 | | 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
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| In English (Mech. Solids): | | 3212 |
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| 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 |
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