On finite element analysis of an inverse problem in elasticity

Autor:	D. W. Nicholson
Rok vydání:	2012
Předmět:	Mathematical optimization Finite element limit analysis Applied Mathematics Linear elasticity General Engineering hp-FEM Mixed finite element method Inverse problem Finite element method Computer Science Applications Matrix (mathematics) Applied mathematics Mathematics Extended finite element method
Zdroj:	Inverse Problems in Science and Engineering. 20:735-748
ISSN:	1741-5985 1741-5977
Popis:	This investigation concerns an inverse problem modelled by the finite element method. For a given mesh and set of physical properties, even though a well-posed direct problem possesses a unique solution in classical linear elasticity, variational arguments establish that a corresponding inverse problem may not. Furthermore, even when the inverse problem admits a unique solution when modelled ‘exactly’ using the classical linear theory of elasticity, an unfortunate mesh choice may cause the finite element model of the inverse problem to fail to do so. The current investigation introduces a simple matrix nonsingularity criterion assuring that the finite element model possesses a unique solution. An apparently new and readily computed numerical test is introduced to verify satisfaction of the criterion. Examples are given illustrating the effectiveness of the criterion and its application to mesh design.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::27528220444aa79ca2d989d59f2e66e2 https://doi.org/10.1080/17415977.2012.668677 Zobrazit plný text záznamu Plný text ve formátu PDF Plný text ve formátu HTML
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