The 2D elastostatic problem in inhomogeneous anisotropic bodies by the meshless analog equation method (MAEM)

Katsikadelis, JT

dc.contributor.author	Katsikadelis, JT	en
dc.date.accessioned	2014-03-01T01:29:18Z
dc.date.available	2014-03-01T01:29:18Z
dc.date.issued	2008	en
dc.identifier.issn	0955-7997	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19211
dc.subject	Meshless method	en
dc.subject	Analog equation method	en
dc.subject	Partial differential equations	en
dc.subject	Inhomogeneous anisotropic elasticity	en
dc.subject	Radial basis functions	en
dc.subject	Optimal multiquadrics	en
dc.subject.classification	Engineering, Multidisciplinary	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.title	The 2D elastostatic problem in inhomogeneous anisotropic bodies by the meshless analog equation method (MAEM)	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.enganabound.2007.10.016	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.enganabound.2007.10.016	en
heal.language	English	en
heal.publicationDate	2008	en
heal.abstract	The meshless analog equation method (MAEM) is employed to solve the 2D elastostatic problem for inhomogenous anisotropic bodies. In this case, the response of the body is governed by two coupled PDEs of second order with variable (position-dependent) coefficients, which are solved using the new meshless method developed by Katsikadelis for solving PDEs. The method is based on the concept of the analog equation of Katsikadelis, hence its name (MAEM), which converts the original coupled PDEs into two uncoupled Poisson's equations, the analog equations, under fictitious sources. The fictitious sources are represented by MQ-RBFs. Integration of the analog equations allows the approximation of the sought solution by new RBFs. Then inserting the solution into the PDEs and BCs and collocating at the mesh-free nodal points yields a system of linear equations, which permit the evaluation of the expansion coefficients. The method exhibits key advantages over other RBF collocation methods as it is highly accurate and the matrix of the resulting, linear equations is always invertible. The accuracy is increased Using optimal values of the shape parameters of the multiquadries and of the integration constants of the analog equation by minimizing the total potential of the elastic body. Several examples are studied. which demonstrate the efficiency and high accuracy of the solution method.	en
heal.publisher	ELSEVIER SCI LTD	en
heal.journalName	ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS	en
dc.identifier.doi	10.1016/j.enganabound.2007.10.016	en
dc.identifier.isi	ISI:000261297300002	en
dc.identifier.volume	32	en
dc.identifier.issue	12	en
dc.identifier.spage	997	en
dc.identifier.epage	1005	en