Mechanics of Solids (about journal) 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

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IssuesArchive of Issues2010-1pp.140-154

Archive of Issues

Total articles in the database: 12854
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8044
In English (Mech. Solids): 4810

<< 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
<< Previous article | Volume 45, Issue 1 / 2010 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100