Cylindrical Shells subjected to compressive forces, Fig. 13-1, must be evaluated in accordance with one of the buckling theories of shells. Two approaches for developing the buckling equations will be discussed. The first is that of Sturm (Sturm 1941) which is well suited for designing cylindrical shells at various temperatures using actual stress— strain curves as discussed in Section 13-5. This approach is used in many pressure vessel codes for the design of cylindrical shells.
The second approach for analyzing buckling of cylindrical shells is that of Donnell (Gerard 1962). This method is discussed in Section 13-6 and is used extensively in the aerospace industry.
We begin Sturm's derivation by taking an infinitesimal element of a cylindrical shell with applied forces and moments as shown in Fig. 13-2. The assumptions made in deriving the pertinent differential equations are
1. The cylinder is round before buckling.
2. The thickness is constant throughout the cylinder.
3. The material is isotropic, elastic, and homogeneous.
4. The thickness is small compared to the radius.
5. Radial stress is negligible compared to the circumferential and longitudinal stresses.