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M. Reilly, B. Szabo, N. Ravi; Finite Element Analysis of a Single Lens Fiber . Invest. Ophthalmol. Vis. Sci. 2006;47(13):1983.
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To determine the mechanical advantage of an archedlens fiber relative to a straight fiber constructed of the samematerial.
Finite element analysis was carried out using StressChecksoftware. A single fiber of hexagonal cross–section wasmodeled using p– and hp–expansion in two differentgeometries. The first geometry was a simple linear shape (Fig.1), while the second was modeled as a geometrically realistic,arbitrarily selected lens fiber (Fig. 2). An axial displacementwas applied to one end of each fiber, while the other end washeld fixed. The force required to cause this displacement wascalculated using superconvergent extraction of the potentialenergy functional, minimizing the relative error.
The force required to compress the straight fiber thespecified amount was approximately 19 times that required toachieve the same displacement of the arched lens fiber. Errorin strain energy was conservatively estimated as 0.0025% forthe linear fiber and 1.16% for the arched lens fiber.
Since nature has a limited number of materialsfrom which to construct tissues, it must vary the geometry ofthese materials to achieve the desired functionality. In thelens, the fiber is arched so that the force requirements ofthe ciliary muscle are minimized. Further, as the displacementrequirement of the ciliary muscle will be less for the archedfiber, the speed of accommodation is enhanced. These effectswould be very significant in the lens due to the vast numberof fibers present. Figure 1. Linear fiber mesh detail. Figure 2. Arched fiber mesh detail.
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