Buckling of a spherical segment under the flat base load

Paper


Bauer, Svetlana and Ermakov, Andrei. 2013. "Buckling of a spherical segment under the flat base load." Lellep, J. and Puman, E. (ed.) 2nd International Conference on Optimization and Analysis of Structures (OAS 2013). Tartu, Estonia 25 - 27 Aug 2013 Tartu, Estonia.
Paper/Presentation Title

Buckling of a spherical segment under the flat base load

Presentation TypePaper
AuthorsBauer, Svetlana (Author) and Ermakov, Andrei (Author)
EditorsLellep, J. and Puman, E.
Journal or Proceedings TitleProceedings of the 2nd International Conference on Optimization and Analysis of Structures (OAS 2013)
Number of Pages4
Year2013
Place of PublicationTartu, Estonia
Web Address (URL) of Paperhttp://oas2015.ut.ee/OAS2013book.pdf
Conference/Event2nd International Conference on Optimization and Analysis of Structures (OAS 2013)
Event Details
2nd International Conference on Optimization and Analysis of Structures (OAS 2013)
Event Date
25 to end of 27 Aug 2013
Event Location
Tartu, Estonia
Abstract

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.

Keywordsintraocular pressure, deformation of shells, method of consequent loading.
ANZSRC Field of Research 2020490303. Numerical solution of differential and integral equations
420701. Biomechanics
401707. Solid mechanics
Public Notes

c. University of Tartu Press, 2013.

Byline AffiliationsSaint Petersburg State University, Russia
Institution of OriginUniversity of Southern Queensland
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