Parametric optimization of laminated rubber bearing with pre-tensioned superelastic SMA springs using minimum mean energy criterion

The seismic optimization design of nonlinear isolation device is a challenging problem. To solve this problem, a new minimum mean energy criterion is presented, on which basis a new mechanical energy-based optimization method is developed to optimize the parameters of laminated rubber bearings with pre-tensioned shape memory alloy (SMA) springs. First, the equation of motion of a multi-degree-of-freedom (MDOF) building with isolation bearings is established, and the force-displacement relation of the pre-tensioned SMA spring is provided. Additionally, the minimum mean energy criterion, which describes the relationship between the mechanical energy and structural responses, is provided. In accordance with this new energy criterion, the parameters of the pre-tensioned SMA springs are optimized. A case study of a six-story reinforced concrete base-isolated building shows that compared with those of the dissipation energy-to-input energy ratio-based and isolator displacement-based optimization methods, the mean values of the maximum inter-story drift, maximum base shear force and maximum absolute acceleration of the proposed optimal system are reduced by 11%, 11% and 14%, respectively, whereas the mean maximum isolator displacement decreases by 29% compared with that of the acceleration-based optimal system. Furthermore, compared with the multi-objective optimization method, the proposed method can reasonably determine the optimal solution due to the usage of the minimum mean energy criterion, which doesn’t need to manually select a final solution from a series of feasible solutions. Under different earthquake waves, the vibration reduction performance of the isolation bearing designed by the proposed method is more stable than that of the bearing designed by the multi-objective optimization method.