Numerical and experimental modeling of the behavior of flexible shell elements of structures

Abstract

This article is devoted to computer and experimental modeling of the behavior of flexible elements of shell structures, and the development of effective algorithms for solving emerging nonlinear boundary value problems of their calculation and optimization of parameters. At the same time, the probability of the results obtained using different approaches to the construction of a nonlinear theory is established. Their comparative analysis, error estimation, which in this case is given by calculation according to linear and corresponding nonlinear theories, is carried out. The results of calculated data and experimental studies of the behavior of real structural elements are compared. The results of a comparative analysis of the application of two mathematical models of deformation of flexible shell elements, obtained by direct integration of boundary value problems of shell mechanics, by the finite element method and experimental research, are presented. The problems of axisymmetric nonlinear bending of thin ring plates, corrugated membranes of a sinusoidal profile and bellows as a shell of rotation with a complex meridian shape are considered. Using the necessary optimality conditions of the principle of maximum L. S. Pontryagin obtained the results of the optimal design of a flexible corrugated membrane with a sinusoidal profile of the highest sensitivity. The results are presented in the form of tables, photos and graphs.