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Exact solution for an approximate differential equation of a straight bar under conditions of a non-linear equilibrium

Authors
Journal
International Journal of Non-Linear Mechanics
0020-7462
Publisher
Elsevier
Publication Date
Volume
21
Issue
5
Identifiers
DOI: 10.1016/0020-7462(86)90024-7
Disciplines
  • Mathematics

Abstract

Abstract In this paper a closed-form solution of the strongly non-linear differential equation of the form: y‴ + y′y″tany − Ay′ cosy = 2Ccos 2y ( A; C are positive constants) is presented under special physical conditions of the problem. This type of differential equation governs the equilibrium of a straight and prismatic bar subjected to a conservative system of arbitrary discrete and distributed co-planar loads in the most general case of response. Whereas all previous solutions are based on several convenient functional transformations, the procedure developed in the paper presents the advantage to yield a straightforward closed-form solution of this general and complicated problem. Special cases of two particular problems, concerning the mode of loading, have been solved. The one of them was selected conveniently from the already solved otherwise problems for reasons of comparison. The results are in complete agreement with the already existing solutions.

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