Collected Works of H. S. Tsien (1938-1956)

Lower Buckling Load in the Non-Linear Buckling Theory for Thin Shells

Hsue-shen Tsien

(Massachusetts Institute of Technology)

For thin shells the relation between the load P and the deflection ε beyond the classical buckling load is very often non-linear. For instance, when a uniform thin circular cylinder is loaded in the axial direction, the load P when plotted against the end-shortening ε has the characteristic shown in Fig. 1. If the strain energy S and the total potential φ = S - Pε are calculated, their behavior can be represented by the curves shown in Figs. 2 and 3. It can be demonstrated that the branches OC and AB corresponds to stable equilibrium configurations and the branch BC to unstable equilibrium configurations. The point