  Mechanics of Solids A Journal of Russian Academy of Sciences   Founded
in January 1966
Issued 6 times a year
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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), 133148 (2005) 
Year 
2005 
Volume 
40 
Number 
2 
Pages 
133148 
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.
Fiberreinforced 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 thinwalled structures along the principal
stress directions was studied for loadings in zero moment conditions only:
either for plates in a generalized plane stress state [13], or for
axisymmetrically loaded shells in zero moment conditions [46]. 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 fiberreinforced composites (carbon and
boronaluminum, boronmagnesium, magnesiumsteel 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 loadcarrying capacity of the reinforcement elements
(fibers) in elastic bending is not used appropriately (sometimes, by only
several percent), which results in low net loadcarrying capacity of the
reinforced plate and inefficient usage of highstrength reinforcement
material. The loadcarrying capacity of RRplates 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 RRplates is the
subject mutter of the current research. 
References 
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equallystressed reinforcement," Mekhanika Kompozit. Mater. Konstr.,
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reinforcement structure and thermal loading on the loadcarrying capacity
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17.  Yu. V. Nemirovskii and A. P. Yankovskii, "Rational profiling of reinforced
rotating disks," Mekhanika Komposit. Materialov, Vol. 38, No. 1,
pp. 324, 2002. 

Received 
10 April 2003 
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