Asymptotically Confirmed Hypotheses Method for the Construction of Micropolar and Classical Theories of Elastic Thin Shells

Abstract

In the present paper asymptotic solution of boundary-value problem of three-dimensional micropolar theory of elasticity with free fields of displacements and rotations is constructed in thin domain of the shell. This boundary-value problem is singularly perturbed with small geometric parameter. Internal iteration process and boundary layers are constructed, problem of their jointing is studied and boundary conditions for each of them are obtained. On the basis of the results of the internal boundary-value problem the asymptotic two-dimensional model of micropolar elastic thin shells is constructed. Further, the qualitative aspects of the asymptotic solution are accepted as hypotheses and on the basis of them general applied theory of micropolar elastic thin shells is constructed. It is shown that both the constructed general applied theory of micropolar elastic thin shells and the classical theory of elastic thin shells with consideration of transverse shear deformations are asymptotically confirmed theories.

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Sargsyan, S. (2015) Asymptotically Confirmed Hypotheses Method for the Construction of Micropolar and Classical Theories of Elastic Thin Shells. Advances in Pure Mathematics, 5, 629-642. doi: 10.4236/apm.2015.510057.

Conflicts of Interest

The authors declare no conflicts of interest.

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