Probabilistic resolution of the twentieth century conundrum in elastic stability

This paper overviews the efforts that led to resolution of the 20th century conundrum in elastic stability of shells. In particular, the dramatic disagreement between theoretical and experimental results and the subsequent introduction of the empirical knockdown factor, is discussed in detail. The mismatch between theory and experiment was qualitatively explained by Warner Tjrdus Koiter, in his now-famous thesis, as well as in the paper by Lloyd H. Donnell and C.C. Wan. However, these studies did not offer means for rigorous, theoretical derivation of the knockdown factor for the shells with generic imperfection patterns encountered in practice. Numerous attempts to resolve the conundrum via deterministic theoretical, experimental and probabilistic analyses remained unsuccessful. The concendrum consists in two facts. On one hand, it consists of impossibility of using of hundreds and perhaps thousands of deterministic studies in predicting the rigorous knockdown factors. On the other hand, it lies in the fact that Wynstone Barrie Fraser and Bernard Budiansky (1969) [79] and numerous other investigators, although recognized the need to utilize probabilistic approach to resolve the above concendrum asserted that the buckling load of stochastic structures was a deterministic quantity. Some investigators suggested to use that result as the design load. 9, this author lucked out on reliability-based theoretical means for derivation of the knockdown factor and its judicious allocation.