Simplifications and reduction of the Sanders-Koiter linear shell equations for various midsurface geometries

Author:
James G. Simmonds

Journal:
Quart. Appl. Math. **28** (1970), 259-275

MSC:
Primary 73.35

DOI:
https://doi.org/10.1090/qam/267821

MathSciNet review:
267821

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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that the twelve linear field equations of the Sanders-Koiter first approximation shell theory, when specialized to shells with midsurfaces of constant mean curvature, can be replaced by eight equations of particularly simple form. This is accomplished by adding certain negligibly small terms to the conventional uncoupled stress-strain relations. On the basis of order of magnitude estimates, it is argued that these equations are actually adequate for shells of arbitrary geometry. For shells of nonzero Gaussian curvature, the simplified field equations are reduced to four coupled scalar equations. For catenoidal and helicoidal shells, these equations are further reduced to two coupled fourth-order equations. Various special forms of these equations are shown to agree with results obtained by Lardner, Reissner, and Wan for shallow shells, shells of revolution undergoing axisymmetric and lateral deformation, and helicoidal shells undergoing axisymmetric deformation.

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DOI:
https://doi.org/10.1090/qam/267821

Article copyright:
© Copyright 1970
American Mathematical Society