Numerical simulation of the stability of three-dimensional elastic composite structures based on the finite element method

Abstract

A numerical method for solving the problem of the stability theory of linearly elastic bodies with small deformations in a general three-dimensional formulation is considered. The problems of this class are poorly studied in contrast to the two-dimensional problems of stability theory. At the same time, classical approaches do not allow one to take into account the effect on the structural stability of various three-dimensional effects: areas of compounds, zones of defects, etc. The study formulates a variation formulation of the problem of the three-dimensional stability theory. Based on the finite element method, a numerical statement is obtained in the form of a generalized eigenvalue problem with symmetric global stiffness matrix. The application of the proposed method is demonstrated by the example of calculating the stability of a composite plate under longitudinal compression. The simulation was carried out using the SMCM software package developed at the Department of Calculus Mathematics and Mathematical Physics of Bauman Moscow State Technical University.