Asymptotic formulae for the flexibility of an infinite row of pin-loaded holes

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Abstract

The problem of the flexibility of an infinite row of pin-loaded holes in an elastic plane or half-plane is considered within the framework of the complex potential method [1] and the theory of compound asymptotic expansions [2]. The holes are loaded by a given distribution of normal stresses with a resultant equal to the overall transmitted force. First, the relative radius of the holes is introduced as a small parameter. Then, an asymptotic expansion of the complex potentials in terms of this small parameter is constructed. This expansion is uniformly valid in the whole domain, i.e. in the vicinity of the holes as well as in the far-field. Finally, the flexibility of the row of pin-loaded holes is evaluated using this solution. In this manner, closed-form analytical approximations of the flexibility of an infinite row of pin-loaded holes in a full plane and a half-plane are obtained. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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