Optimization of inelastic multistory structures under seismic vibrations using shape-memory-alloy material

This paper develops a novel optimization methodology for designing Shape-memory-alloy resisting devices (SMARDs) and optimally allocating them to inelastic multistory structures. The solution algorithm is a control gains optimization procedure that refers to a formal optimization problem with an objective function subject to the state-space equation and design limitations. The objective function integrates the squared state components in time, and the state-space equation consists of a newly introduced state vector form that reflects the system's inelasticity. The control gains are the number of total Shape-memory-alloy (SMA) wires attached to the devices in each story, and the design limitations dictate the minimum/maximum number of wires. The solution algorithm consists of five iterative steps that employ the defined Hamiltonian gradients in state and gains and cater to the necessary optimality conditions. The numerical example deals with upgrading an eight-story shear-type frame system. It studies the algorithm efficiency and elaborates on the effect of the optimal weighting matrix by investigating three different configurations. In all cases, the algorithm improves the system's inelastic seismic response—showcasing the reliability of the developed design methodology and the utilization of SMA material.