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
 


IPMech RASWeb hosting is provided
by the Ishlinsky Institute for
Problems in Mechanics
of the Russian
Academy of Sciences
IssuesArchive of Issues2005-2pp.133-148

Archive of Issues

Total articles in the database: 9179
In Russian (. . ): 6485
In English (Mech. Solids): 2694

<< Previous article | Volume 40, Issue 2 / 2005 | Next article >>
Yu. V. Nemirovskii and A. P. Yankovskii, "Elastoplastic transverse bending of profiled plates reinforced along the principal stress and strain directions," Mech. Solids. 40 (2), 133-148 (2005)
Year 2005 Volume 40 Number 2 Pages 133-148
Title Elastoplastic transverse bending of profiled plates reinforced along the principal stress and strain directions
Author(s) Yu. V. Nemirovskii (Novosibirsk)
A. P. Yankovskii (Novosibirsk)
Abstract The problem of rational reinforcement of Kirchhoff plates along the principal stress and strain directions in the case of purely elastic and elastoplastic transverse bending is formulated. In addition, the problem of rational profiling of such structures under the condition that the fibers of one of the families are equistressed at the plate faces is formulated. A qualitative analysis of relevant systems of governing equations is carried out. It is shown that the problem posed may have several solutions, and it is possible to control them. Example calculations are carried out which demonstrate that, with rational profiling, the plates subjected to bending loads may be manufactured with substantial (up to several times) reduction in the amounts of phase materials in comparison with the reference structure designs.

Fiber-reinforced composites, possessing high strength and stiffness when loaded along the fiber orientation direction, perform much worse under loadings which cause relative shear displacement of the reinforcement fibers. Therefore, one of the criteria for rational design of composite structures is the condition that the reinforcement fibers are oriented along the principal stress and strain directions. Up to now, however, the problem of reinforcement of thin-walled structures along the principal stress directions was studied for loadings in zero moment conditions only: either for plates in a generalized plane stress state [1-3], or for axisymmetrically loaded shells in zero moment conditions [4-6]. Therefore, studies of transverse bending of thin plates reinforced along the the principal stress and strain directions are topical. We refer here to this problem as the "rational reinforcement" (RR) problem. It is known [7] that for many modern fiber-reinforced composites (carbon- and boron-aluminum, boron-magnesium, magnesium-steel etc.) the ultimate elastic strain of the reinforcement fibers several times (sometimes by an order of magnitude) exceeds that of the binder matrix. This means that for such composites the load-carrying capacity of the reinforcement elements (fibers) in elastic bending is not used appropriately (sometimes, by only several percent), which results in low net load-carrying capacity of the reinforced plate and inefficient usage of high-strength reinforcement material. The load-carrying capacity of RR-plates may be increased if inelastic deformation of the phase materials is allowed to occur, as well as "rational profiling" (RP) of the structure under bending loads is achieved. Studying the elastoplastic bending of profiled RR-plates is the subject mutter of the current research.
References
1.  G. I. Bryzgalin, "On the rational reinforcement of anisotropic plane bodies with weak binder," Izv. AN. MTT [Mechanics of Solids]old, No. 4, pp. 123-131, 1969.
2.  V. V. Vasili'ev and V. V. Martsinovskii, "Optimal design of composite materials in plane stressed state," in Design, Analysis, and Testing of Composite Structures [in Russian], No. 6, pp. 142-152, TsAGI, Moscow, 1978.
3.  A. A. G. Cooper and E. M. Wu, "Trajectorial reinforcement of composites," in Composite Materials in Engineering Design. Proc. 6th Symp., pp. 377-382, St. Louis, 1973.
4.  N. N. Kolerov, "Design and construction of composite pressure vessels," in Design, Analysis and Testing of Composite Structures [in Russian], No. 6, pp. 152-160, TsAGI, Moscow, 1978.
5.  V. V. Vasil'ev, "Optimal design of zero moment reinforced shells of revolution," In Studies in Elasticity and Plasticity [in Russian], LGU, Leningrad, pp. 7-13, 1980.
6.  V. A. Bunakov and A. L. Radovinskii, "On the determination of rational shape of zero moment shells of revolution manufactured by winding high-modulus materials," Mekhanika Polimerov, No. 5, pp. 822-828, 1975.
7.  Composite Materials. A Handbook [in Russian], Naukova Dumka, Kiev, 1985.
8.  N. N. Malinin, Applied Theory of Plasticity and Creep [in Russian], Mashinostroenie, Moscow, 1968.
9.  V. V. Sokolovskii, Theory of Plasticity [in Russian], Vyssh. Shkola, Moscow, 1969.
10.  Yu. V. Nemirovskii, "On the elastoplastic behavior of a reinforced layer," Zh. Prikl. Mekhaniki i Tekhn. Fiziki, No. 6, pp. 81-89, 1969.
11.  Yu. V. Nemirovskii, and A. P. Yankovskii, "On some features of equations of shells reinforced by constant cross-section fibers," Mekhanika Kompozit. Mater. Konstr., Vol. 3, No. 2, pp. 20-40, 1997.
12.  I. G. Petrovskii, Lectures on Partial Differential Equations [in Russian], Fizmatgiz, Moscow, 1961.
13.  T. D. Dzhuraev, Boundary-value Problems for Equations of Mixed and Mixed-Composite Type [in Russian], Fan, Tashkent, 1978.
14.  Yu. V. Nemirovskii and A. P. Yankovskii, "On some properties of solutions of the problem of transverse bending of a plate with equally-stressed reinforcement," Mekhanika Kompozit. Mater. Konstr., Vol. 2, No. 2, pp. 15-28, 1996.
15.  I. S. Berezin and N. P. Zhidkov, Computational Methods. Volume 2 [in Russian], Fizmatgiz, Moscow, 1959.
16.  Yu. V. Nemirovskii and A. P. Yankovskii, "Effects of the reinforcement structure and thermal loading on the load-carrying capacity of annular plates subjected to bending ," Izv. Vuzov. Stroitel'stvo, No. 12, pp. 4-12, 2002.
17.  Yu. V. Nemirovskii and A. P. Yankovskii, "Rational profiling of reinforced rotating disks," Mekhanika Komposit. Materialov, Vol. 38, No. 1, pp. 3-24, 2002.
Received 10 April 2003
<< Previous article | Volume 40, Issue 2 / 2005 | 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, Branch of Power Industry, Machine Building, Mechanics and Control Processes of RAS, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100