The Problem of Minimizing Stress Concentration at a Rigid Inclusion

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Abstract
With the objective of minimizing stress concentration, the plane-strain problem of the optimum shape for a rigid inclusion in an elastic matrix of unbounded extent is investigated. It is shown rigorously that the underlying variational problem is reducible to a more elementary problem which can be solved by conventional methods to arrive at the optimum shape, which is a suitably proportioned ellipse.

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