Abstract
In this paper we present a variational formulation of the problem of determining the elastic stresses in a contact lens on an eye and the induced suction pressure distribution in the tear film between the eye and the lens. This complements the force-balance derivation that we used in earlier work [K. L. Maki and D. S. Ross, J. Bio. Sys., 22 (2014), pp. 235–248]. We investigate the existence of solutions of the relevant boundary value problem for the singular, second-order Euler–Lagrange equation. We prove that, for lenses of constant thickness, solutions exist. We present an example to show that in some cases in which the lens thickness increases with distance from the lens center no solution exists.
Publication Date
2016
Document Type
Article
Department, Program, or Center
School of Mathematical Sciences (COS)
Recommended Citation
Ross, David S.; Maki, Kara L.; and Holtz, Emily K., "Existence Theory for the Radically Symmetric Contact Lens Equation" (2016). SIAM Journal on Applied Mathematics, 76 (3), 827-844. Accessed from
https://repository.rit.edu/article/1818
Campus
RIT – Main Campus
Comments
Copyright 2016 Society for Industrial and Applied Mathematics