Summary
In the standard treatments for anisotropic shells based on the Kirchoff hypothesis, it is necessary to make certain restrictions on the type of anisotropy and the resulting theories involve only six elastic constants.
In the present work, a shell theory is obtained by an “asymptotic” or “perturbation” method which does not require any restriction on the anisotropy.
It is found that, in those cases in which the extensional and bending strains are of the same order of magnitude, the leading terms satisfy the classical equations and depend only on the same six elastic constants.
It is seen however that in some cases the full anisotropy is significant and it is shown that in the extension of a plate the anisotropy can produce displacements normal to the plate.
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References
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Westbrook, D.R. A linear asymptotic theory for anisotropic shells. J Eng Math 6, 305–312 (1972). https://doi.org/10.1007/BF01535191
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DOI: https://doi.org/10.1007/BF01535191