Title

On finite element analysis of an inverse problem in elasticity

Authors

Authors

D. W. Nicholson

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

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

Share

COinS