 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 41, Issue 6 / 2006 | Next article >> |
| 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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