A boundary element solution to the soap bubble problem

Katsikadelis, JT; Nerantzaki, MS

dc.contributor.author	Katsikadelis, JT	en
dc.contributor.author	Nerantzaki, MS	en
dc.date.accessioned	2014-03-01T01:15:58Z
dc.date.available	2014-03-01T01:15:58Z
dc.date.issued	2001	en
dc.identifier.issn	0178-7675	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/13862
dc.subject	Boundary Element	en
dc.subject	Boundary Element Method	en
dc.subject	Computational Method	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.classification	Mechanics	en
dc.subject.other	Boundary value problems	en
dc.subject.other	Computational methods	en
dc.subject.other	Differential equations	en
dc.subject.other	Integral equations	en
dc.subject.other	Laplace transforms	en
dc.subject.other	Problem solving	en
dc.subject.other	Analogue equation method	en
dc.subject.other	Engineering analysis	en
dc.subject.other	Molecular forces	en
dc.subject.other	Soap bubble problem	en
dc.subject.other	Boundary element method	en
dc.title	A boundary element solution to the soap bubble problem	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s004660000224	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s004660000224	en
heal.language	English	en
heal.publicationDate	2001	en
heal.abstract	The boundary element method (BEM) is applied to the soap bubble problem, that is to the problem of determining the surface that a soap bubble constrained by bounding contours assumes under the action of molecular forces. This is also the shape of a uniformly stretched membrane bounded by one or more non-intersecting curves. As the slopes of the membrane surface are finite, their square can not be neglected and the resulting governing equation is non-linear. The problem is solved using the analogue equation method (AEM). According to this method the non-linear membrane is substituted by a linear one subjected to a fictitious transverse load. The fictitious load is established using the BEM. Numerical examples are presented which illustrate the method and demonstrate its accuracy. This application of the BEM to non-linear problems shows that BEM is a versatile computational method for all-purpose use in engineering analysis. The solution of the problem at hand is very important in engineering, since the soap bubble surface can be used as the best initial form for membrane roofs.	en
heal.publisher	SPRINGER-VERLAG	en
heal.journalName	Computational Mechanics	en
dc.identifier.doi	10.1007/s004660000224	en
dc.identifier.isi	ISI:000167535200007	en
dc.identifier.volume	27	en
dc.identifier.issue	2	en
dc.identifier.spage	154	en
dc.identifier.epage	159	en