Analysis of a Circular Cylindrical Shell Perforated by a Large Number of Radial Holes

Abstract

The present paper considers a circular cylindrical shell perforated by many radially aligned circular holes that pierce its surface in repeating rectangular patterns (Fig. 1). Eight “effective” stiffness coefficients are developed for this configuration by comparing the elastic strain energy density for an idealized perforated cylindrical shell element (shown in Fig. 2) to the energy density of an orthotropic cylindrical shell element. General equations for the perforated shell element are obtained by utilizing these eight “effective” stiffness coefficients. The general set of equations is then reduced to the usual three partial differential equations in terms of the u, v, and w-displacements. This set of displacement equations is solved for two specific cases; the first case is the rotationally symmetric one where the shell is considered completely perforated; the second case is that of a partially perforated shell. Here a portion of a perforated shell is joined with a portion of an isotropic cylindrical shell along two edges, where θ is constant (see Fig. 4).