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

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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
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

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