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Models of shells and plates in the problems of ophthalmology

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Abstract

This review is devoted to mathematical models created jointly with ophthalmologists. Models for calculating the stress-strain state of an eye shell after surgeries related to the treatment of retinal detachment and models of the theory of accommodation have been described briefly. Mathematical models describing the determination of the actual intraocular pressure (IOP) using application techniques have been discussed. Models making it possible to assess the effect of deviations of the shapes of the cornea and sclera from a spherical shape based on the IOP parameters and the effect of the cornea thickness on them have been also considered. It has been noted that models of ocular biomechanics helped in obtaining a number of new results in mechanics of solids, for example, in solving the problem on the stability of a spherical shell under a concentrated force and normal internal pressure, the stability of an axisymmetric equilibrium form of orthotropic nonuniform circular plates under normal pressure, the problem on the stability of a segment of an orthotropic shell under normal internal pressure and an applied load with a flat base, and solving problems of deformation of transversely isotropic spherical and cylindrical layers under internal and external pressures. The comparison of these solutions with those obtained using nonclassical shell theories made it possible to assess the precision of some theories.

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Authors and Affiliations

  1. St. Petersburg State University, Universitetskaya nab. 7/9, St. Petersburg, 199034, Russia

    S. M. Bauer & E. B. Voronkova

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  1. S. M. Bauer
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  2. E. B. Voronkova
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Correspondence to S. M. Bauer.

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Original Russian Text © S.M. Bauer, E.B. Voronkova, 2014, published in Vestnik Sankt-Peterburgskogo Universiteta. Seriya 1. Matematika, Mekhanika, Astronomiya, 2014, No. 3, pp. 90–110.

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Bauer, S.M., Voronkova, E.B. Models of shells and plates in the problems of ophthalmology. Vestnik St.Petersb. Univ.Math. 47, 123–139 (2014). https://doi.org/10.3103/S1063454114030029

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