Wrinkling in finite plane-stress theory
Authors:
Chien H. Wu and Thomas R. Canfield
Journal:
Quart. Appl. Math. 39 (1981), 179-199
MSC:
Primary 73B99
DOI:
https://doi.org/10.1090/qam/625468
MathSciNet review:
625468
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Abstract: A general and complete formulation is given for the wrinkling phenomenon in the context of finite plane-stress theory. The planar portion of the true three-dimensional displacement field, called the pseudo-displacement field, is used as a basis for the necessary kinematic analysis. It is assumed that the principal directions associated with the pseudo-deformation field are the same as those associated with the true stress field. The true stress field is governed by equilibrium and the assumption that one of the principal stresses vanishes, and hence is statically determinate. The difference between the pseudo-strain and the true strain calculated from the true stress is a new tensor, called the wrinkle-strain tensor, and serves as a measure of the wrinkliness of the surface.
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H. Wagner, Flat sheet metal girders with a very thin metal web, Z. Flugtechnik u. Motorluftschiffahrt 20, 200–314 (1929)
E. Reissner, On tension field theory, in Proc. 5th Int. Congr. Appl. Mech., 88–92 (1938)
M. Stein, and J. M. Hedgepeth, Analysis of partly wrinkled membranes, NASA TN-D-813 1961
E. H. Mansfield, Tension field theory, in Proc. 12th Int. Congr. Appl. Mech., 305–320 (1969)
E. H. Mansfield, Load transfer via a wrinkled membrane, Proc. Roy. Soc. Lond. (A) 316, 269–289 (1970)
G. P. Cherepanov, On the buckling under tension of a membrane containing holes, PMM 27, 275–286 (1963)
C. H. Wu, Plane linear wrinkle elasticity without body force, Report, Dept. Mat. Engrg, University of Ill. at Chicago Circle, 1974
E. H. Mansfield, Analysis of wrinkled membranes with anisotropic and nonlinear elastic properties, Proc. Roy. Soc. Lond. (A) 353, 475–498 (1977)
C. H. Wu, The wrinkled axisymmetric air bags made of inextensible membrane, J. Appl. Mech. 41, 963–968 (1974)
C. H. Wu, Nonlinear wrinkling of nonlinear membranes of revolution, J. Appl. Mech. 45, 533–538 (1978)
J. A. Schouten, Tensor analysis for physicists, Oxford, Clarendon Press, 1953
W. Jaunzemis, Continuum mechanics, Macmillan, New York, 1967
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© Copyright 1981
American Mathematical Society
