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IssuesArchive of Issues2006-6pp.36-47

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V. V. Vasil'ev and L. V. Fedorov, "Plane axisymmetric geometric elasticity problem and disk optimization," Mech. Solids. 41 (6), 36-47 (2006)
Year 2006 Volume 41 Number 6 Pages 36-47
Title Plane axisymmetric geometric elasticity problem and disk optimization
Author(s) V. V. Vasil'ev (Moscow)
L. V. Fedorov (Moscow)
Abstract On the basis of the equations of geometric elasticity, which relate the stress state of a medium to the geometry of the Riemannian space generated by the stresses, we consider an axisymmetric plane problem for the disk loaded in its plane by boundary and centrifugal forces. The metric coefficient of the Riemannian space corresponding to the coordinate normal to the disk plane is treated as the variable thickness of the disk located in three-dimensional Euclidean space. We claim that the thickness thus obtained determines the optimal law of material distribution along the disk radius. To justify this conjecture, we construct solutions of classical elasticity problems and compare them with known solutions of the disk optimization problems.
References
1.  V. Z. Vlasov, "Strain continuity equations in curvilinear coordinates," in Collected Works. Volume 1 [in Russian], pp. 425-430, Izd-vo AN SSSR, Moscow, 1962.
2.  V. V. Vasiliev, "Geometric theory of elasticity and shape optimization for solids," Izv. RAN. MTT [Mechanics of Solids], No. 1, pp. 16-27, 2006.
3.  D. Sing, General Relativity [Russian translation], Izd-vo Inostr. Lit-ry, Moscow, 1963.
4.  Yu. N. Rabotnov, Mechanics of Solids [in Russian], Nauka, Moscow, 1979.
Received 09 February 2006
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