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Linear theory of Cosserat surface and elastic plates of variable thickness

Published online by Cambridge University Press:  24 October 2008

A. E. Green ,
P. M. Naghdi  and
M. L. Wenner
A. E. Green
Affiliation:
University of Oxford and University of California, Berkeley
P. M. Naghdi
Affiliation:
University of Oxford and University of California, Berkeley
M. L. Wenner
Affiliation:
University of Oxford and University of California, Berkeley
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Abstract

Within the scope of the linear isothermal theory of an elastic Cosserat surface, constitutive equations are derived for an initially flat Cosserat surface in which the initial director (along the normal to the initial surface) is allowed to depend on the surface coordinates. These constitutive equations correspond to those for bending and stretching of a transversely isotropic three-dimensional plate. Special attention is given to the relevance and applicability of the results to bending of (three-dimensional) plates of variable thickness and comparison is made with a set of equations for elastic plates of variable thickness obtained, by an approximation procedure, from the three-dimensional equations.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 69 , Issue 1 , January 1971 , pp. 227 - 254
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

REFERENCES

(1)Essenburg, F. and Naghdi, P. M.Proc. 3rd. U.S. National Congress Appl. Mech. (Providence, B.I.), (1958), 313.Google Scholar
(2)Green, A. E., Laws, N. and Naghdi, P. M.Proc. Cambridge Philos. Soc. 64 (1968), 895.CrossRefGoogle Scholar
(3)Green, A. E. and Naghdi, P. M.Proc. Cambridge Philos. Soc. 63 (1967), 537CrossRefGoogle Scholar
Green, A. E. and Naghdi, P. M.Proc. Cambridge Philos. Soc. 63 (1967), 922.CrossRefGoogle Scholar
(4)Green, A. E. and Naghdi, P. M.Int. J. Solids Structures, 4 (1968), 585.CrossRefGoogle Scholar
(5)Green, A. E. and Naghdi, P. M.Quart. J. Mech. Appl. Math. 21 (1968), 135.CrossRefGoogle Scholar
(6)Green, A. E. and Naghdi, P. M.Proc. IUTAM Symp. on Theory of thin shells (Copenhagen). Springer-Verlag (1969), 39.CrossRefGoogle Scholar
(7)Green, A. E. and Naghdi, P. M.Int. J. Solids Structures, 6 (1970), 209.CrossRefGoogle Scholar
(8)Green, A. E., Naghdi, P. M. and Wainwright, W. L.Arch. Rational Mech. Anal. 20 (1965), 287.CrossRefGoogle Scholar