Optimal design of trusses according to a plastic shakedown criterion

The optimal design of elastic-perfectly plastic truss structures subjected to quasi-statically loads variable within a given load domain is studied. The actions are given as the combination of fixed load and perfect cyclic load. Suitably chosen load multipliers are given. A minimum volume formulation of the design problem with assigned limit load multiplier is developed and it is provided on the grounds of a statical approach as well as of a kinematical approach. The incremental collapse (ratchetting) of the optimal structure is prevented, as long as the loads are not greater than some prescribed values, by special constraints suitably introduced in the search problem. The Kuhn-Tucker equations related to the above-described search problems are deduced and studied. The duality between the statical and the kinematical problem formulations is proved. A special iterative technique devoted to the solution of the above referred optimization problems is utilized for computational purposes. A numerical example concludes the paper. The comparison between different designs is effected.