A method is presented for determining the two levels of instability that are associated with thin web materials traveling through process machinery. The first level of instability involves the out-of-plane buckling of expanses of web supported only by rollers at opposing ends. A method is developed using linear plate theory, which is verified by tests that show that this first level of instability can be predicted. The second level of instability involves the buckling of the web when it has taken the form of a cylindrical shell as it transits a roller. A nonlinear finite element method with strain dependent constitutive relations is developed and verified by tests to predict this second level of instability.

1.
Kuhn
,
P.
,
Peterson
,
J. P.
, and
Levin
,
L. R.
, 1952, “
A Summary of Diagonal Tension: Part 1 Methods of Analysis
,” NACA Technical Note No. 2661.
2.
Timoshenko
,
S. P.
, and
Gere
,
J. M.
, 1961,
Theory of Elastic Stability
, 2nd ed.,
McGraw-Hill
,
New York
, pp.
348
359
.
3.
Good
,
J. K.
, and
Beisel
,
J. A.
, 2007, “
Calculations Relating to Web Buckling Resulting From Roller Misalignment
,”
Tappi J.
0734-1415,
5
(
12
), pp.
9
16
.
4.
Timoshenko
,
S. P.
, and
Gere
,
J. M.
, 1961,
Theory of Elastic Stability
, 2nd ed.,
McGraw-Hill
,
New York
, pp.
457
460
and pp.
485
486
.
5.
Weingarten
,
V. I.
,
Morgan
,
E. J.
, and
Seide
,
P.
, 1965, “
Elastic Stability of Thin-Walled Cylindrical and Conical Shells under Combined Internal Pressure and Axial Compression
,”
AIAA J.
0001-1452,
3
(
6
), pp.
1118
1125
.
6.
Miller
,
R. K.
, and
Hedgepeth
,
J. M.
, 1982, “
An Algorithm for Finite Element Analysis of Partly Wrinkled Membranes
,”
AIAA J.
0001-1452,
20
(
12
), pp.
1761
1763
.
7.
Shelton
,
J. J.
, and
Reid
,
K. N.
, 1971, “
Lateral Dynamics of a Real Moving Web
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
93
(
3
), pp.
180
186
.
8.
Przemieniecki
,
J. S.
, 1968,
Theory of Matrix Structural Analysis
,
McGraw-Hill
,
New York
, pp.
70
80
and
388
391
.
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