Elastica of a variable-arc-length circular curved beam subjected to an end follower force
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Publication Details
Author list: Pulngern T., Sudsanguan T., Athisakul C., Chucheepsakul S.
Publisher: Elsevier
Publication year: 2013
Journal: International Journal of Non-Linear Mechanics (0020-7462)
Volume number: 49
Start page: 129
End page: 136
Number of pages: 8
ISSN: 0020-7462
Languages: English-Great Britain (EN-GB)
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Abstract
This paper presents postbuckling behaviors of a variable-arc-length (VAL) circular curved beam subjected to an end follower force. One end of the VAL circular curved beam is hinged while the other end is supported by a frictionless slot, which is fixed horizontally and vertically but is allowed to rotate corresponding to loading direction. When the VAL circular curved beam is deformed, the total arc-length of the circular curved beam varies. Two approaches have been applied for the solution of this problem. The first approach is an elliptic integrals method based on elastica theory, which yields the exact closed-form solution in terms of the first and second kinds of elliptic integrals. For validation of the results, the shooting method is employed for a numerical solution by developing the set of nonlinear governing differential equations together with boundary conditions, and then integrating them by using the fourth-order Runge-Kutta algorithm. The results from both approaches are in very good agreement. From the results, it is found that the VAL circular curved beam subjected to an end follower force can be deformed in many mode shapes. For the first and third modes, the beam exhibits both stable and unstable configurations, whereas for the second mode only an unstable configuration exists. The influences of initial curvature on the critical load and the deformed configurations are highlighted. ฉ 2012 Elsevier Ltd.
Keywords
Circular curved beam, Elastica, Elliptic integral, Follower force, Postbuckling, Variable-arc-length
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