TY - RPRT

T1 - Comparative Study of Upper Bound Methods for the Calculation
of Residual Deformations After Shakedown

AU - Lange-Hansen, Preben

PY - 1998

Y1 - 1998

N2 - 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

AB - 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

M3 - Report

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

ER -