Abstract
In this paper, based on the step reduction method, a new method, the exact element method for constructing finite element, is presented. Since the new method doesn't need the variational principle, it can be applied to solve non-positive and positive definite partial differential equations with arbitrary variable coefficient. By this method, a triangle noncompatible element with 6 degrees of freedom is derived to solve the bending of nonhomogeneous plate. The convergence of displacements and stress resultants which have satisfactory numerical precision is proved. Numerical examples are given at the end of this paper, which indicate satisfactory results of stress resultants and displacements can be obtained by the present method.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Cowper, G. R., E. Kosko, G. M. Lindberg and M. D. Olson, Statics and dynamics of high-precision triangular plate bending element,AIAA Journal,7, 10 (1969), 1957.
Argyris, J. H. and K. E. Buck, A sequel to technical note 14 on the TUBA family of plate element,Aeronautical Journal,72 (1968), 977.
Irons, B. M., A conforming quartic triangular element for plate bending,International Journal for Numerical Methods in Engineering,1, 1 (1969), 29.
Hermman, J. R., A bending analysis for plates, AD 646300 (1966), 577.
Hermman, L. R., Finite element bending analysis for plates,Journal of the Engineering Mechanics Division, Proceedings of the ASCE,93, EM5 (1967), 13.
Morley, L. S. D., On the constant moment plate bending element,Journal of Strain Analysis,6, 1 (1971), 20.
Zienkiewicz, O. C.,The Finite Element Method, 3rd Ed., McGraw-Hill Book Company (1977).
Irons, B. and S. Ahmad,Techniques of Finite Elements, Ellis Horwood, Ltd., Chichester, UK (1979).
Yeh Kai-yuan, General Solutions on certain problems of elasticity with non-homogeneity and variable thickness, IV. Bending, buckling and free vibration of non-homogeneous variable thickness beams,Journal of Lanzhou University, Special Number of Mechanics, 1 (1979), 133–157, (in Chinese)
Ji Zhen-yi and Yeh Kai-yuan, Exact analytic method for solving variable coefficient differential equation,Applied Mathematics and Mechanics (English Ed.),10, 10 (1989), 885–896.
Timoshenko, S. and S. Woinowsky-Krieger,Theory of Plates and Shell, 2nd Ed., McGraw-Hill Book Company, Inc. (1959).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zhen-yi, J., Kai-yuan, Y. An exact element method for bending of nonhomogeneous thin plates. Appl Math Mech 13, 683–690 (1992). https://doi.org/10.1007/BF02451534
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02451534