Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-25T06:30:23.251Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Morland, L. W., A plane theory of inextensible transversely isotropic elastic composites. Int. J. Solids Structures, 9 (1973), 1501–1518.CrossRefGoogle Scholar
[2]England, A. H., Ferrier, J. E., and Thomas, J. N., Plane strain and generalised plane stress problems for fibre-reinforced materials. J. Mech. Phys. Solids, 21 (1973), 279–301.CrossRefGoogle Scholar
[3]Everstine, G. C. and Pipkin, A. C., Stress channelling in transversely isotropic elastic composites. Z. Angew. Math. Phys., 22 (1971), 825–834.CrossRefGoogle Scholar
[4]Everstine, G. C. and Pipkin, A. C., Boundary layers in fibre-reinforced materials. J. Appl. Mech., 40 (1973), 518–522.CrossRefGoogle Scholar
[5]Spencer, A. J. M., Boundary layers in highly anisotropic plane elasticity. Int. J. Solids Structures, 10 (1974), 1103–1123.CrossRefGoogle Scholar
[6]Pipkin, A. C. and Sanchez, V. M., Existence of solutions of plane traction problems for ideal composites. SIAM J. Appl. Math., 26 (1974), 213–220.CrossRefGoogle Scholar
[7]Sternberg, W. J. and Smith, T. L., The Theory of Potential and Spherical Harmonics. University of Toronto Press 1944.CrossRefGoogle Scholar
[8]Tricomi, F. G., Integral Equations. Interscience Publishers, New York, 1957.Google Scholar