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.

中文翻译：

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微极弹性薄板和浅壳静变形的几何非线性模型

本文考虑了微极板和浅壳，它们的弹性挠度与其厚度相当，与特征截面尺寸相比较小。同时，法线相对于变形前的中间表面的旋转角度以及它们的自由旋转都较小。另外，在变形和弯曲扭转​​的张量中，考虑了位移梯度中的非线性成员。提出了假设方法，在此基础上构造了微极性弹性柔性板和浅壳静变形的通用模型。在这些模型的基础上，解决了在边界受铰链支撑的情况下，微极性弹性柔性矩形板和矩形浅壳的特殊问题。