Abstract
The problem of a stressed state in elliptic plates has been considered in general for a rigid contour fixation. It is much more difficult to obtain a solution for the freely supported plates, even for isotropic materials. In this paper we suggest an approach for defining the stressed state of thin elliptic plates with layered structure under the condition of a freely supported contour. The solution is obtained in a rectangular cartesian coordinate system. The displacements, which are the fundamental unknowns, are given in the form of polynomials with unknown coefficients defined by a system of algebraic equations. The resolving equations and three out of the four boundary conditions are satisfied precisely. One boundary condition, is satisfied by means of collocation method of separate points of the contour. Estimation of the accuracy of the suggested approach is carried out by comparing the obtained results with the known ones. The problem of deformation of a twolayered plate has been discussed, in which the principal direction of elasticity does not coincide with the coordinate directions.
Similar content being viewed by others
References
S. G. Lekhnitskii, Anisotropic Sheets [in Russian], Gostekhizdat, Moscow-Leningrad (1947).
S. P. Timoshenko and S. Voinovskii-Kriger, Plates and Shells [in Russian], Fizmatgiz, Moscow (1963).
E. H. Mansfield, “Analysis of unbalanced multilayered elliptical plates under linearly varying pressure”, Int. J. Mech. Sci.,32, No. 5, 417–422 (1990).
A. L. Malmeister, V. P. Tamuzh, and G. A. Teters, Strength of Polymer and Composite Materials [in Russian], Zinatne, Riga (1980).
Ya. S. Sidorin, “Bending of freely supported orthotropic elliptical plates”, Mekh. Polim., No. 6, 1048–1050 (1977).
B. G. Galerkin, Collected Works, Vol. 11, Academy of Sciences of the USSR, Moscow (1953).
Van Fo Fy, “Bending of an elliptical plate”, Prikl. Mekh., 5, No. 1 29–37 (1959).
S. A. Ambartsumyan, Theory of Anisotropic Shells [in Russian], Nauka, Moscow (1961).
I. S. Berezin and N. P. Zhidkov, Computation Methods, Vol. 1 [in Russian], Fizmatgiz, Moscow (1959).
E. K. Ashkenazi and É. V. Ganov, Anisotropy of Structural Materials [in Russian], Mashinostroenie, Leningrad (1980).
Additional information
S. P. Timoshenko Institute of Mechanics, National Academy of Science of the Ukraine, Kiev. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 4, pp. 496–504, July–August, 1997. Original article submitted March 19
Rights and permissions
About this article
Cite this article
Vasilenko, A.T., Urusova, G.P. Stress state of freely supported multilayered elliptical plates of anisotropic materials. Mech Compos Mater 33, 349–355 (1997). https://doi.org/10.1007/BF02256286
Issue Date:
DOI: https://doi.org/10.1007/BF02256286