wiley & Sons, Inc., New York, N.Y.
7.
Sahney, B. N. (1978). Polynomial and spline approximation . D. Reidel Publishing Co., Boston, Mass.
8.
Shen, P. C., and Kang, H. B.(1991). “Multivariable spline element analysis for plate bending problems.”Comp. and Struct., 40(6), 1343–1349.
9.
Timoshenko, S. P., and Woinowsky-Krieger, S. (1959). Theory of plates and shells . 2nd Ed., McGraw-Hill, New York, N.Y.
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Timoshenko, S. P., and Gere, J. M. (1972). Mechanics of materials . Van Nostrand Reinhold Co., New York, N.Y.
11.
Wang, X., and Bert, C. W.(1993). “A new approach in applying differential quadrature to static and free vibrational analysis of beams and plates.”J. Sound and Vibration, 162(3), 566–572.

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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 122Issue 4April 1996
Pages: 375 - 378

History

Published online: Apr 1, 1996
Published in print: Apr 1996

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Authors

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Charles W. Bert
Perkinson Chair, School of Aerosp. and Mech. Engrg., The Univ. of Oklahoma, Norman, OK 73019-0601.
Youngkwang Sheu
Grad. Student, School of Aerosp. and Mech. Engrg., The Univ. of Oklahoma, Norman, OK.

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