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IssuesArchive of Issues2014-4pp.413-421

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R.N. Neskorodev, "Representation of the Solution of Refined Bending Theory for Isotropic Plates," Mech. Solids. 49 (4), 413-421 (2014)
Year 2014 Volume 49 Number 4 Pages 413-421
DOI 10.3103/S0025654414040062
Title Representation of the Solution of Refined Bending Theory for Isotropic Plates
Author(s) R.N. Neskorodev (Donetsk National University, ul. Universitetskaya 24, Donetsk, 83001 Ukraine, nesrom@cable.netlux.org)
Abstract A solution of the bending problem for isotropic plates in a refined statement based on the system of six-order differential equations is proposed. A procedure for determining the general solutions of the corresponding biharmonic and metaharmonic equations is suggested. A method for satisfying the boundary conditions is given. The results of numerical studies of the stress state of an infinite plate with an elliptic cavity are given.
Keywords bending, plate, refined theory, stress, moment, elliptic cavity
References
1.  E. Reissner, "On the Theory of Bending of Elastic Plates," J. Math. Phys. 23 (4), 184-191 (1944).
2.  E. Reissner, The Effect of Transverse Shear Deformation on the Bending of Elastic Plates," Trans. ASME 67 (4), A69-A77 (1945).
3.  B. L. Pelekh, Stress Concentration near Holes in Bending of Transversally Isotropic Plates (Naukova Dumka, Kiev, 1977) [in Russian].
4.  B. L. Pelekh and A. A. Syaj'kii, Stress Distribution near Holes in Shear Compliant Anisotropic Shells (Naukova Dumka, Kiev, 1975) [in Russian].
5.  V. V. Vasil'ev, "Classical Theory of Plates: Historical Perspective and State-of-the-Art," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 3, 46-58 (1998) [Mech. Solids (Engl. Transl.) 33 (3), 35-45 (1998)].
6.  S. G. Lekhnitskii, Anisotropic Plates (Gostekhizdat, Moscow, 1957) [in Russian].
7.  A. S. Kosmodamianskii and R. N. Neskorodev, "The Relation Between the Equations of the Two-Dimensional Theory of Elasticity for Anisotropic and Isotropic Bodies," Prikl. Mat. Mekh. 62 (2), 344-346 (1998) [J. Appl. Math. Mech. (Engl. Transl.) 62 (2), 319-321 (1998)].
8.  A. F. Nikiforov and V. B. Uvarov, Special Functions of Mathematical Physics (Nauka, Moscow, 1984) [in Russian].
9.  I. S. Berezin and N. P. Zhidkov, Computational Methods, Vol. 1 (Nauka, Moscow, 1966) [in Russian].
10.  A. S. Kosmodamianskii, Stress State of Anisotropic Media with Holes or Cavities (Vishcha Shkola, Kiev-Donetsk, 1976) [in Russian].
Received 16 May 2012
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