Buckling of a spherical segment under the flat base load

Bauer, Svetlana and Ermakov, Andrei (2013) Buckling of a spherical segment under the flat base load. In: 2nd International Conference on Optimization and Analysis of Structures (OAS 2013), 25–27 Aug 2013 , Tartu, Estonia.


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.

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Item Type: Conference or Workshop Item (Commonwealth Reporting Category E) (Paper)
Refereed: Yes
Item Status: Live Archive
Additional Information: c. University of Tartu Press, 2013.
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences
Date Deposited: 27 Oct 2016 00:12
Last Modified: 07 Nov 2017 03:20
Uncontrolled Keywords: intraocular pressure, deformation of shells, method of consequent loading.
Fields of Research : 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
11 Medical and Health Sciences > 1106 Human Movement and Sports Science > 110601 Biomechanics
09 Engineering > 0913 Mechanical Engineering > 091308 Solid Mechanics
URI: http://eprints.usq.edu.au/id/eprint/29908

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