Numerical and Analytical Modeling of the Stability of the Cylindrical Shell under the Axial Compression with the Use of the Non-classical Theories of Shells

The problem of the buckling of a transveral-isotropic cylindrical shell under axial compression by means of new non-classical shell theories is studied. The local approach is used to solve the systems of differential equations. According to this approach the buckling deflection is sought in the form of a doubly periodic function of curvilinear coordinates. The well-known solutions obtained by classical shell theories are compared with the results of non-classical shell theories. For the non-classical theories of anisotropic shell of moderate thickness the buckling equations are constructed by the linearization of nonlinear equilibrium equations. Analytical and numerical results obtained with the use of 3D theory by the FEM code ANSYS 13 are also compared.