Finite Element Solutions for the Elastica

by William F. Schmidt,

Serial Information: Journal of the Engineering Mechanics Division, 1977, Vol. 103, Issue 6, Pg. 1171-1175

Document Type: Journal Paper


The finite deflection analysis of flexible bars subjected to vertical loads as well as the prediction of the buckling load and post-buckling response in the case of horizontal loading has attract the attention of numerous researchers. Publications related to large deflections of slender beams are referenced in and the monograph contains several applications as well as additional references to previous work. In the present note an efficient finite element procedure is developed for the problem of the elastica including variable loading and foundation stiffness. The effectiveness of the procedure is demonstrated by considering a number of example problems. Because of the generality of the finite element method extensions to more general problems than those presented here can easily be accomplished.

Subject Headings: Vertical loads | Horizontal loads | Finite element method | Elastic analysis | Displacement (mechanics) | Bars (structure) | Post buckling | Case studies

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