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We study asymptotic expansions for the displacement field of a long elastic cyfinder under various constitutive assumptions. We show that under simple hypotheses it is possible to derive from the equations of continuum mechanics two known beam equations and several different string models. Some of the string models correspond to those studied by S. Antman and R. Dickey. We also show that under our assumptions the problem of asymptotic expansion can be reduced to that of algebraic geometry.

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