Application of virtual elements for determination of stress state of rotational shells

In the present work, to describe the behavior of the shell, the classical theory based on the Kirchhoff-Love hypotheses is used. An approach is proposed which allows us to approximate model equations, taking account of any external loads. Virtual elements and expansion in Fourier's series are applied to determine the stress state of isotropic and orthotropic rotational shells under local loading conditions. Calculation results for shells subjected to different types of local mechanical loads are presented. Comparison of the stress state obtained using virtual elements and that calculated by the finite elements method is carried out. Calculations indicate that the application of the concept of a virtual shell element and the decomposition of loading in Fourier's series make it possible to reduce the dimensionality of the problem by 1.In addition, the high accuracy of approximation of external loads and the characteristics of the stress state of isotropic and orthotropic rotational shells is provided.