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IssuesArchive of Issues2005-2pp.133-148

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Total articles in the database: 9179
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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.
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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.
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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.
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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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