 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
|
| In English (Mech. Solids): | | 3212 |
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| << Previous article | Volume 45, Issue 1 / 2010 | Next article >> |
| A.D. Chernyshov, "Improving the Differentiability of Generalized Fourier Series Solutions of Boundary Value Problems of Mechanics by Using Boundary Functions," Mech. Solids. 45 (1), 140-154 (2010) |
| Year |
2010 |
Volume |
45 |
Number |
1 |
Pages |
140-154 |
| DOI |
10.3103/S0025654410010176 |
| Title |
Improving the Differentiability of Generalized Fourier Series Solutions of Boundary Value Problems of Mechanics by Using Boundary Functions |
| Author(s) |
A.D. Chernyshov (Voronezh State Technological Academy, pr-t Revolyutsii 19, Voronezh, 394000 Russia, chernyshovad@mail.ru) |
| Abstract |
We prove a theorem on conditions for the differentiation of generalized Fourier series. We show that Fourier series solutions of boundary value problems can in general be differentiated term by term only once. To improve the differentiability properties of such series, we suggest to use pth-order boundary functions. We suggest an algorithm for constructing boundary functions for classical domains. This approach is illustrated by a new solution, with improved differentiability properties, of the problem on the torsion of an elastic rod of rectangular cross-section. |
| Keywords |
solution, problem, mechanics, generalized Fourier series, theorem, differentiation, torsion, rod |
| References |
| 1. | V. A. Il'in,
Spectral Theory of Differential Operators. Self-Adjoint Differential Operators
(Nauka, Moscow, 1991)
[in Russian]. |
| 2. | G. P. Tolstov,
Fourier Series
(Dover, New York, 1976; Nauka, Moscow, 1980). |
| 3. | A. N. Tikhonov and A. A. Samarskii,
Equations of Mathematical Physics
(Nauka, Moscow, 1977; Dover, New York, 1990). |
| 4. | S. G. Mikhlin,
Variational Methods in Mathematical Physics
(Pergamon, New York, 1964; Nauka, Moscow, 1970). |
| 5. | P. V. Tsoi,
Computational Methods for Several Problems of Heat and Mass Transform
(Energiya, Moscow, 1971)
[in Russian]. |
| 6. | A. D. Chernyshov,
"Solution of Nonstationary Problems of Heat Conduction
for Curvilinear Regions by Direct Construction of Eigenfunctions,"
Inzh.-Fiz. Zh.
77 (2), 160-166 (2004)
[J. Engng Phys. Thermophys. (Engl. Transl.)
77 (2), 445-453 (2004)]. |
| 7. | A. D. Chernyshov,
"Two-Dimensional Dynamic Boundary-Value Problems
for Curvilinear Thermoviscoelastic Bodies,"
Zh. Prikl. Mekh. Tekh. Fiz.
46 (2), 158-169 (2005)
[J. Appl. Mech. Tech. Phys. (Engl. Transl.)
46 (2), 281-290 (2005)]. |
| 8. | A. D. Chernyshov, I. S. Savichev, O. A. Chernyshov, and A. A. Dan'shin,
"The Problem of Finding Boundary Functions for Curvilinear Elastic Bodies under Complex Boundary Conditions,"
in Problems of Mechanics of Deformable Rigid Bodies and Rocks,
Collected Papers Dedicated to the 75th Birthday of E. I. Shemyakin
(Fizmatlit, Moscow, 2006)
[in Russian],
pp. 829-839. |
| 9. | S. P. Timoshenko and J. N. Goodyear,
Theory of Elasticity
(McGraw-Hill, New York, 1951; Nauka, Moscow, 1975). |
| 10. | N. Kh. Arutyunyan,
Torsion of Elastic Bodies
(Fizmatlit, Moscow, 1963)
[in Russian]. |
| 11. | E. M. Kartashev,
Analytic Methods in the Theory of Heat Conduction of Solids
(Vysshaya Shkola, Moscow, 2001)
[in Russian]. |
|
| Received |
03 July 2007 |
| Link to Fulltext |
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