Minimum volume design of structures with constraints on ductility and stability

• We propose a wide optimal design problem formulation for elastic plastic frames.
• The optimal frame must respect constraints on shakedown, collapse and buckling.
• A bound on the structure ductility is imposed within the design formulation.
• Both continuous and discrete variable design are accounted by the formulation.
• Two special computational algorithms are utilized for the numerical applications.

A minimum volume design problem of elastic perfectly plastic frame structures subjected to different combinations of fixed and seismic loads is presented, in which the design variables are considered as appertaining alternatively to a continuous assigned range as well as to appropriate discrete sets. The structure is designed so as to behave elastically for the applied fixed loads, to shakedown in presence of serviceability seismic conditions and to prevent the instantaneous collapse for suitably chosen combinations of fixed and high seismic loadings. In order to avoid further undesired collapse modes, the P-Delta effects are considered and the structure is also constrained to prevent element buckling. Furthermore, some suitable constraint on the structure ductility is imposed referring to the plastic strains generated during the transient phase structural response. The dynamic structural response is obtained by utilizing an appropriate modal technique referring to the response spectrum defined by the Italian code. The proposed minimum volume design problem 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.