SCIENTIFIC ABSTRACT SOKOLOVSKIY, V.V. - SOKOLOWSKA, M.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001652120020-2
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: August 25, 2000
• Sequence Number: 20
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

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D214/'D30'1
AUTHOR: Sokolovskiy, V.V. (Moscow)
TITLE: Axial pla'Wtic flow between non-circular cylinders
PERIODICAL: Archiwum. mechaniki stoswanej, v. 12, no. 2, 1960,
173 - 183
TEXTz In this paper a method is given for reducing the solution of
different problems with a non-linear law to that of the same Prob-
Ism with a linear law. A flow is considered between rough cylindeis
with the outer cylinder stationary, and the inner one with a velo-
citiy 71 in the negative direction of the z-axis. The velocity com-
ponents -u = v = 0, the strain rate components and the stress com-
ponents are:
"~z~yxy~o or =- Cr =0.
y z 0 xy
The velocity component w, as well as the strain rate components
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kxial plastic flow D214/D301
zx~'(x 1y YZ~=yyand the stress componentsTzx ~ Tx9 TYZTyare independ
of z; thus, they are functions of x and y only. The strain rate
components Ix and are expressed by the velocity component w as
follows
2yx = aw? 27Y = (9w (1.1)
OIX- ~-Yo
The basic relations between the strain rate components and the
stress components have the usual form. The strain rate components
YX and yy can be expressed by the function as follows:
2kyx ML _;a -CP
x1p 2kyY - yq9 cp= k(w + W) (1-5)
while the stress $omponents T X and TY - by the function Y as
RV1 8*
?F T - - ax" (1.6)
x Oy Y
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where k is a mechanical constant to be introduced below. The basic
relations together with-Eq. (1-5) and Eq. (1.6) yield the follow-
ing system of equations
alp alp
2 k 1-Ty a- - ~ -ry, Txt (1-7)
dy 'r X FY
This system takes the simplest form when y and T are connected-by
linear relation
T = 2 ky (1-9)
which contains one mechanical constant k. The system of Eq. (1-7)
can be reduced to a rather convenient form when y and T are connec-
ted by non-linear relation
2_ k-y (1.10)
Vl + (2 my
which contains two mechanical constants k, and m. The equations are
then transformed by means of
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Axial plastic flow ... D214/D301
Irx = T Cos 8, T si-n 8.
and a ne%v quantity t by
t2 2-' t 2 2
1 - m t 1 + M u
into %
COS 0, Ly le 2
7 = - _ sin 0,
t t
dx I +,rn2 t2 sin 0, dy + M2 t2 Cos 0, (2-5)
j-'P ~ -t ~dv -t
and the determinant of the transformation A is
,4==Lxqy -dXaY I -wee. (2.6)
dip alp TV j1p -if
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Axial plastic flow ... D2!4/D-';Ol
Since the complex quantities subsequently introduced T/ w are con-
jugate and the quantity mt is real and varies within the range
0,