Stochastic Seismic Response Analysis And Optimization Design Of Damage-reduction System

With the rapid development of economy and society,there will be more serious consequences for the buildings suffering earthquakes,which puts forward new requirements for performance-based seismic design.Damage-reduction design is one of the basic methods of structural seismic design by designing the whole structure as two parts:the main part for structural function and the secondary part of structural fuses to dissipate seismic energy.However,the damage-reduction system includes main function part and structural fuses,so the structural characteristics are more complex,and the correlation among randomness of ground motions,structural parameters and responses are considerable.It is extremely difficult to calculate the random response of the damage-reduction system efficiently,and it is also necessary to improve the structural design process of deamage-reduction system.Moreover,for the life-cycle cost optimization of damage-reduction structures,further research on damage assessment in consideration of stochastic damage index and fuzzy damage limit states are needed.This paper is funded by National Natural Science Foundation of China,the project of"Research on integration of earthquake evolution of major buildings and bridges" in the major project of "Damage evolution of civil infrastructures under strong earthquake and wind",and focuses on the random response analysis method,damage-reduction structural design and life-cycle optimization method of the damage-reduction system with structural fuses under earthquakes.Firstly,an approximate method of multi-mode pushover analysis based on energy balance is introduced to take into account the higher mode effects,which is a development of capacity method with formats of energy demand and capacity diagrams.Two kinds of modified methods are proposed to improve the computational efficiency.One is the combination method in which solution of pushover analysis and higher-order elastic solutions are combined in modal analysis.The other is the envelope method in which the envelope of pushover response and all the elastic responses from modal analysis is considered.The results of examples show the effectiveness of the proposed method.Secondly,stochastic damage-reduction spectrum is proposed based on stochastic synthetic ground motions.A dimensionless single-degree-of-freedom system with trilinear restoring force is obtained via structural pushover analysis.And a stochastic model of ground motions is introduced to simulate earthquake excitation.Then stochastic damage-reduction spectrum is proposed and the parameter set of the stochastic damage-reduction spectrum is studied.An example of 9-story building with buckling restrained braces is presented to demonstrate the advantages of the stochastic damage-reduction spectrum,compared the design obtianed by the determinstic damage-reduction spectrum.Thirdly,a general framework for the stochastic seismic analysis of buildings with structural fuses based on copula model is established.To implement the stochastic analysis,the copula model is introduced as an advanced uncertainty statistics method,which can connect any marginal distribution functions to a joint distribution function.The proposed stochastic analysis method based on copula model is equivalent to establish the "spectrum" of the structural response distribution through the joint probability distribution of copula function,which simplifies the structural stochastic analysis and improves the structural optimization efficiency.Then the stochastic analysis of damage-reduction system is calculated as the conditional distribution function of joint distribution.A single degree of freedom model for damage-reduction system is used to examine the specific implementation of stochastic analysis based on copula theory.Finally,a multi-objective life-cycle cost optimization design method of damage-reduction system is studied.The structural life-cycle cost is mainly composed of the initial cost of structural materials and the damage loss in the life-cycle.Considering the opposing characteristics of the two parts,a multi-objective optimization strategy is used to establish the life-cycle optimization process of damage-reduction system.Aiming at the difficulty of life-cycle damage assessment in damage-reduction system,the stochastic seismic analysis technology based on copula function is used to model the damage index and the fuzzy function is used to model the damage limit state.Taking the size and layout of amage-reduction components as design variables,a optimization design of typical damage-reduction frame structure is performed by using NSGA-Ⅱ algorithm,and the results are discussed.