We present the dual variational principles of the rigid perfectly plastic material due to Markov and Hill, from which ones the bound theorems of limit analysis can be deduced. Following the same kind of method, the bound theorems can be extended to variable repeated loads. They provide two dual ways to calculate the shakedown load α a by solving constrained optimization problems. Finally, the duality between the variational principles of shakedown is discussed from the viewpoint of the non smooth mechanics.
KeywordsVariational Principle Admissibility Condition Dissipation Power Function Shakedown Analysis Lagrangean Multiplier Technique
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