Additional separated-variable solutions of the biharmonic equation in polar coordinates

Stampouloglou, IH; Theotokoglou, EE

dc.contributor.author	Stampouloglou, IH	en
dc.contributor.author	Theotokoglou, EE	en
dc.date.accessioned	2014-03-01T01:32:36Z
dc.date.available	2014-03-01T01:32:36Z
dc.date.issued	2010	en
dc.identifier.issn	0021-8936	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20188
dc.subject	differential equations	en
dc.subject	elastic constants	en
dc.subject	stress analysis	en
dc.subject.classification	Mechanics	en
dc.subject.other	Biharmonic equations	en
dc.subject.other	Direct determination	en
dc.subject.other	Displacement field	en
dc.subject.other	Elastic solids	en
dc.subject.other	Fourth order	en
dc.subject.other	Plane problem	en
dc.subject.other	Polar coordinate	en
dc.subject.other	Polar coordinate systems	en
dc.subject.other	Radial coordinates	en
dc.subject.other	Ordinary differential equations	en
dc.title	Additional separated-variable solutions of the biharmonic equation in polar coordinates	en
heal.type	journalArticle	en
heal.identifier.primary	10.1115/1.3197157	en
heal.identifier.secondary	http://dx.doi.org/10.1115/1.3197157	en
heal.identifier.secondary	021003	en
heal.language	English	en
heal.publicationDate	2010	en
heal.abstract	From the biharmonic equation of the plane problem in the polar coordinate system and taking into account the variable-separable form of the partial solutions, a homogeneous ordinary differential equation (ODE) of the fourth order is deduced. Our study is based on the investigation of the behavior of the coefficients of the above fourth order ODE, which are functions of the radial coordinate r. According to the proposed investigation additional terms, Phi(-m)(r,theta) (1 < m < n) other than the usually tabulated in the Michell solution (1899, "On the Direct Determination of Stress in an Elastic Solid, With Application to the Theory of Plates," Proc. Lond. Math. Soc., 31, pp. 100-124) are found. Finally the stress and the displacement fields due to each one additional term of Phi-(m)(r,theta) are determined.	en
heal.publisher	ASME-AMER SOC MECHANICAL ENG	en
heal.journalName	Journal of Applied Mechanics, Transactions ASME	en
dc.identifier.doi	10.1115/1.3197157	en
dc.identifier.isi	ISI:000273036700003	en
dc.identifier.volume	77	en
dc.identifier.issue	2	en
dc.identifier.spage	1	en
dc.identifier.epage	8	en