Constrained Buckling of Spatial Elastica: Application of Optimal Control Method

[+] Author and Article Information
Anna Liakou

Department of Civil, Environmental, and Geo- Engineering, University of Minnesota

1Corresponding author.

ASME doi:10.1115/1.4040118 History: Received March 09, 2018; Revised April 25, 2018


Abstract An optimal control method is adopted to analyze the buckling response of a constant or variable length spatial elastica constrained by a cylindrical wall. We first present the optimal control formulation for the constrained buckling problem of a constant length spatial elastica, including its associated necessary optimality conditions that constitute the Pontryagin's minimum principle. This fundamental constrained buckling problem is used to validate the proposed methodology. The general buckling problem of a variable length spatial elastica is then analyzed that consists of two parts; (1) the solution of the optimal control problem that involves the inserted elastica inside the conduit and (2) the derivation of the buckling load by taking into account the generation of the configurational or Eshelby-like force at the insertion point of the sliding sleeve. A variety of examples are accordingly presented, where the effects of factors, such as the presence of uniform pressure, the clearance of the wall, and the torsional rigidity, on the buckling response of the spatial elastica are investigated.

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