On finite element analysis of an inverse problem in elasticity

    Authors

    D. W. Nicholson

    Comments

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    Abbreviated Journal Title

    Inverse Probl. Sci. Eng.

    Keywords

    finite element modelling; inverse modelling; matrix nonsingularity; condition; mesh modification; Engineering, Multidisciplinary; Mathematics, Interdisciplinary; Applications

    Abstract

    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.

    Journal Title

    Inverse Problems in Science and Engineering

    Volume

    20

    Issue/Number

    5

    Publication Date

    1-1-2012

    Document Type

    Article; Proceedings Paper

    Language

    English

    First Page

    735

    Last Page

    748

    WOS Identifier

    WOS:000306833100011

    ISSN

    1741-5977

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