In this paper we derive and mathematically justify models of micropolar rods and plates from the equations of linearized micropolar elasticity. Derivation is based on the asymptotic techniques with respect to the small parameter being the thickness of the elastic body we consider. Justification of the models is obtained through the convergence result for the displacement and microrotation fields when the thickness tends to zero. The limiting microrotation is then related to the macrorotation of the cross-section (transversal segment) and the model is rewritten in terms of macroscopic unknowns. The obtained models are recognized as being either the Reissner-Mindlin plate or the Timoshenko beam type. Mathematics Subject Classification (2000)74K20 · 74K10 · 74A35

An asymptotic expansion method is applied to nonlinear three-dimensional elastic straight slender rods. Nonlinear ordinary differential equations for approximate displacements and explicit formulas for approximate stress distributions are obtained. Mathematical properties of these models are studied.R~sum~. On applique la m&hode des d6veloppements asymptotiques ~ des poutres tridimensionnelles droites, 61anc+es et non lin6airement 61astiques. On en d6duit des 6quations diff6ren-tielles ordinaires non lin6aires pour des d~placements approch+s, ainsi que des formules explicites pour des approximations des distributions de contraintes. On 6tudie les propri6t6s math6matiques de ces mod61es.

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