Double Curvature Bending of Variable-Arc-Length Elasticas

[+] Author and Article Information
S. Chucheepsakul, T. Monprapussorn

Department of Civil Engineering, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand

C. M. Wang

Department of Civil Engineering, The National University of Singapore, Kent Ridge 119260, Singapore

X. Q. He

Department of Mechanical and Production Engineering, The National University of Singapore, Kent Ridge 119260, Singapore

J. Appl. Mech 66(1), 87-94 (Mar 01, 1999) (8 pages) doi:10.1115/1.2789173 History: Received February 11, 1998; Revised September 25, 1998; Online October 25, 2007


This paper deals with the double curvature bending of variable arc-length elasticas under two applied moments at fixed support locations. One end of the elastica is held while the other end portion of the elastica may slide freely on a frictionless support at a prescribed distance from the held end. Thus, the variable deformed length of the elastica between the end support and the frictionless support depends on the relative magnitude of the applied moments. To solve this difficult and highly nonlinear problem, two approaches have been used. In the first approach, the elliptic integrals are formulated based on the governing nonlinear equation of the problem. The pertinent equations obtained from applying the boundary conditions are then solved iteratively for solution. In the second approach, the shooting-optimization method is employed in which the set of governing differential equations is numerically integrated using the Runge-Kutta algorithm and the error norm of the terminal boundary conditions is minimized using a direct optimization technique. Both methods furnish almost the same stable and unstable equilibrium solutions. An interesting feature of this kind of bending problem is that the elastica can form a single loop or snap-back bending for some cases of the unstable equilibrium configuration.

Copyright © 1999 by The American Society of Mechanical Engineers
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