Computational methods for optimal shakedown design of FE structures

The paper concerns the optimal shakedown design of structures discretized by elastic perfectly plastic finite elements. The design problem is formulated in four alternative versions, i.e. as the search for the minimum volume design whose shakedown limit load multiplier is assigned or as the search for the maximum shakedown limit load multiplier design whose volume is assigned; both problems are approached on the grounds of the shakedown lower bound and upper bound theorems. Correspondingly four computational methods, one for each original problem, are presented. These methods consist in solving iteratively new problems which are simpler than the original ones, but expressed in such a way that the obtained design and behavioural variables fulfill the optimality conditions of the relevant original problems, and thus they provide the true optimal design. Finally, an alternative numerical approach devoted to obtaining the optimal shakedown design is presented. Several numerical examples confirm the theoretical results.