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Existence of solutions of plane traction problems for inextensible transversely isotropic elastic solids

Published online by Cambridge University Press:  17 February 2009

L. W. Morland
L. W. Morland
Affiliation:
Department of Mathematics, University of Queensland, Australia.
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Abstract

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A plane strain or plane stress configuration of an inextensible transversely isotropic linear elastic solid with the axis of symmetry in the plane, leads to a harmonic lateral displacement field in stretched coordinates. Various displacement and mixed displacement-traction boundary conditions yield standard boundary-value problems of potential theory for which uniqueness and existence of solutions are well established. However, the important case of prescribed tractions at each boundary point gives a non-standard potential problem involving linking of boundary values at opposite ends of chords parallel to the axis of material symmetry. Uniqueness and existence of solutions, within arbitrary rigid motions, are now established for the traction problem for general domains.

Type
Research Article
Information
The ANZIAM Journal , Volume 19 , Issue 1 , June 1975 , pp. 40 - 54
Copyright
Copyright © Australian Mathematical Society 1975

References

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