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

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In this paper we prove that the one-dimensional model of elastic beam is an approximation to the three-dimensional linear theory of elasticity. Tutek and I. AganoviCDepartment of Mathematics University of Zagreb p.0. box 187 41001 Zagreb, Yugoslavia (ReceivedMay31. 198s)

In this paper we derive a model of curved elastic rods from the threedimensional linearized micropolar elasticity. Derivation is based on the asymptotic expansion method with respect to the thickness of the rod. The method is used without any a priori assumption on the scaling of the unknowns. The leading term, displacement and microrotation, is identified as the unique solution of a certain onedimensional problem. Appropriate convergence results are proved.

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