Geometrically nonlinear models of static deformation of micropolar elastic thin plates and shallow shells

The present paper considers micropolar plates and shallow shells, the elastic deflections of which are comparable with their thickness and are small in comparison with characteristic cross-section size. At the same time, both rotation angles of the normal to the median surface before deformation and their free rotations are small. Also, in the tensors of deformation and flexures-torsions, the nonlinear members in the gradients of the displacement are considered. Hypothesis method is developed, on the basis of which general applied models of static deformation of the micropolar elastic flexible plates and shallow shells are constructed. On the basis of these models, specific problems for the micropolar elastic flexible rectangular plates and shallow shells rectangular in cross-section are solved in case, when bounds are hinge-supported. On the basis of numerical analysis, certain effective features of the micropolar material are established in comparison with the corresponding classical material.