Models of shells and plates in the problem of ophthalmology

Abstract

In this paper an overview of the mathematical models, developed in collaboration with ophthalmologists is presented. Models for the stress-strain state analyses of the eyeball after retinal detachment surgery, models related to the theory of accommodation of the eye are briefly described. The mathematical model for applanation tonometry and determination of true intraocular pressure (IOP) are discussed. Models that can be used for assessment of the effect of out-of-sphericity of the cornea and the scleral shapes, the central corneal thickness on intraocular pressure readings are displayed. New results in solid mechanics were obtained while developing biomechanical models of the eye. For example, the problem of stability of spherical shell subjected to concentrated force and inner pressure, the problem of axisymmetric stability of annular plates, the problem of stability of orthotropic spherical segments under inner pressure and load with flatted foundation, the problems of deformation of spherical and cylindrical layers subjected to inner and outer pressure were solved. For pressurized spherical and cylindrical layers, the accuracy of the approximate solutions, obtained with the refined shell theories is analyzed by comparison of these solutions with the 3D exact solutions. Refs 49. Figs 9.

Keywords:

mathematical simulation, shell theory, nonclassical models