Reduction of the Sanders-Koiter Equations for Fully Anisotropic Circular Cylindrical Shells to Two Coupled Equations for a Stress and a Curvature Function

[+] Author and Article Information
T. J. McDevitt

Department of Mathematics, Millersville University, Millersville, PA 17551

J. G. Simmonds

Department of Civil Engineering, University of Virginia, Charlottesville, VA 22903

J. Appl. Mech 66(3), 593-597 (Sep 01, 1999) (5 pages) doi:10.1115/1.2791465 History: Received December 23, 1998; Revised April 15, 1999; Online October 25, 2007


With the aid of the static-geometric duality of Goldenveizer (1961), Cartesian tensor notation, and nondimensionalization, it is shown that the equations of linear shell theory of Sanders (1959) and Koiter (1959), when specialized to a circular cylindrical shell with stress-strain relations exhibiting full anisotropy (21 elastic-geometric constants), can be reduced, with no essential loss of accuracy, to two coupled fourth-order partial differential equations for a stress function F and a curvature function G. Auxiliary formulas for the midsurface displacement components are also given. For isotropic shells with uncoupled stress-strain relations, the equations reduce to a form given by Danielson and Simmonds (1969). The reduction is achieved by adding certain negligibly small terms to the given stress-strain relations. For orthotropic shells of mean radius R and thickness h with uncoupled stress-strain relations, it is shown that the very short decay length of O(hR) and the very long decay length of O(RR/h) (associated with separable solutions of the form e−Rz sin nθ) depend, respectively, to within a relative error of O(h/R), only on the products of different pairs of the eight possible elastic constants.

Copyright © 1999 by The American Society of Mechanical Engineers
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