Abstract
In the earlier chapters, we developed a geometric description of the middle surface of a shell which proved to be adequate to derive the equations of equilibrium. In turn, a simplified subset of the equilibrium equations formed the basis of the membrane theory of shells, for which many important practical applications were illustrated. Although membrane action in a shell is desirable from the dual standpoints of mathematical simplification and material efficiency, the requisite conditions for corresponding behavior cannot always be simulated in an actual structure. Consequently, to expand our base of understanding of shell behavior, we must develop relationships between the forces and the deformations of the shell. The first step is a description of the displacements, where we follow the vector approach suggested by Novozhilov.1
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References
V. V. Novozhilov, Thin Shell Theory [translated from 2nd Russian ed. by P. G. Lowe (Groningen, The Netherlands: Noordhoff, 1964), pp. 14-27].
H. Kraus, Thin Elastic Shells (New York: Wiley, 1967), chap. 1.
P. Bergan and M. K. Nygard, “Nonlinear Shell Elements with Six Freedoms per Node,” Proc. First World Congress on Computational Mechanics, University of Texas at Austin, Austin, September 1985.
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A. L. Gol’denveizer, Theory of Elastic Thin Shells [translated from Russian ed. (New York: Pergamon Press, 1961), pp. 92-96].
S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, 2nd ed. ( New York: McGraw-Hill, 1959 ), pp. 165 - 173.
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© 1988 Springer-Verlag New York Inc.
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Gould, P.L. (1988). Deformations. In: Analysis of Shells and Plates. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3764-8_5
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DOI: https://doi.org/10.1007/978-1-4612-3764-8_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8340-9
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