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Nonlocal effects in the passage from 3d to 1d in linearized, anisotropic, heterogeneous elasticity. (Effets non locaux dans le passage 3d-1d en élasticité linéairisée anisotrope hétérogène.) (French. Abridged English version) Zbl 0962.74009
Summary: We reduce to three equations in \((\zeta_1, \zeta_2, \zeta_3)\) the system in \((u,v,w)\), which we obtained by passing to the limit from three to one dimension for an elastic anisotropic heterogeneous cylinder, the diameter of which tends to zero. In particular, we show that the conjunction of three phenomena (the heterogeneity of material in \(x_3\) direction, its anisotropy, and the clamping condition prescribed at both ends of the cylinder) leads to nonstandard rod equations with nonlocal terms.

MSC:
74B15 Equations linearized about a deformed state (small deformations superposed on large)
74E10 Anisotropy in solid mechanics
74A30 Nonsimple materials
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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