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The Quarterly Journal of Mechanics and Applied Mathematics 1979 32(4):473-498; doi:10.1093/qjmam/32.4.473
© 1979 by Oxford University Press
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THE STRESS BOUNDARY-VALUE PROBLEM FOR FINITE PLANE DEFORMATIONS OF A FIBRE-REINFORCED MATERIAL

M. S. CRAIG and V. G. HART

( School of Mathematical Sciences, New South Wales Institute of Technology Sydney, N.S.W. 2007
Department of Mathematics, University of Queensland Brisbane 4067, Australia )

Basic equations for finite plane deformations of an idealised incompressible fibre-reinforced material are derived. The fibres are arranged in a single family, are assumed inextensible and are initially straight and parallel. The solution corresponding to the case of zero external forces is shown to exist uniquely, and, assuming small boundary forces, the solutions of linear equations derived from a perturbation scheme are shown to have the same property.

Some exact solutions of the basic equations are found, and a second-order perturbation solution is obtained for the problem of a disc with pressurized opposite quadrants. A singular strip crosses the disc in this case.


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