Minimum volume design of structures with constraints on ductilityand stability

A minimum volume design problem of elastic perfectly plastic frame structures subjected to differentcombinations of fixed and seismic loads is presented, in which the design variables are considered as appertainingalternatively to a continuous assigned range as well as to appropriate discrete sets. The structure isdesigned so as to behave elastically for the applied fixed loads, to shakedown in presence of serviceabilityseismic conditions and to prevent the instantaneous collapse for suitably chosen combinations of fixed andhigh seismic loadings. In order to avoid further undesired collapse modes, the P-Delta effects are consideredand the structure is also constrained to prevent element buckling. Furthermore, some suitable constraint onthe structure ductility is imposed referring to the plastic strains generated during the transient phase structuralresponse. The dynamic structural response is obtained by utilizing an appropriate modal techniquereferring to the response spectrum defined by the Italian code. The proposed minimum volume designproblem is formulated, according to the required structural behaviour, on the ground of a statical approach.Different numerical applications related to steel frames conclude the paper.