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Nonlinear static behavior of a cantilever subjected to an inclined follower force

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Abstract

The nonlinear static behavior of a linearly elastic cantilever subjected to a nonconservative force of the follower type is formulated and examined. The formulation allows for finite rotations with small strains (the elastica). Exact solutions are found. The investigation is greatly facilitated by means of a phase plane analysis in which the phase plane variables are related to slope angle and bending moment. Some of the interesting and unusual effects occurring in this system are discussed and illustrated with a set of deflection curves for a typical case.

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Abbreviations

x, y :

coordinates of a point on the deformed elastic axis

ψ :

slope angle

s :

arc length

L :

length of beam (assumed constant)

x L , y L , ψ L :

values of x, y, ψ at s=L

P :

applied force

γ :

constant angle between P and end tangent

α :

angle between P and the horizontal

EI :

beam stiffness (assumed constant)

u, θ :

dimensionless variables defined by (7) and (8)

c 2 :

load parameter defined by (10)

k, φ :

transformation parameters defined by (21)

F(Φ, k), E(Φ, k):

elliptic integrals of the first and second kind

Φ :

argument of elliptic integrals

Φ 0, Φ 1 :

values of Φ at u=0 and u=1

m, n :

positive integers

N :

mode number

References

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Authors and Affiliations

  1. Dept. of Theor. and Appl. Mechanics, Univ. of Illinois, 61801, Urbana, Ill., U.S.A.

    J. C. Wiley

  2. School of Aeron., Astron. and Engng. Sciences, Purdue University, 47907, Lafayette, Ind., U.S.A.

    J. Genin

Authors
  1. J. C. Wiley
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  2. J. Genin
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Wiley, J.C., Genin, J. Nonlinear static behavior of a cantilever subjected to an inclined follower force. Appl. Sci. Res. 23, 1–15 (1971). https://doi.org/10.1007/BF00413183

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  • DOI: https://doi.org/10.1007/BF00413183

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