Stability of a three-layer cylindrical shell

Abstract

Problem. The article presents the results of studies of the stability of a three-layer cylindrical shell. Factors that have a significant impact on the strength and stability of the three-layer cylindrical shell were taken into account, namely the reduced modules of elasticity of the three-layer wall. Goal. The purpose of the study is to develop a methodology for calculating the stability of a three-layer cylindrical shell, which will significantly improve the calculation practice of such structures in relation to determining the critical external pressure for a three-layer cylindrical shell. Methodology. The method of variational calculation using the Euler equation of the mixed variational problem was used to determine the critical pressure. To determine the stability of the three-layer cylindrical shell, those factors that have a significant impact on its strength and stability were taken into account, namely the reduced modulus of elasticity of the three-layer wall. The bending stiffness Dh was replaced by the bending stiffness of the three-layer shell taking into account the shear deformation. Results. The current state of the issue of the stability of a three-layer cylindrical shell has been studied. Using the methods of variational calculation with the Euler equation of the mixed variational problem, the equation of the condition of equality of the internal and external forces of the orthotropic structure, which is in a state of indifferent equilibrium with radial displacement, is compiled. Accepting the previously obtained equation for radial movements and substituting it into the equation for the potential energy of the system per unit length, we obtained the equation for determining the critical pressure. The obtained analytical solution was tested for the design of the crane running wheel, which has an elastic insert. We will get pkr=1267 MPa. For crane running wheels, the allowable pressure of the wheel on the rail is taken within 250 MPa, that is, we have a reserve of stability of the rail nc=1267/250=5.1. As you can see, the margin of stability is more than sufficient. In addition, a comparison was made between the obtained method of calculating the stability of a three-layer cylindrical shell and the method described in [20]. Originality. A new method of calculating a three-layer cylindrical shell under the action of external pressure has been developed. A quantitative assessment of the critical pressure of the traveling crane wheel, which has an elastic insert, was carried out. Practical value A technique for determining the critical pressure of a three-layer cylindrical structure under the action of external pressure has been created.