About the applicability limits of the Tymoshenko model and the principle of two-dimensional similarities in problems of elastic plastic bending and stability of densely perforated plates and shells

Abstract

The applicability limits of the Tymoshenko model are determined for the elastic-plastic bending problems of densely perforated plates by the finite element method. The boundaries of applicability of the two-dimensional similarity principle are investigated for stability problems of densely perforated elastoplastic cylindrical shells under axial compression. Cylindrical densely perforated shell is represented as a set of cyclically repeating structural elements. The principle of two-dimensional similarity makes it possible to reduce the number of these elements while maintaining the porosity, thickness and length of the shell. The calculations were carried out by the theory of the Timoshenko-type shells and continuum theory. The nature of the change in the applicability of this principle is shown in the article, depending on the thickness of the shell. The values of the critical load are determined with a decrease in the number of structural elements for different values of porosity. Based on these calculations, the applicability limits of the two-dimensional similarity principle are estimated for stability problems to axial compression of a densely perforated cylindrical shell by the continuum theory and theory of the Timoshenko-type shells.