 | | 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
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| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 41, Issue 3 / 2006 | Next article >> |
| K. F. Chernykh, "An aternative method in elasticity: boundary condition splitting," Mech. Solids. 41 (3), 55-68 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
3 |
Pages |
55-68 |
| Title |
An aternative method in elasticity: boundary condition splitting |
| Author(s) |
K. F. Chernykh (St. Petersburg) |
| Abstract |
Of wide use in plane linear elasticity is the traditional method based on
Cauchy-type integrals. Being a student (1951), the author noticed that all
problems that can be solved on the basis of the traditional approach can also
be solved by a simpler method, which does not require a special mathematical
background,
- the so-called boundary condition splitting method. Later that method
was extended to cover conjugation conditions and two-dimensional problems of
nonlinear elasticity (plane problem, anti-plane strain, axisymmetric strain of
bodies of revolution). This new method was used in a new version of the
nonlinear elasticity theory proposed by the author. This version is extremely
simple and entails no loss of generality. In this way (with the development of
the method of complex variable, the introduction of new types of boundary
conditions, conjugation conditions, and constitutive relations of elasticity),
it turned out possible to obtain exact solutions of two-dimensional boundary
value problems.
The next step was the introduction of conjugate static and distortional
resolving functions, which are obtained from a compact system of resolving
functions. The resolving functions determined in this way were used to
determine "secondary" quantities, such as the coordinates of material points
of a strained domain, rotations and stresses. Statically determinate problems
for arbitrary (not only elastic) materials, as well as distortionally
determinate problems, were identified.
This paper contains mostly new results, in particular, the splitting method demonstrated
on a nonlinear plane problem. |
| References |
| 1. | V. V. Novozhilov, Theory of Elasticity [in Russian], Sudpromgiz, Leningrad, 1958. |
| 2. | K. F. Chernykh, Nonlinear Elasticity in Engineering [in Russian], Mashinostroenie, Leningrad, 1986. |
| 3. | K. F. Chernykh, An Introduction to Anisotropic Elasticity [in Russian], Mauka, Moscow, 1988. |
| 4. | K. F. Chernykh, An Introduction to the Geometrically and Physically Nonlinear Theory of
Cracks [in Russian], Nauka, Moscow, 1996. |
| 5. | K. F. Chernykh, Nonlinear Theory of Anisotropic Elasticity, Begell Publishing House,
New York, 1998. |
| 6. | K. F. Chernykh, Nonlinear Singular Elasticity. Part I. Theory [in Russian]. Izd-vo St. Peterburg. Univ.,
St. Petersburg, 1999. |
| 7. | K. F. Chernykh, Nonlinear Singular Elasticity. Part II. Applications [in Russian]. Izd-vo St. Peterburg. Univ.,
St. Petersburg, 1999. |
| 8. | K. F. Chernykh, "Complex nonlinear theory of elasticity," Uspekhi
Mekhaniki, Vol. 1, No. 4, pp. 212-161, 2002. |
| 9. | K. F. Chernykh, "On the approach to nonlinear physical
mesomechanics," Fiz. Mezomekh., Vol. 5, No. 2, pp. 5-15, 2002. |
| 10. | K. F. Chernykh, Nonlinear Elasticity (Theory and Applications) [in Russian], Izd-vo St. Peterb. Univ.,
St. Petersburg, 2004. |
|
| Received |
26 March 2004 |
| << Previous article | Volume 41, Issue 3 / 2006 | Next article >> |
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