 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| A. D. Chernyshov, "The application of the eigenfunction technique to the solution of dynamic problems for curved thermoelastic bodies," Mech. Solids. 40 (3), 51-56 (2005) |
| Year |
2005 |
Volume |
40 |
Number |
3 |
Pages |
51-56 |
| Title |
The application of the eigenfunction technique to the solution of dynamic problems for curved thermoelastic bodies |
| Author(s) |
A. D. Chernyshov (Voronezh) |
| Abstract |
The problem of thermoelasticity in the general formulation can be
decomposed into three more simple problems. In the first problem, the
trial method is utilized to find the boundary functions which must satisfy
only the boundary conditions. The second problem with homogeneous boundary
and the inhomogeneous initial conditions is reduced to the eigenfunction-
eigenvalue (EFV) problem by means of the introduction of specific
ξ-variables and the separation of time. For solving this problem, a
system of linear algebraic equations is obtained as a result of the
satisfaction of the boundary conditions at the points of division of
the curvilinear boundary of the body into small parts. When the
eigenfunctions and eigenvalues are found, the solution of the third
problem with homogeneous boundary and initial conditions is determined
using the spectral decomposition of the desired functions and the
nonhomogeneous terms in a coupled system of differential equations.
The thermoelastic model is used in the calculations of the units of
engines of different type, mechanisms, and in other cases. Even the linear
version of the model is fairly complicated. This is especially the case
for the derivation of the solution of the boundary-value and
initial-boundary value problems for bodies with complex curved shape. |
| References |
| 1. | W. Nowacki, Theory of Elasticity [in Russian], Mir, Moscow, 1975. |
| 2. | G. Parkus, Unsteady Temperature Stresses [Russian translation],
Fizmatgiz, 1963. |
| 3. | V. D. Kupradze, T. G. Gegeliya, M. O. Basheleishvili, and
T. V. Burchiladze, Three-dimensional Problems of Mathematical Theory of
Elasticity and Thermoelasticity [in Russian], Nauka, 1976. |
| 4. | S. P. Timoshenko and J. Gudier, Theory of Elasticity [Russian
translation], Nauka, Moscow, 1979. |
| 5. | I. O. Osipov, "On complex-valued solutions in terms of potentials
for dynamic problems of plane elasticity theory for anisotropic media,"
Izv. AN. MTT [Mechanics of Solids], No. 3, pp. 78-89, 2002. |
| 6. | G. Ya. Popov, "Exact solutions of some mixed problems of
uncoupled thermoelasticity for a finite circular hollow cylinder with a
cut along the generatrix," PMM [Applied Mathematics and Mechanics], Vol. 66,
No. 4, pp. 694-704, 2002. |
| 7. | G. Yu. Ermolenko, "Quadratures of the solutions of the first and second initial-boundary
value problems of elasticity for an anisotropic material," PMM [Applied Mathematics and Mechanics], Vol. 66, No. 2,
pp. 325-329, 2002. |
| 8. | V. A. Babeshko and V. V. Kalinchuk, "The fictitious absorbtion
method in coupled mixed problems of elasticity and mathematical physics
for a layered inhomogeneous half-space," PMM [Applied Mathematics and Mechanics],
Vol. 66, No. 2, pp. 285-292, 2002. |
| 9. | V. L. Leont'ev, "A variational-grid method involving orthogonal finite functions
for solving problems of natural vibrations of 3D elastic solids,"
Izv. AN. MTT [Mechanics of Solids], No. 3,
pp. 117-126, 2002. |
| 10. | A. A. Samarskii, Theory of Finite-difference Schemes [in
Russian], Nauka, Moscow, 1983. |
| 11. | V. A. Il'in, Spectral Theory of Differential Operators.
Self-adjoint Differential Operators [in Russian], Nauka, Moscow, 1991. |
| 12. | V. V. Stepanov, A Course in Differential Equations [in Russian],
Fizmatgiz, Moscow, 1958. |
| 13. | A. D. Chernyshov, "Unsteady flow of viscous fluid in a pipe of a
triangular cross-section," Izv. AN. MZhG [Fluid Dynamics], No. 5,
pp. 199-203, 1998. |
| 14. | A. D. Chernyshov, "On a method of solving linear dynamical problems in elasticity," Izv.
AN. MTT [Mechanics of Solids], No. 5, pp. 131-142, 2000. |
|
| Received |
30 May 2003 |
| << Previous article | Volume 40, Issue 3 / 2005 | Next article >> |
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