Development of a general algorithm for solving the stability problem of anisotropic plates

Abstract

This paper is devoted to the development of general algorithm for solving to the stability problem of anisotropic plates using the additional load discretization method. The study of the stability problem is relevant for all types of structural elements and machine parts, and its importance is especially increasing with respect to anisotropic thin plates. This is due to the fact that with the use of new structures and materials, the material intensity is reduced, the area of application of thin-walled systems with low stiffness, for which the danger of elastic loss of stability increases, and, therefore, the importance and relevance of the theory and methods of practical solution of problems of elastic stability of such structures increases. In many works, analytical expressions for determination of critical load are given. At present, the determination of critical loads causes great difficulties in their numerical determination. Therefore, the article presents the most effective numerical and analytical solution of this problem. As a rule, to solve stability problems of anisotropic plates, different representations of the bending deflection function in different rows are used. But the use of such representations is justified only under certain boundary conditions and under the condition of uniformly distributed load. The study described in this paper offers a way to overcome these difficulties, allowing the numerical values of critical forces to be determined without much difficulty. With increasing grid density, the accuracy of the critical load value increases rapidly and with an 8×8 grid, the deviation from the exact solution equal to is 1 %. From a practical point of view, the discovered mechanism of numerical realization of this problem allows to improve engineering design calculations of stability of anisotropic plates with different conditions on supports and with different loading