Abstract
A unified theory for the complementary-dual bounding theorems of limit analysis is established with the aid of convex analysis. Based on the property of superpotential in this theory, various variational principles are constructed, which include a new lower bound theorem, a more precise estimation for the safety factor and a penalty-duality type variational principle. Furthermore, an efficient penalty-duality algorithm for limit analysis is suggested and the applications of these theorems are illustrated.
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