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

Panayotounakos, DE; Theocaris, PS

dc.contributor.author	Panayotounakos, DE	en
dc.contributor.author	Theocaris, PS	en
dc.date.accessioned	2014-03-01T01:06:36Z
dc.date.available	2014-03-01T01:06:36Z
dc.date.issued	1986	en
dc.identifier.issn	0020-7462	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/9491
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-0022907257&partnerID=40&md5=d5b30c02b7e96e93a99b734003c88f0c	en
dc.subject.classification	Mechanics	en
dc.subject.other	MATHEMATICAL TECHNIQUES - Differential Equations	en
dc.subject.other	APPROXIMATE DIFFERENTIAL EQUATION	en
dc.subject.other	NON-LINEAR EQUILIBRIUM	en
dc.subject.other	STRAIGHT BAR	en
dc.subject.other	BEAMS AND GIRDERS	en
dc.title	Exact solution for an approximate differential equation of a straight bar under conditions of a non-linear equilibrium	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	1986	en
heal.abstract	In this paper a closed-form solution of the strongly non-linear differential equation of the form: y‴ + y′y″tany - Ay′ cosy = 2Ccos2y (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. © 1986.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	International Journal of Non-Linear Mechanics	en
dc.identifier.isi	ISI:A1986F169200007	en
dc.identifier.volume	21	en
dc.identifier.issue	5	en
dc.identifier.spage	421	en
dc.identifier.epage	429	en