The Buckling of a Column With Random Initial Deflections
W. Barrie Fraser, Bernard Budiansky · Journal of Applied Mechanics · 1969
We consider the buckling of an ensemble of infinitely long columns, with initial deflections, resting on nonlinear elastic foundations. The initial deflections are assumed to be Gaussian stationary random functions of known autocorrelation, and the problem is solved by the method of equivalent linearization. We find that each column in the ensemble has the same buckling load that depends only on the autocorrelation of the initial deflection functions. Results are presented for columns whose initial deflection functions have an exponential-cosine autocorrelation.