Post-buckling analysis of viscoelastic plates with fractional derivative models

Katsikadelis, JT; Babouskos, NG

dc.contributor.author	Katsikadelis, JT	en
dc.contributor.author	Babouskos, NG	en
dc.date.accessioned	2014-03-01T01:34:19Z
dc.date.available	2014-03-01T01:34:19Z
dc.date.issued	2010	en
dc.identifier.issn	0955-7997	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20695
dc.subject	Analog equation method	en
dc.subject	Boundary element method	en
dc.subject	Buckling	en
dc.subject	Fractional derivatives	en
dc.subject	Large deflections	en
dc.subject	Plates	en
dc.subject	Viscoelasticity	en
dc.subject.classification	Engineering, Multidisciplinary	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.other	Analog equation methods	en
dc.subject.other	Boundary elements	en
dc.subject.other	Fractional derivatives	en
dc.subject.other	Large deflection	en
dc.subject.other	Plates	en
dc.subject.other	Beams and girders	en
dc.subject.other	Boundary element method	en
dc.subject.other	Buckling	en
dc.subject.other	Control nonlinearities	en
dc.subject.other	Differentiation (calculus)	en
dc.subject.other	Elasticity	en
dc.subject.other	Initial value problems	en
dc.subject.other	Ordinary differential equations	en
dc.subject.other	Plates (structural components)	en
dc.subject.other	Poisson equation	en
dc.subject.other	Viscoelasticity	en
dc.subject.other	Viscosity	en
dc.subject.other	Nonlinear equations	en
dc.title	Post-buckling analysis of viscoelastic plates with fractional derivative models	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.enganabound.2010.07.003	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.enganabound.2010.07.003	en
heal.language	English	en
heal.publicationDate	2010	en
heal.abstract	The post-buckling response of thin plates made of linear viscoelastic materials is investigated. The employed viscoelastic material is described with fractional order time derivatives. The governing equations, which are derived by considering the equilibrium of the plate element, are three coupled nonlinear fractional partial evolution type differential equations in terms of three displacements. The nonlinearity is due to nonlinear kinematic relations based on the von Karman assumption. The solution is achieved using the analog equation method (AEM), which transforms the original equations into three uncoupled linear equations, namely a linear plate (biharmonic) equation for the transverse deflection and two linear membrane (Poisson's) equations for the inplane deformation under fictitious loads. The resulting initial value problem for the fictitious sources is a system of nonlinear fractional ordinary differential equations, which is solved using the numerical method developed recently by Katsikadelis for multi-term nonlinear fractional differential equations. The numerical examples not only demonstrate the efficiency and validate the accuracy of the solution procedure, but also give a better insight into this complicated but very interesting engineering plate problem (C) 2010 Elsevier Ltd. All rights reserved.	en
heal.publisher	ELSEVIER SCI LTD	en
heal.journalName	Engineering Analysis with Boundary Elements	en
dc.identifier.doi	10.1016/j.enganabound.2010.07.003	en
dc.identifier.isi	ISI:000282112900005	en
dc.identifier.volume	34	en
dc.identifier.issue	12	en
dc.identifier.spage	1038	en
dc.identifier.epage	1048	en