# 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

Corner Point Specific Weight Horizontal Force Tension Line Tension Strip
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## 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

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

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