Abstract

This paper presents a very brief review of models constructed in cooperation with ophthalmologists, namely, for the change in the stress-strain state of the eye membrane after vision-correction operations and the change in the intraocular pressure after the injection of drugs into the vitreous body. The mathematical models describing the process of measuring the true intraocular pressure (IOP) by applanation methods are discussed. The models of eye biomechanics provide the possibility to obtain a series of new results in solid mechanics, i.e., to solve the problem of the stability of a spherical shell under a concentrated force and inner pressure and the stability of an axisymmetric equilibrium state of inhomogeneous annular orthotropic plates under a uniformly distributed normal load. The problems of the deformation of transversally isotropic spherical and cylindrical layers under inner and outer pressure are analyzed and the solutions obtained within the framework of the three-dimensional theory are compared with those found by the non-classical theories of shells. This comparison makes it possible to estimate the precision of some theories.

中文翻译：

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眼科问题中的固体力学模型

摘要

本文对与眼科医生合作构建的模型进行了简要回顾，即视力矫正手术后眼膜应力应变状态的变化和玻璃体注射药物后眼压的变化身体。讨论了描述通过压平方法测量真实眼压（IOP）过程的数学模型。眼睛生物力学模型为获得一系列固体力学新结果提供了可能，即解决球壳在集中力和内压力下的稳定性问题以及非均匀环形轴对称平衡状态的稳定性问题正交各向异性板在均匀分布的法向载荷下。分析了横向各向同性球层和柱层在内外压力作用下的变形问题，并将三维理论框架内得到的解与非经典壳理论得到的解进行了比较。这种比较可以估计一些理论的精度。