Buckling of a spherical segment under the flat base load

The analysis of stress-strain states of soft and almost soft shells under internal pressure and flat base load are important in study of intraocular pressure, which is an important characteristic in ophthalmology. In the Maklakoff method of tonometry a human eye is deformed by flat base load. The diameter of the contact zone with cornea is measured and the measured diameter length is used in estimating the intraocular pressure. When the intraocular pressure is not very high and the thickness of an eye shell (cornea) is small (for example, after refractive surgery) the cornea may buckle and detach from tonometer. It leads to errors in estimates of intraocular pressure. Shells deformations under the flat base load are large and therefore described by equations of geometrically nonlinear theory of shells. In our study the Paliy-Spiro theory of anisotropic shells of moderate thickness was applied. The problem was solved by means of the method of consequent loading (delta method). Since only linear physical relations are used in delta method one can trace each step of solution of linear systems with constant coefficients. The results obtained with i) linearized non-linear equilibrium equations, ii) the method of minimization of shell elastic potential and iii) finite element method are compared. The research leads us to the following conclusions: The flatter form of the shell makes larger the radius of the contact area between the cornea and the load and makes larger the radius of the inner unloaded area. Decreasing of the shell thickness also leads to increasing of the radius of the contact area, however, this parameter has affect less on the measurement of the intraocular pressure, than the parameter of flatness.