Applicability of a Structurally Orthotropic Model in Problems on Tension, Bending, and Stability of Densely Perforated Plates and Shells

Abstract

The applicability of a structurally orthotropic model to the calculation of perforated plates and cylindrical shells subjected to tension and bending is studied by the finite-element method. The parameters of the orthotropic material are used in the form of coefficients of stiffness reduction. They are determined from the solution to the problem on deformation of a cyclically repeating structural element, with a varying degree of perforation (porosity), in tension, shear, and bending. The structural element is investigated by the methods of continuum mechanics and the theory of Timoshenko-type shells, and the limit of applicability of the theory of shells to such problems is found. The numerical results obtained are compared with the analytical estimates given by E. I. Grigolyuk and L. A. Filshtinskii. Verification of the numerically obtained orthotropic parameters is carried out based on the solution to the problem of bending of one quarter of a cylindrical strip and a plate perforated with one row of holes. It is shown that the approach chosen is applicable to perforated plates and shells in bending problems with waves whose length exceeds the characteristic size of their structural element. The stability of a perforated elastic cylindrical shell under external pressure, with two variants of boundary conditions, is investigated. Values of the critical pressure and the corresponding buckling modes in relation to the length of the shell and the degree of perforation are obtained.