Wrinkling in Thin Plates due to In-plane Body Forces

  • F. P. J. Rimrott
  • Michal Cvercko
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)

Summary

In-plane body forces, i.e. the weight, of a vertically mounted blanket, i.e. a plate of near-zero flexural stiffness and near-zero compressive strength, lead to the formation of curved wrinkles. Wrinkle lines bordering each finite size tension strip, and tension lines within each tension strip, assume shapes that are governed by the differential equation
$$\frac{{d^2 y}}{{dx^2 }}\,\, \pm \,\,\frac{q}{H}\,\, = \,\,0$$
where q is the reduced distributed weight force, and H a horizontal pretension force parameter.

The case of a blanket with sinusoidal boundaries, supported at two corner points is discussed in detail.

Keywords

Stein 

Nomenclature

B

Bending energy stored in wrinkles, J

F

Horizontal component of tension strip tension force, N

H

Horizontal force component parameter, N

P

Potential energy change, J

Q

\(\frac{{a_{i - 1} }}{{a_i }} = \frac{{m_{i - 1} }}{{m_i }}\)

T

Tension strip tension force, N

U

Work done by horizontal force, J

V

Vertical component of tension strip tension force, N

W

Weight force of blanket, N

a

Amplitude of cosine curve, m

e

Horizontal displacement, m

h

Height of blanket, m

l

Distance between supports, m

q

Reduced distributed load, N/M

α

Slope angle, rad

γ

Specific weight of blanket (× blanket thickness), N/m2

σ

Stress (× blanket thickness), N/m

τ

Shear stress(× blanket thickness), N/m

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References

  1. Wagner, Herbert “Ebene Blechwandtrager mit sehr dunnem Stegblech” Zeitschrift für Flugtechnik and Motorluftschiffahrt, 20, (1929), 8, 200–207; 9, 227–233, 10, 256–262; 1 1, 279–284; 12, 306–314.Google Scholar
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  4. Mansfield, E.H. “Tension Field Theory” Applied Mechanics (M. Hetenyi and W.G. Vincenti, editors) Springer-Verlag, Heidelberg, (1969), 305–320.Google Scholar
  5. Mansfield, E.H. “Gravity-induced Wrinkle Lines in Vertical Membranes” Proceedings of the Royal Society, London, A 375, (1981), 307–325.Google Scholar
  6. Kingsland, Blair “In-plane Loading of Blankets” M.A.Sc. Thesis, University of Toronto, (1983), 1–130.Google Scholar
  7. Rimrott, F.P.J. Blair Kingsland “Tension Line Fields in a Simply Supported Blanket Subjected to In-plane Body Forces” Journal of Spacecraft and Rockets, 22, 2, (1985), 141–148CrossRefGoogle Scholar

Copyright information

© Springer, Berlin Heidelberg 1986

Authors and Affiliations

  • F. P. J. Rimrott
    • 1
  • Michal Cvercko
    • 1
  1. 1.University of TorontoTorontoCanada

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