General Mathematical Models of Micropolar Thin Elastic Bars, Plates and Shells

The present paper is aimed at considering the general system of the three-dimensional micropolar theory of elasticity and corresponding boundary conditions with independent fields of transition and rotation in the shell’s thin sphere. Depending on the values of physical sizeless parameters there are formulated hypotheses (assumptions) of asymptotic origin, on the basis of which there are constructed general applied twodimensional theories of thin elastic shells with independent fields of transition and rotation; with constraint rotation; and the theory with small shift rigidity. As special cases of the theory of shells there are also developed the basic equations and boundary conditions for micropolar thin elastic bars (onedimensional theories) and for plates (two-dimensional theories) with independent fields of transition and rotation; with constraint rotation; and with small shift rigidity. In the present paper there are also considered special bending problems of micropolar bars and plates, as well as the problem aimed at defining the stressdeformed state in micropolar cylindrical shell. As a result of numerical analysis, the specific peculiarities of micropolar elastic materials are exposed.

Keywords:

models , micropolar , shell , plate , bar