Seismic topology optimization based on spectral approaches

Abstract

In this study, the structural design problem under earthquake excitations is handled using the proposed topology optimization scheme that successfully copes with the complexity of seismic loading. To achieve this success, the optimization scheme is formulated based on response spectrum method, adequately balancing the accuracy and computational cost in calculating seismic responses of structures. Also, an interpolation strategy, providing smooth curves to supersede the non-differentiable response spectra, is suggested to ensure that the derivatives of spectral values can be obtained for the sensitivity analysis. In addition, the terms including the derivatives of eigenvectors in the sensitivity expressions are annihilated through the derived adjoint approach, which is more accurate and convenient compared with directly solving the derivatives of eigenvectors. In the present numerical examples, the specified seismic responses of the optimized structures are significantly reduced, and these reductions are also observed in the time-domain measurement. Therefore, the efficacy of the proposed optimization scheme is validated.