Instability of orthotropic cylindrical shells under combined torsionand hydrostatic pressure.

Abstract

The problem of general instability of an orthotropic circular cylindrical shell of elastic material under combined torsion and hydrostatic pressure is investigated for two sets of boundary conditions: simply supported and clamped ends. The analysis is based on the assumptions of linear elasticity, small deflection theory, thin shell theory, and uniform geometry (the stiffnesses are independent of the space coordinates). Furthermore, the Poisson effect, the effect of transverse shear forces on deformations, and the effect of eccentricitie s have been assumed negligible. The governing differential equations and proper boundary conditions are derived by variational methods, and they are expressed in terms of the displacement components. By elimination the in-plane displacement components, a Donnell-type equation in the normal displacement component is obtained. A Galerkin procedure is employed and the characteristic equation relating the applied loads to the shell geometry, stiffnesses, and the number of sine waves in the circumferential direction is derived. From this, the critical conditions are obtained with the aid of a computer program. The results are presented in graphical form for a range of values of the different stiffnesses. When isotropic stiffnesses are used the results reduce to the well-known curves for isotropic cylinders.