A multicriterion design of steel frames with shakedown constraints

Elasto-plastic optimal profile of the flanges of a double-T steel beam

“…Because of the linear relationship between load and descent, we get a descent given byd ( Second, because of the sudden collapse of the Heyman beam, which is not desirable for safety reasons, we could use as a second performance measure the ductility, so the objective function will be An important problem that was not studied here, but seems totally feasible, is that of optimizing frames under lateral loads. The optimization of the ductility of a structure using a dynamic approach like that of [9] for example, could also be confronted. Considering lateral torsional buckling is an important issue, that might also be studied in future works.…”

Bounds on transient phase plastic deformations in optimal design of steel frames subjected to cyclic loads

“…However, it has to be emphasized that the performed numerical applications showed that, if an appropriate loading history is selected and an elasto-plastic analysis is performed, during the transient phase plastic deformations not compatible with the serviceability and the ductility of the structure can be arise. This undesirable effect depends on the above mentioned intrinsic limit of the formulation proposed in [16], which explicitly takes into account the steady-state load history and the consequent actual elastic plastic response, while it does not take into account neither the load history during the transient phase nor the consequent actual plastic deformations.…”

“…For example, in the former case, the proposed problem is formulated as search for the minimum volume structure according to a plastic shakedown criterion, in such a way that incremental and instantaneous collapse are certainly prevented when the structure is subjected to the prescribed amplified fixed and cyclic loads; the further condition that the structure must behave elastically in serviceability conditions is also considered. The main difference with papers proposed by other authors lies in the fact that the optimal design problem proposed in [16] is based on the plastic shakedown criterion which guarantees the desired behaviour during the steady-state phase only. However, it has to be emphasized that the performed numerical applications showed that, if an appropriate loading history is selected and an elasto-plastic analysis is performed, during the transient phase plastic deformations not compatible with the serviceability and the ductility of the structure can be arise.…”

“…[16]), the authors and co-workers proposed to formulate the optimal design problem on the grounds of both statical and kinematical approach. For example, in the former case, the proposed problem is formulated as search for the minimum volume structure according to a plastic shakedown criterion, in such a way that incremental and instantaneous collapse are certainly prevented when the structure is subjected to the prescribed amplified fixed and cyclic loads; the further condition that the structure must behave elastically in serviceability conditions is also considered.…”

“…The present paper is devoted to propose an extension of the multicriterion plastic shakedown optimal design proposed in [16], able to bound the plastic deformations arising in the structure during the transient phase, as well as during the steady-state one, by imposing appropriate constraints on the plastic transient and steady-state deformations. In particular, making reference to a special bounding theorem based on a perturbation method [17], suitable bounds on the plastic deformations related to the transient phase are imposed, whatever the real loading history is during the unknown transient phase; further suitable limits on the alternated plastic deformations related to the known steady-state response are also taken into account, imposing that suitably chosen measure of the plastic deformations occurring in the elements at the limit state of plastic shakedown be not greater than some assigned values.…”