On the structural optimization in presence of base isolating devices

Abstract

The minimum volume design of plane frames constituted by elastic perfectly plastic material and subjected to appropriate combinations of fixed, cyclic and dynamic loads is studied. The influence on the design, in terms of cost (volume) and behavioural features, of seismic protecting devices is particularly focused. The considered protecting device is a lead rubber bearing base isolation system. Two optimal design problem formulations are proposed for the structure with or without the protecting device, both based on the so-called statical approach. The minimum volume frame is reached accounting for three different resistance limits: the purely elastic limit, the (elastic) shakedown limit and the instantaneous collapse limit. The adopted load combinations are alternatively characterized by the presence of only fixed loads, of amplified fixed loads and quasi-static perfect cyclic loads due to the wind action, of suitably reduced fixed loads and dynamic actions due to the earthquake. The linear elastic effects of the dynamic actions are studied by utilizing a modal technique. Reference is made to the most recent Italian code related to the structural analysis and design. The solution of the optimization problem is reached by using a suitable subroutine available into the optimization toolbox of MATLAB® appropriate to the proposed formulations. A flexural frame is studied with and without the relevant seismic protecting device in order to study the influence on the design of such a base isolation system. The related minimum volume structures are obtained assuming the stiffness and the damping feature of the base isolation system as variables within assigned suitable ranges. The Bree diagrams of the obtained optimal designs are also determined in order to characterize and compare their structural and safety behaviour