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A perturbation analysis to solve the linear equations for symmetric deformation of a deep spherical shell. (English) Zbl 1165.74340

Summary: In her recent Ph.D. thesis, J. Thredgold [Mathematical modelling of the deformation of spectacle lenses, Ph.D. thesis, University of South Australia (2007)] considered the numerical solution of equations for the deformation of a spherical shell using a finite difference methodology. In this paper, we use an elementary perturbation analysis to find an analytic solution to the linear equations for the small symmetric deformation of a deep spherical shell.

MSC:

74K25 Shells
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References:

[1] Jane Thredgold, Mathematical modelling of the deformation of spectacle lenses, Ph.D. thesis, University of South Australia, 2007; Jane Thredgold, Mathematical modelling of the deformation of spectacle lenses, Ph.D. thesis, University of South Australia, 2007
[2] Love, A. E.H., A Treatise on the Mathematical Theory of Elasticity (1944), Dover Publications, Inc.: Dover Publications, Inc. New York · Zbl 0063.03651
[3] Soedel, W., Vibrations of Shells and Plates (1993), Marcel Dekker: Marcel Dekker New York · Zbl 0865.73002
[4] Seide, P., Small Elastic Deformations of Thin Shells (1975), Noordhoff International Publishing: Noordhoff International Publishing Leyden · Zbl 0313.73070
[5] Timoshenko, S. P.; Woinowsky-Krieger, S., Theory of Plates and Shells (1959), McGraw-Hill Book Company · Zbl 0114.40801
[6] Thredgold, J. M.; Lucas, S. K.; Howlett, P. G., On the contact of a rigid sphere and a thin plate, Journal of Mathematical and Computer Modelling, 43, 119-131 (2006) · Zbl 1124.74317
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