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The Quarterly Journal of Mechanics and Applied Mathematics 1964 17(1):1-15; doi:10.1093/qjmam/17.1.1
© 1964 by Oxford University Press
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PLANE ELASTOSTATIC BOUNDARY VALUE PROBLEMS OF DOUBLY CONNECTED REGIONS I

V. T. BUCHWALD and G. A. O DAVIES

( (Department of Applied Mathematics, University of Sydney)
(Department of Aeronautical Engineering, University of Sydney) )

If one of the boundaries of a doubly connected region is a circle or can be mapped on to a circle, then, using the method of analytic continuation, a combination of potentials is obtained which satisfies conditions on the circular boundary exactly. The remaining complex potential is found either exactly, or approximately, by considering the conditions on the other boundary. The method is illustrated by solutions (i) to the first boundary value problem of the annulus, where an infinite series solution is obtained, and (ii) to the case of a circular hole under.uniform pressure inside an elliptic plate with stress-free edges.


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