USE OF A 3D TECHNIQUE FOR CALCULATION OF BUCKLING OF THICK ANISOTROPIC SHELLS AT TORSION ACTION

Abstract

Cylindrical shells from composites are widely used in the most various designs of the modern equipment. Sometimes conditions of their operation are that that in shells there is tension from the torsion moment that can reach critical values. In the majority of works, structural idealization of a composite, which imposes to material existence of three planes of symmetry, is accepted. However, at production of covers, for example, the effect of anisotropy caused by a divergence of the direction of reinforcing with shells axes arises winding. Therefore, there is a need for development of methods of the solution of problems of stability of shells from composite materials with use of more general model of a composite with the smaller level of symmetry of material.

The elastic anisotropic composite cylindrical shells carried to cylindrical (curvilinear) system of coordinates are considered. Spatial approach is based on use of the three-dimensional equations of balance. For the solution of a problem of stability of cylindrical anisotropic shells, according to static criterion of Euler, we will carry out linearization of the three-dimensional system, which is written down rather derivative on a variable. One of ways of the solution of the three-dimensional task received thus is the possibility of her transformation in one-dimensional for what we will use Bubnov-Galerkin's procedure. According to her, we will spread out all functions in trigonometrical ranks on coordinate along forming the cylinder so that they met regional conditions at shell end faces. After some mathematical transformations and division of variables, we will receive the infinite system of the ordinary differential equations of stability in a normal form of Cauchy. Which realization, under boundary conditions on internal and external surfaces of a shell, is carried out with use of a numerical method of discrete orthogonalization. Using the offered approach the problem of stability at torsion of single-layer, two-layer shells is solved taking into account and without the anisotropic constants of material arising at the described type of anisotropy. The dependence of sizes of critical loadings on an angle of rotation of the main directions of elasticity of initial material relatively curvature designs is investigated. Results are presented in the form of schedules