Abstract
In this paper the first three terms of the uniform asymptotic solution for some two-dimensional elasticity problems for the domain exterior to a thin region $\mathcal{D}$ are given. The small parameter $\varepsilon $ is the thinness ratio of $\mathcal{D}$. The perturbation of the external field by the presence of the thin region is represented as a superposition of elastic potentials due to concentrated forces and moments on a line inside the thin region. The boundary conditions lead to a system of linear integral equations which are solved by using the asymptotic method of Handelsman and Kelley [J. Fluid Mech., 28 (1967), pp. 131–142]. The formulae given in the Appendix, allow the explicit writing of the solution in the case of the polynomial boundary data.
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