Abstract
The spline-finite-strip method in conjunction with the subparametric mapping concept is employed in the analysis of arbitrary shaped plates. Numerical examples of static and free vibration analyses are included to demonstrate the accuracy, veratility and efficiency of the proposed method.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Carrington, H. (1925): The frequencies of vibration of flat circular plates fixed at the circumference. Phil. Mag. 50, 6, 1261–1264.
Chen, M. J., Tham, L. G.; Cheung, Y. K. (1984): Spline finite strip for parallelogram plate. Proc. of Intern. Conf. on Accuracy Estimates and Adaptive Refinements in Finite Element Computations (ARFEC), Lisbon, Portugal, Vol. l, pp. 95–104; 19–22
Cheung, Y. K; Fan, S. C.; Wu, C. Q.,(1982): Spline finite strip in structural analysis. Proc. of Intern. Conf. on Finite Element Method, Shangi, pp. 704–709
Cheung, Y. K.; Tahm, L. G.; Li, W. Y. (1986): Application of spline-finite-strip method in the analysis of curved slab bridge. Proc. Instn. Civ. Engrs. 81/2, 111–124
Cheung, Y. K.; Zhu, D. S. (1987): Large deflection analysis of arbitrary shaped thin plates. J. Comp. & Struct. (submitted for publ.)
Conway, H. D.; Farnham, K. A. (1965): The free flexural vibrations of triangular, rhombic and parallelogram plates and some analogies. Int. J. Mech. Sci. 7, 811–816
Contugno, N.; Mengotti-Marzolla C. (1943): Approssimazione per eccesso della più bassa frequenza di una piastra ellittica omogenea incastrata. Atti Accad. Na. Lincei, Rend., Classe Sci. Fis., Mat. Nat. 5, ser. 8, sem. 2, pp. 324–327
Fan, S. C.; Cheung, Y. K. (1984): Flexural free vibration of rectangular plates with complex support conditions. J. Sound & Vibration 93/1, 81–94
Gontkevich, V. S. (1964): Natural vibrations of plates and shells.
Filippov, A. P. (ed), Nauk. Dumka (Kiev), (Translation by Lockheed Missiles & Space Co., Sunnyvale, Calif.)
Hamade, M.; Kondo, H. (1959): Fundamental frequency of a rhomboidal plate with all edges clamped. Bull. JSME 2/8, 520–526
Hasegawa, M. (1957): Vibration of clamped parallelogrammic isotropic flat plates. J. Aeron. Sci. 24/2, 145–146
Kaul, R. K.; Cadambe, V. (1956): The natural frequencies of thin skew plates. Aeron. Quart. 7, 337–352
Leissa, A. W. (1969): Vibration of plates. NASA SP-160, Scien. and Tech. Inform. Division, Office of Tech. Utili. National Aero. and Space Admin., Washington, D. C.
Li, W. Y.; Cheung, Y. K.; Tham, L. G. (1986): Spline finite strip analysis of general plates. ASCE J. Eng. Mech. 112/1, 43–54
Shibaoka, Y. (1956): On the transverse vibration of an elliptic plate with clamped edge. J. Phys. Soc. Jpn. 11/7, 1124–1125
Solecki, R. (1960): Free and forced vibration of a triangular plate. Rozprawy Inzh. 142 (In Polish) 8/l, 65–81
Tham, L. G.; Li, W. Y.; Cheung, Y. K; Chen, M. J. (1986): Bending of skew plates by spline-finite-strip method. J. Comp. & Struct. 22/l, 31–38
Timoshenko, S.; Woinowsky-Krieger, S. (1959): Theory of plates and shells. 2nd ed.; London: McGraw-Hill
Zienkiewicz, O. C. (1977): The finite element method. 3rd ed., London: McGraw-Hill
Author information
Authors and Affiliations
Additional information
Communicated by S. N. Atluri, December 31, 1986
Rights and permissions
About this article
Cite this article
Cheung, Y.K., Tham, L.G. & Li, W.Y. Free vibration and static analysis of general plate by spline finite strip. Computational Mechanics 3, 187–197 (1988). https://doi.org/10.1007/BF00297445
Issue Date:
DOI: https://doi.org/10.1007/BF00297445