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.
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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. (www.newsoft-eng.it).
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