Direct expression of incompatibility in curvilinear systems

Nicolas Van Goethem

Abstract


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.


doi:10.1017/S1446181116000158

Keywords


incompatibility; dislocations; elasticity; differential geometry; curvilinear basis; spherical system



DOI: http://dx.doi.org/10.21914/anziamj.v58i0.10213



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.