Computational procedures for plastic shakedown design of structures
The minimum volume design problem of elastic perfectly plastic finite element structures subjected to a combination of fixed and perfect cyclic loads is studied. The design problem is formulated in such a way that incremental collapse is certainly prevented. The search for the structural design with the required limit behaviour is effected following two different formulations, both developed on the grounds of a statical approach: the first one operates below the elastic shakedown limit and is able to provide a suboptimal design; the second one operates above the elastic shakedown limit and is able to provide the/an optimal design. The Kuhn-Tucker conditions of the two problems provide useful information about the different behaviour of the obtained structures. An application concludes the paper; the comparison among the designs is effected, pointing out the different behaviour of the obtained structures as well as the required computational effort related to the numerical solutions.
shakedown design elastic shakedown limit optimization bree diagrams elastic plastic behaviour