Optimal Seismic Design of Multiple Isolation Systems and Viscous Dampers in Vertically Irregular Frame Buildings

This paper presents a gradient‐based optimization framework for the preliminary seismic design of alternative isolation systems and fluid viscous dampers in vertically irregular 2D shear frames. The proposed method simultaneously optimizes the number, locations, and properties of isolation layers together with viscous damper coefficients, allowing base isolation to naturally emerge as an optimal configuration when appropriate. This is done while adopting an equivalent linear model of the isolators. The methodology integrates the mixed Lagrangian formulation as analysis, adjoint sensitivity, the solid isotropic material with penalization (SIMP) approach, and penalty functions to minimize realistic costs while satisfying drift constraints (at both isolation levels and regular stories) and absolute floor acceleration limits, while also achieving binary (active/inactive) topology decisions for isolation placement. A numerical example using a suite of ground motions demonstrates the method's efficiency, achieving convergence in 330 iterations and a final design cost 4.7% lower than particle swarm optimization (PSO) while requiring three orders of magnitude fewer function evaluations. Results confirm that multi‐floor isolation can achieve target seismic performance at significantly lower cost than conventional base isolation. Additionally, a comparison with nonlinear time‐history analysis was performed, which highlighted the differences between linear and nonlinear responses and emphasized the importance of such analysis in the design verification stage to accurately capture the true seismic behavior. These findings underscore the method's computational efficiency, cost‐effectiveness, and applicability to complex irregular buildings.