МАТЕМАТИЧЕСКАЯ МОДЕЛЬ СТАТИЧЕСКОЙ ДЕФОРМАЦИИ МИКРОПОЛЯРНОГО УПРУГОГО СТЕРЖНЯ С КРУГОВОЙ ОСЬЮ ПО ТЕОРИИ СО СТЕСНЁННЫМ ВРАЩЕНИЕМ И МЕТОД КОНЕЧНЫХ ЭЛЕМЕНТОВ

In present paper the applied (one-dimensional) model of micropolar elastic thin beam with a circular axis is constructed including the variation principles, on the basis of the two-dimensional equations of micropolar theory of elasticity with constrained rotation written in the polar coordinate system and previously developed hypotheses for thin bodies. Within the framework of this mathematical model, boundary problems with applied values are formulated, which are solved in the final form. Further, the scheme of application of finite element method (FEM) is developed for the boundary problems of micropolar elastic beam with a circular axis with constrained rotation. The boundary problems stated above are solved by using the FEM and on the basis of an analysis obtained through the numerical results, the specific property of micropolarity of the material is established, that it raises the rigidity of the beam as compared with the classical theory. [ABSTRACT FROM AUTHOR]