Research On Stochastic Optimization Method For Seismic Mitigation Of Structures Under Non-stationary Earthquake Excitation

China is an earthquake-prone country,and the damage of civil structures,e.g.,buildings and bridges,may pose a great threat to the security of peoples’ lives and properties.Building structures and bridge structures are the barriers of disaster resistance and the lifelines of disaster relief,respectively,and their earthquake resistance capacity and resilience capacity are of vital importance to the earthquake relief and the post-earthquake recovery.As the standard of seismic design increases,the energy-dissipating techniques have been developed rapidly and used widely for the structures exposed to seismic hazard.The energy-dissipating dampers can provide damping to the primary structures and dissipate the earthquake energy imposed on the structures.To obtain a better performance of seismic mitigation,it is required that the parameters and layouts of energy-dissipating dampers should be determined through an optimal design procedure.Due to the inherent uncertainty of the seismic excitation,a large limitation of application may exist in the traditional deterministic optimal design methods of energy-dissipating structures only based on several ground motion accelerations.In view of this,it is necessary to introduce the random vibration theory into the optimal design of energy-dissipating structures,and the optimization results can naturally reflect the random characteristic of the seismic excitation.However,in the stochastic optimal design of energy-dissipating structures,generally speaking,large-scale nonstationary random vibration problems and the corresponding sensitivity problems of nonlinear structures need to be solved iteratively,and traditional random vibration methods still can not be applied to engineering structures.To tackle this difficult task,this dissertation is dedicated to developing an explicit time-domain approach for the nonstationary random vibration analysis and the corresponding sensitivity analysis of linear and nonlinear energy-dissipating structures.On the above basis,combining the random vibration theory with the optimal design theory,an efficient stochastic parametric and topology optimization framework of energy-dissipating dampers is proposed.The current research can facilitate the engineering application of the stochastic optimal design method of the energy-dissipating structure.The main contributions of this dissertation are described as follows:(1)A literature review is carried out for the linear and nonlinear random vibration analysis methods of energy-dissipating structures,the sensitivity analysis methods of linear and nonlinear random vibration of energy-dissipating structures,and the stochastic parametric and layout optimization methods of energy-dissipating dampers.(2)An explicit time-domain method(ETDM)is proposed for the random vibration analysis and the corresponding sensitivity analysis of energy-dissipating structures installed with fractional viscoelastic dampers under nonstationary seismic excitation.Employing the Newmark-β integration scheme as well as the direct differentiation method(DDM)and the adjoint variable method(AVM)for sensitivity analysis,the explicit time-domain expressions of dynamic responses and their sensitivities are first derived for fractionally-damped systems,which reveals the physical evolution mechanism of the fractionally-damped system.On this basis,with the moment operation rule,the evolutionary statistical moments of responses and moment sensitivities are obtained,and an ETDM is proposed for the nonstationary random vibration analysis and the corresponding sensitivity analysis of energy-dissipating structures with fractional viscoelastic dampers.A numerical example involving a shear-type structure with fractional viscoelastic dampers under nonstationary seismic excitation is investigated to demonstrate the accuracy and efficiency of the proposed method.(3)An equivalent linearization – explicit time-domain method(EL-ETDM)is proposed for the random vibration analysis and the according sensitivity analysis of energy-dissipating structures equipped with nonlinear viscous dampers or nonlinear hysteretic dampers subjected to nonstationary seismic excitation.Employing the statistical linearization technique and the DDM for sensitivity analysis,the equivalent linear equation of motion and linear sensitivity equation for the original energy-dissipating structure with nonlinear dampers are constructed,and the ETDM is utilized to iteratively solve the response statistics and moment sensitivities with high efficiency.On this basis,the EL-ETDM is proposed for the nonstationary random vibration analysis and the according sensitivity analysis of energy-dissipating structures with nonlinear dampers.Two numerical examples involving a shear-type structure with nonlinear viscous dampers and a shear-type structure with nonlinear hysteretic dampers subjected to nonstationary seismic excitation are investigated to demonstrate the computational accuracy and efficiency of the proposed method.(4)A stochastic parametric optimization framework is proposed for energy-dissipating dampers under nonstationary seismic excitation.The mathematical model of the stochastic parametric optimization problem of energy-dissipating dampers is constructed,in which the design variables are taken as the damper parameters,and the objective function and the constraint function are determined according to the performance requirement of the energydissipating structure and the performance index of the energy-dissipating damper,respectively.The stochastic parametric optimization problem is solved using the gradient-based method of moving asymptotes(MMA),and the repetitive nonstationary random vibration analyses and the corresponding sensitivity analyses are conducted with the proposed explicit time-domain approach.On this basis,an ETDM-based stochastic parametric optimization framework is proposed for the energy-dissipating dampers under nonstationary seismic excitation.Three numerical examples including a shear-type structure with fractional viscoelastic dampers,a shear-type structure with nonlinear hysteretic dampers and a long-span suspension bridge with nonlinear viscous dampers are investigated to demonstrate the feasibility of the proposed method.(5)A stochastic topology optimization framework is proposed for energy-dissipating dampers under nonstationary seismic excitation.The mathematical model of the stochastic topology optimization problem of energy-dissipating dampers is constructed.The objective function and the constraint function are determined based on the performance requirement of the energy-dissipating structure and the performance index of the energy-dissipating damper,respectively.The design variables are taken to be the damper parameters and the existence parameters,and the solid isotropic material with penalization technique is utilized to build the connection between the performance of dampers and these design variables.The present stochastic topology optimization problem is solved using the gradient-based MMA,and the repeated nonstationary random vibration analyses and the corresponding sensitivity analyses involved are conducted with the proposed explicit time-domain approach.An ETDM-based stochastic topology optimization framework is therefore proposed for the energy-dissipating dampers considering nonstationary seismic excitation.Three numerical examples involving a shear-type structure with fractional viscoelastic dampers,a planar frame structure with nonlinear hysteretic dampers and a building frame structure with nonlinear viscous dampers are investigated to demonstrate the feasibility of the proposed method.The results of the current research show that the proposed two methods,i.e.,the ETDM for fractionally-damped systems and the EL-ETDM for nonlinear systems can effectively solve the random vibration problems and the corresponding sensitivity problems of energydissipating structures under nonstationary seismic excitation.The present methods can break through the limitation on computation scales of the traditional random vibration methods,and can yield the results with good accuracy and high efficiency.On this basis,the proposed stochastic parametric and topology optimization framework can obtain reasonable optimal damper parameters and optimal layout schemes with high efficiency,and therefore they are applicable to the engineering practice.