Deformations of the orthotropic spherical layer under normal pressure

Abstract

The deformation of the orthotropic spherical layer under normal pressure applied on the outer and inner surfaces is analyzed. The layer is assumed to be slightly othotropic, it permits to apply asymptotic methods. The equations of zeroth and first approximations are derived. For the shell, which is much softer in the transverse direction than in the tangential plane, one gets singularly perturbed boundary value problem. Solving this problem in the zeroth approximation the asymptotic formula for the change of the relative layer thickness under normal pressure is obtained. Also the effect of Poisson ratio and the layer thickness on the deformation is studied. For the cases of the thick and thin layers the last formula may be simplified. The asymptotic results well agree with the exact solution. The developed formulas are used in analysis of the scleral shell under intraocular pressure and may also be used in solution of the inverse problem, i.e. in analysis of the stress-strain state of a human eye under injection. The solution of the problem helps to estimate the mechanical parameters of the sclera, i.e. to find the ratio of the tangential and transversal Young modules using clinical data for the sclera thickness change. Refs 10. Figs 5.

Keywords:

spherical layer, Lame problem, transverse isotropy