Abstract
Continuing the analysis in [1,2] of the problem of the theory of elasticity in regions of small diameter, methods derived from the asymptotic theory for calculating the stiffnesses of cylindrical beams are considered, and the results are compared with those of classical theory [3, 4]. The technique of two-scale expansions [5–8], as formulated in [1], is employed (in this case the averaging methods for homogeneous problems are not applicable [9]. It is shown that, if Poisson's ratio ν is constant, the stiffnesses of a beam may be computed from formulae derived from the classical theory of plane sections, though the local deformations need not generally coincide. If ν ≠ const the stiffnesses differ from their classical values. Two-sided estimates are obtained for that case. The classical stiffnesses are exact lower bounds.
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