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Derivation and justification of the models of rods and plates from linearized three-dimensional micropolar elasticity. (English) Zbl 1158.74401
Summary: 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.

MSC:
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74K20 Plates
74A35 Polar materials
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