Ellipsoidal-bound convex model for the non-linear buckling of a column with uncertain initial imperfection |
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Authors: | Zhiping Qiu Lihong Ma Xiaojun Wang |
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Institution: | Institute of Solid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing 100083, PR China |
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Abstract: | Ellipsoidal-bound convex model approach for computing the non-linear buckling load of a non-linear elastic foundation-based column with uncertain initial imperfection is presented. In this study, the uncertain initial deflections are considered to be unknown except that they belong to a given set in the ellipsoidal space. The non-zero central values for uncertain initial deflections are considered here, so this is the general case. It is different from Ref. I. Elishakoff, G.Q. Cai, J.H. Starnes Jr., Non-linear buckling of a column with initial imperfection via stochastic and non-stochastic convex models, Int. J. Non-Linear Mech. 29(1) (1994) 71-82], where only the zero central values for them are considered. On the other hand, the presented ellipsoidal-bound convex model is directly based on the exact model, whereas convex models in previous literatures are based on the first-order or second-order approximate models to solve uncertain problems. The influences of the central values and bounds of uncertain initial deflections on the buckling load are investigated. Comparisons between the ellipsoidal-bound convex model and interval-bound convex model are performed, where the stochastic results at different reliability levels and different truncated normal distribution are taken as the benchmarks of accuracy for judgment. |
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Keywords: | Non-linear buckling Ellipsoidal-bound convex model Interval-bound convex model Uncertain initial imperfection |
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