Comparison among different dynamic shakedown approaches

The paper concerns the search for the limit load multiplier of structures subjected to seismic actions under shakedown conditions. The search problem is treated referring to two fundamental different approaches: The unrestricted dynamic shakedown approach and a new stochastic one recently proposed. The comparison between the above cited approaches is effected with the aim of evaluate the goodness of the obtainable results and the related computational effort. The structure sensitivity with respect to shakedown is evaluated through the analysis of the shakedown limit load multiplier cumulative distribution function. This function is determined by means of the stochastic approach, adopting the Monte Carlo method and on the grounds of a suitably defined generalized Ceradini theorem. For the sake of simplicity and without loss of generality, the search problems are formulated referring to elastic perfectly plastic steel frames. The effected numerical applications allow obtaining very interesting information on the structure shakedown behaviour, they confirm the great reliability of the stochastic approach and they provide useful suggestions for the improvement of the method.