Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

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: 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

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