Postbuckling Behavior of Variable-Arc-Length Elastica Linked with Elastic-Plastic Rotational Spring Joint within the Span-Length of the Elastica
Keywords:
Elastica, Postbuckling, Shooting Method, Elastic-Plastic, Rotational Spring JointAbstract
This paper reports the investigation on postbuckling behavior of a variable-arc-length elastica connected with a rotational spring joint where three types of the spring joint (i.e., linear elastic, bilinear elastic, and elastic-plastic) were considered. One end of the elastica was attached on the hinged joint while the remote end was placed on the horizontal slider support. The rotational spring joint was located at a given distance apart from the hinged joint. Compression force was exerted at the horizontal slider support to push the arc-length into the system; the postbuckling behavior was then observed. A set of governing differential equations were obtained from the equilibrium equations, moment-curvature relation and geometric relations. Since this problem is a two-point boundary value problem, the shooting method was employed in this study. Numerical integration (i.e., Runge-Kutta method) was performed so that the boundary conditions were satisfied. It was found that the elastica became unstable after buckling and, after yielding of the spring joint, the compression might drop suddenly, depending on the ratio of the stiffness, r = 2 /
1. The elastica could turn into stable equilibrium for an interval of total arc-length. Moreover, reverse rotation of the spring joint could occur, representing another interesting aspect of the problem.
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