Shakedown Analysis of 3D Frames with an Effective Treatment of the Load Combinations

  • Giovanni GarceaEmail author
  • Leonardo Leonetti
  • Raffaele Casciaro


Using the Melan static theorem and an algorithm based on dual decomposition, a formulation for the shakedown analysis of 3D frames is proposed. An efficient treatment of the load combinations and an accurate and simple definition of the cross-section yield function are employed to increase effectiveness and to make shakedown analysis an affordable design tool. The section yield function, obtained by its support function values associated with presso-flexural mechanisms, is defined as the Minkowski sum of ellipsoids. The return mapping process, resulting from the dual decomposition, is solved at the element level by means of an algorithm based again on the dual decomposition. It allows the separation of the problem at the ellipsoid level and the use of a simple and inexpensive radial return mapping process for its solution. A series of numerical tests are presented to show both the accuracy and the effectiveness of the proposed formulation.


Convex Hull Proximal Point Algorithm Load Combination Elastic Domain Elastoplastic Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The research leading to these results has received regional funding from the European Communitys Seventh Framework Programme FP7-FESR: “PIA Pacchetti Integrati di Agevolazione industria, artigianato e servizi” in collaboration with the Newsoft s.a.s. (


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Giovanni Garcea
    • 1
    Email author
  • Leonardo Leonetti
    • 1
  • Raffaele Casciaro
    • 1
  1. 1.Dipartimento di Modellistica per L’IngegneriaUniversità della CalabriaCosenzaItaly

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