A Variational Deduction of the Upper and Lower Bound Shakedown Theorems by Markov and Hill’s Principles Over a Cycle

  • Géry De Saxce
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 36)


This work was part of the author's doctoral thesis and was briefly presented at the first Belgian Congress of Mechanics in Brussels (cf. DE SAXCE [1986,1987]). Some additional developments can be found in a European report (cf.SAVE et al. [1991]). The paper presents two dual variational principles governing the collapse behaviour of the elastic-perfectly plastic structures under variable loading. On this basis, an original deduction of the bound shakedown theorems is given, in a similar way to MANDEL’s corresponding approach for the rigid plastic material under proportional loading. In the second part, the regularity of the solutions is discussed. Applying the theorems to the thick wall tube problem, we show that DIRAC’s distribution is required to obtain the plastic fatigue kinematical solution.


Residual Stress Admissibility Condition Proportional Loading Dissipation Power Function Shakedown Analysis 
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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • Géry De Saxce
    • 1
  1. 1.Mechanics of Materials and StructuresPolytechnic Faculty of MonsMonsBelgium

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