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DIRECT EXPRESSION OF INCOMPATIBILITY IN CURVILINEAR SYSTEMS

Part of: Elliptic equations and systems Classical differential geometry Generalities, axiomatics, foundations of continuum mechanics of solids Elastic materials

Published online by Cambridge University Press:  08 July 2016

NICOLAS VAN GOETHEM Open the ORCID record for NICOLAS VAN GOETHEM [Opens in a new window]
NICOLAS VAN GOETHEM*
Affiliation:
Universidade de Lisboa, Faculdade de Ciências, Departamento de Matemática, CMAF+CIO, Alameda da Universidade, C6, 1749-016 Lisboa, Portugal email [email protected]
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Abstract

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We would like to present a method to compute the incompatibility operator in any system of curvilinear coordinates (components). The procedure is independent of the metric in the sense that the expression can be obtained by means of the basis vectors only, which are first defined as normal or tangential to the domain boundary, and then extended to the whole domain. It is an intrinsic method, to some extent, since the chosen curvilinear system depends solely on the geometry of the domain boundary. As an application, the in-extenso expression of incompatibility in a spherical system is given.

Keywords

incompatibilitydislocationselasticitydifferential geometrycurvilinear basisspherical system

MSC classification

Primary: 35J48: Higher-order elliptic systems
Secondary: 35J58: Boundary value problems for higher-order elliptic systems 53A05: Surfaces in Euclidean space 74A45: Theories of fracture and damage 74B99: None of the above, but in this section
Type
Research Article
Information
The ANZIAM Journal , Volume 58 , Issue 1 , July 2016 , pp. 33 - 50
Copyright
© 2016 Australian Mathematical Society 

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