A General Theory of Shells and the Complementary Potentials

[+] Author and Article Information
G. Wempner

Georgia Institute of Technology, Atlanta, GA 30332

J. Appl. Mech 53(4), 881-885 (Dec 01, 1986) (5 pages) doi:10.1115/1.3171875 History: Received December 01, 1985; Revised May 21, 1986; Online July 21, 2009


This theory incorporates the attributes which are essential to the approximation of shells by finite elements. It is limited only by one assumption: Displacement is a linear function of distance along the normal to a reference surface. Deformation is decomposed into rotation and strain; the rotation carries elements of the reference surface to the same surface in any subsequent state. Transverse-shear deformations accommodate simple elements. The theory is couched in the potential P v and in the complementary potential P c ; these have the property, P v + P c = 0 for all admissible (equilibrated) states. The theory is also cast in the complementary functional P̄ c of stress and displacement, and the functional P̄ v of displacement, strain and stress; P̄ c and P̄ v are akin to the functionals of Hellinger-Reissner and Hu-Washizu. These alternate functionals provide the means to develop various hybrid elements.

Copyright © 1986 by ASME
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