Stability of Orthotropic Cylindrical Shells Under Combined Loading

Abstract

N THE design of modern missiles and space vehicles, in­ creasing use is made of the newer materials, such as rein­ forced plastics, whisker materials and fiber reinforced metals. Materials of this sort are elastically orthotropic; that is, they have three mutually perpendicular planes of elastic symmetry. This means that the material composing the wall of a shell has a modulus of elasticity and Poisson's ratio different in the axial than in the circumferential direction, and a shear modulus which is completely independent of these. The critical item in the design of structures utilizing these materials may be stability, depending on the strength, duc­ tility and stiffness of the material. If such is the case, a method of predicting the buckling load is required. One possibility is to use an isotropic analysis such as given in (l), 2 assuming some average material properties. However, this approach could lead to results that would be unduly conserva­ tive in some cases, and disastrously nonconservative in other cases. Therefore, the purpose of this report is to present a method of determining the buckling loads on shells composed of an orthotropic material. In this report the small deflection differential equations describing the action of an orthotropic cylindrical shell under arbitrary loading are derived. These equations are then transformed into the large deflection equations effectively, describing the stability of the shell under the action of ex­ ternal pressure and axial compression (2). The solution of the latter equations yields an expression for the critical loads in terms of shell geometry, material properties and buckling modes. There is an infinite number of possible buckling modes but the only one of practical interest is the one cor­ responding to minimum load. A family of curves is plotted giving the critical axial load and critical external pressure for an orthotropic cylinder. For a conical shell of small vertex angle, the equivalent cylinder method developed by Bijlaard (7) and discussed in (1) is recommended.