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RESEARCH PAPERS

Nonlinear Corrections for Edge Bending of Shells

[+] Author and Article Information
G. V. Ranjan

Shelltech Associates, Stanford, Calif. 94304

C. R. Steele

Division of Applied Mechanics, Department of Mechanical Engineering, Stanford University, Stanford, Calif. 94305

J. Appl. Mech 47(4), 861-865 (Dec 01, 1980) (5 pages) doi:10.1115/1.3153803 History: Received May 01, 1980; Online July 21, 2009

Abstract

Asymptotic expansions for self-equilibrating edge loading are derived in terms of exponential functions, from which formulas for the stiffness and flexibility edge influence coefficients are obtained, which include the quadratic nonlinear terms. The flexibility coefficients agree with those previously obtained by Van Dyke for the pressurized spherical shell and provide the generalization to general geometry and loading. In addition, the axial displacement is obtained. The nonlinear terms in the differential equations can be identified as “prestress” and “quadratic rotation.” To assess the importance of the latter, the problem of a pressurized spherical cap with roller supported edges is considered. Results show that whether the rotation at the edge is constrained or not, the quadratic rotation terms do not have a large effect on the axial displacement. The effect will be large for problems with small membrane stresses.

Copyright © 1980 by ASME
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