Dynamic Shakedown Sensitivity Analysis by Means of a Probabilistic Approach
The shakedown limit load multiplier problem for elastic plastic structures subjected to a combination of fixed and seismic loads is treated. In particular, reference is firstly made to the unrestricted dynamic shakedown theory. The relevant seismic load history is modeled as a repeated one and, with reference to classically damped structures, appropriate modal analyses are utilized. With the aim of evaluating the reliability of the results arising from the application of the cited theory, a recent probabilistic approach is also utilized. This approach adopts the Monte Carlo method in order to define the necessary seismic acceleration histories and finally compute the related shakedown limit load multiplier distribution. The probabilistic approach relies on a generalized Ceradini theorem which allows to define the limit load multiplier cumulative distribution function and, therefore, to characterize the shakedown sensitivity of the structure. The comparison between the two described approaches is effected and an improved computational procedure is proposed. The effected applications are related to plane steel frames.
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