The Buckling of Cylindrical Shells Under Longitudinally Varying Loads

Two problems illustrating the effect of nonuniformity of loading on the buckling characteristics of circular cylinders are investigated. The first problem deals with the effect of linearly varying axial compressive stress, such as would be produced by the weight of the propellant in a solid-propellant engine case. The results indicate that the ratio of the maximum critical compressive stress induced by the shear load to the critical uniform compressive stress varies from 1.9 for the curvature parameter Z equal to 0 to 1.0 as Z becomes infinite. In particular, the increase in stress is less than 20 per cent for Z greater than 100. The stability of thin cylinders loaded by lateral external pressure, varying linearly in the longitudinal direction, is also investigated. The results indicate that for Z greater than 100, the buckling coefficients are proportional to Z^1/2.