Plane problems in second-order elasticity theory

Abstract
The approximate two-dimensional theory of finite elastic deformations developed by Adkins, Green & Nicholas (1954), is applied to problems involving infinite bodies bounded internally by simple closed contours. Expressions for the force and couple resultants on a single internal boundary are derived; the nature of the solution for a uniform distribution of stress and strain at infinity is also examined. The equations governing the deformation are expressed in a form which enables corresponding first and second boundary-value problems to be solved simultaneously. The theory is formulated in complex variable notation, and this permits solutions to be obtained by making use of the Hilbert problem along the lines developed by Muskhelishvili (1953) and others for problems in classical elasticity. The procedure is illustrated by an examination of problems involving uniform distributions of stress and displacement along a single internal circular boundary and at infinity.

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