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

Buckling of a Column with Non-Linear Lateral Supports

H.S. Tsien*

(California Institute of Technology)

During the investigation of the buckling phenomenon of thin spherical shells^[1] and thin cylindrical shells^[2], it was found that for these structures the load sustained is not a linear function of the deflection even when the stresses are below the elastic limit and are proportional to the corresponding strains. This non-linear load vs. deflection relation gives a buckling phenomenon entirely different from that of the classical theory. However, the exact solution of these problems involves a pair of non-linear partial differential equations. It is difficult to obtain an exact solution. The method adopted in these investigations is the so-called ...