Reliability-based topology optimization of fractionally-damped structures under nonstationary random excitation

Abstract

This contribution proposes an effective reliability-based topology optimization (RBTO) framework for the layout of viscoelastic dampers of energy-dissipating structures under nonstationary seismic excitation, in which the constitutive behavior of viscoelastic damper is described by the novel fractional derivative models. To formulate the RBTO problem, the installation number of fractional viscoelastic dampers is minimized under the constraints of dynamic reliability, and the design variables are chosen as the damper parameters and the existence variables of the potential fractional viscoelastic dampers. The explicit responses are first established for the fractionally-damped structure, and the explicit response sensitivities with respect to the design variables are further derived through the adjoint variable method (AVM). On this basis, an explicit time-domain method (ETDM) is developed for explicit formulation of the statistical moments of responses and the moment sensitivities of the fractionally-damped structure, which are further employed to analytically derive the first-passage dynamic reliabilities and the reliability sensitivities of the structure based on the classical level-crossing process theory. Finally, the RBTO problem for the layout of fractional viscoelastic dampers is solved with the gradient-based method of moving asymptotes (MMA), in which the existence variables of fractional viscoelastic dampers can be driven to binary solutions by the solid isotropic material with penalization (SIMP) technique. An engineering application involving a building frame structure installed with fractional viscoelastic dampers is presented to validate the feasibility of the proposed ETDM-based RBTO framework.