Numerical modelling of perforated shells stability

In this paper, the finite element method is applied to investigate the stability of densely perforated cylindrical shells under external pressure. The problem is resolved based on the shell theory with an orthotropic material model. The orthotropic material parameters in the form of softening coefficients are determined from the solution of the problem of deformation of cyclically repeating structural elements under tensile, shear and bending with variable rates of perforation (porosity). The research of the structural elements has been produced using methods of continuum mechanics and Timoshenko-type theory. As a result of these considerations, softening coefficients are obtained for different values of porosity, also the limits of applicability of the shell theory were defined for the similar problems. The comparison of numerical results with the analytical estimates, obtained by Grigolyuk and Filshtinsky [1] is provided. Verification of the numerically obtained orthotropic parameters is based on solving the problem of bending of a band quarter, which has been performed with one row of holes. The problem is solved in the framework of continuum mechanics and the shell theory in conjunction with the structurally orthotropic model with different rates of porosity. It is confirmed that using the finite element method for the structurally orthotropic shell with parameters, determined from the solution of three-dimensional tensile and shear behavior, is applicable to the long waves bending problem. Investigation of the stability of perforated elastic cylindrical shell under external pressure is provided for two boundary conditions based on the shell theory and the structurally orthotropic mode. As a result, the critical pressure value and corresponding buckling modes are obtained depending on the shell length and perforation rates.