Nonclassical Theories of Shells in Application to Soft Biological Tissues

Voronkova, Eva B.; Bauer, Svetlana M.; Eriksson, Anders

doi:10.1007/978-3-642-21855-2_42

Cited by 6 publications

(3 citation statements)

References 6 publications

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“…The elastic moduli of each layer of the cornea in normal direction E are taken 20 times less than in tangential direction E, the average modulus of elasticity of the cornea is taken one order less than the modulus of elasticity of the sclera [3].…”

Section: Resultsmentioning

confidence: 99%

Biomechanical analysis of the human eye after the surgical correction of hyperopia

Bauer

Венатовская

2015

2015 International Conference "Stability and Control Processes" in Memory of V.I. Zubov (SCP)

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Abstract-Changes in the stress-strain state of the cornea and the intraocular pressure (IOP) readings obtained by Goldmann (GAT) and Maklakov (MAT) applanation tonometers after hyperopia correction performed by the most effective in such type of corretion procedures LASIK and IntraLASIK is analized. In the software package ANSYS the elastic system cornea-sclera is presented as two conjugate transversely isotropic spherical segments loaded with internal pressure. The cornea is simulated as multi-layered transversely isotropic elastic shell and the sclera as transversely isotropic homogeneous elastic shell. In order to estimate changes of the IOP readings obtained by GAT and MAT after hyperopia surgery the problem of deformation of the cornea under the load with a flat base is considered. A comparison of the results of two different surgeries, and a comparison of two methods of measuring of the IOP for each of these surgeries is carried out using in all cases the same true intraocular pressure.

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Section: Resultsmentioning

confidence: 99%

Biomechanical analysis of the human eye after the surgical correction of hyperopia

Bauer

Венатовская

2015

2015 International Conference "Stability and Control Processes" in Memory of V.I. Zubov (SCP)

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“…3 2014 BAUER, VORONKOVA anisotropic shells of moderate thicknesses [26], and the refined iterative theory of Rodionova-Titaev-Chernykh (RTCh) [28]. For uniform plates, the relations for the deflections of plates using approximate models were obtained [41,49].…”

Section: Deformation Of the Lamina Cribrosa Of The Optic Nerve Headmentioning

confidence: 99%

“…The explicit expressions for the deflections and stresses according to the RTCh theory are cumbersome and given in [41,49].…”

Section: Deformation Of the Lamina Cribrosa Of The Optic Nerve Headmentioning

confidence: 99%

Models of shells and plates in the problems of ophthalmology

Bauer

Voronkova

2014

Vestnik St.Petersb. Univ.Math.

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This review is devoted to mathematical models created jointly with ophthalmologists. Models for calculating the stress-strain state of an eye shell after surgeries related to the treatment of retinal detachment and models of the theory of accommodation have been described briefly. Mathe matical models describing the determination of the actual intraocular pressure (IOP) using applica tion techniques have been discussed. Models making it possible to assess the effect of deviations of the shapes of the cornea and sclera from a spherical shape based on the IOP parameters and the effect of the cornea thickness on them have been also considered. It has been noted that models of ocular bio mechanics helped in obtaining a number of new results in mechanics of solids, for example, in solving the problem on the stability of a spherical shell under a concentrated force and normal internal pres sure, the stability of an axisymmetric equilibrium form of orthotropic nonuniform circular plates under normal pressure, the problem on the stability of a segment of an orthotropic shell under normal internal pressure and an applied load with a flat base, and solving problems of deformation of trans versely isotropic spherical and cylindrical layers under internal and external pressures. The compari son of these solutions with those obtained using nonclassical shell theories made it possible to assess the precision of some theories.

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Nonclassical Shell Theories in Ocular Biomechanics

Bauer

Voronkova

2014

Shell and Membrane Theories in Mechanics and Biology

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Nonclassical Theories of Shells in Application to Soft Biological Tissues

Cited by 6 publications

References 6 publications

Biomechanical analysis of the human eye after the surgical correction of hyperopia

Biomechanical analysis of the human eye after the surgical correction of hyperopia

Models of shells and plates in the problems of ophthalmology

Nonclassical Shell Theories in Ocular Biomechanics

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