Derivation and justification of the model of micropolar elastic shells from three-dimensional linearized micropolar elasticity

Abstract

In this paper we derive a two-dimensional model of elastic shell-like body from the three-dimensional linearized micropolar elasticity. Derivation is based on the asymptotic expansion method with respect to the thickness of the shell. 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 two-dimensional problem well defined for W^1,∞ shells. Appropriate convergence results are proved.