Comparative Study of Upper Bound Methods for the Calculation of Residual Deformations After Shakedown

Purpose: None of the published formulae for obtaining upper bounds for residual deflections in elastoplastic structures with quasistatically varying loads (shakedown problems) has been able to result in theoretical maximum values of residual deflections. Therefore, the purpose of the report is to attempt a preliminary assessment of four of the previously derived formulae, namely those of Lange-Hansen and Nielsen, Dorosz, Capurso, and Ponter.Method: Analytic optimum upper bounds from the four formulae are derived for 6 examples and compared individually and with the theoretically correct residual deflection.Results: The assessment has resulted in placing Ponter's formula as the best, followed the formulae of Lange-Hansen and Nielsen, Capurso and finally that of Dorosz, the results of three last mentioned being found to lie in average 4%, 46% and 60%, respectively, over the average results from Ponter's formula. The difference between the results of the formulae varies greatly from example to example. Further, it was found that the work involving finding an analytical optimum solution according to Capurso's formula is about the double of the work involving finding a solution according to one of the other formulae.Keywords: Plastic analysis, shakedown, residual deflections