Nonlinear Time History analysi

Qin, C.L. Zhang, A.H. 2004. Nonlinear time history analysis based on section fiber model. Journal of Zhejiang University (Engineering Science) 39(7) 1003-1008. 

This brief overview deals mainly with the nonlinear procedures in ECS. Other seismic codes contain similar approaches (ATC 40, 1996 EEMA 356, 2000). Two nonlinear methods of analysis are considered in ECS the nonlinear pushover analysis (NPO) and the nonlinear time history analysis (NTH). 

The nonlinear time-history analysis is the most general nonlinear method of analysis. It is deemed unpractical by some becanse of the compntational length of the analysis, but as computer speeds increase, NTH becomes increasingly feasible. Time-history analysis is a general dynamic method of analysis and there are no compntational peculiarities related to earthquake engineering analysis. The inpnt force is the inpnt ground motion, expressed in the form of one or more accelerograms. The dynamic equations of motion are ... 

A novel solution proposed by Han et al. (2012) used a GPU to accelerate urban seismic damage prediction based on refined building models and nonlinear time-history analysis (THA). Figure 2 shows the flow chart of the Han s program in which the CPU reads the data, copies the data into the GPU, and assigns the computational tasks to each GPU core, whereas the GPU implements the nonlinear THA for individual buildings and copies the results back to the host memory for output. 

Fan (1998) investigated the behavior of nonductile reinforced concrete frame buildings with viscoelastic dampers. He derived an equivalent elastic-viscous model based on the complex stiffness and energy dissipation of the viscoelastic system and proposed a simplified design procedure for a stmcture with viscoelastic dampers. Lee et al. (2005, 2009) applied this method to structures with elastomeric dampers and validated the simplified design procedure by comparing the design demand with the results from nonlinear time-history analysis. 

Performance-Based Design Procedure for Structures with Magneto-Rheological Dampers, Table 5 Median and standard deviation of maximum and residual story drift from nonlinear time history analysis... 

The simplified analysis procedure enables the design demand to be determined without performing a nonlinear time-history analysis by linearizing the structure and utilizing the response spectrum analysis method. 

The current trend in seismic design of dams is to conduct linear or nonlinear time-history analysis to obtain dynamic response of dam to earthquake loads. Time-history analysis of dam requires input ground motion time histories (acceleration, velocity, and displacement). 

The EDPs required in this approach for loss calculations are interstory drift ratio (SDR), peak floor accelerations (PFA), and residual drift ratio (ResDR). The SDR values are used to predict the damage of SD and NSD components at each story level, the PFA values are used to predict those of the NSA components, and ResDR is used to determine if a building would have to be demolished after an earthquake. The EDPs are first calculated based on nonlinear time-history analysis of buildings for a suite of grormd-motion records. But it is nearly impossible to select records that satisfy conditional distribution of Sa at multiple periods (which is can be more than ten for tall buUdings) (see, e.g., Jayaram et al. 2012). Hence it is efficient and also accurate to fit regression models to predict independently the different EDPs at different stories and use these fitted models subsequently to estimate the EDPs for the simulated response spectra, which have the right conditional distribution of S iT). 

Hence the pirrpose of computing these EDPs by nonlinear time-history analysis for different recorded groimd motions is to develop regression models to predict EDPs as functions of Sa(T) while carrying out simulations. 

Nonlinear dynamic analysis is undoubtedly the most realistic and accurate analysis method available. It is also referred as nonlinear time history analysis, nonlinear response history analysis, or according to ASCE 41-06 (2007) as nonlinear dynamic procedure (NDP). Earthquake loading is taken into consideration as a natural or a synthetic ground motion on a structural model... 

The theory of elasto-plastic time history analysis based on section fiber model has been rapid developed in recent years, especially in seismic technology developed country such as American and Japan (D Ambrisi Filippou 1999, Spacone et al. 1999). In this paper, Shenzhen Nanshan Bridge is taken as the engineering background. Time history method based on section fiber model is used to analyze the nonlinear seismic responses of the bridge under rare earthquake. 

Preparation of 3D dynamic models suitable for a time history analysis of the racks which includes the assemblage of all racks in the SFP, all fluid coupling interactions, and mechanical couplings appropriate for a nonlinear simulation. 

Nonlinear dynamic analysis Nonlinear response history analysis Time history analysis... 

If the response is obtained from at least seven nonlinear time-history analyses with (triplets or pairs of) ground motions chosen in accordance with the above, the relevant verifications may use the average of the response quantities from all these analyses as action effect. The set of seven pairs in Fig. 4 meets this condition for analysis in 3D under two simultaneous horizontal components of ground motion. If less records are used (but not less than three), the most unfavorable value of the response quantity among the analyses should be used. 

Use the nonlinear time-history dynamic analysis to check the design performance of building structure under an ensemble of selected ground motions scaled to match the design response spectrum corresponding to 2 % probability of exceedance in 50 years (NBCC 2010). 

For a nonlinear earthquake analysis (time-history analysis), the general equation of motion in the incremental form... 

Both deterministic and stochastic simulations can be used for response-history dynamic analysis, but only stochastic simulations can be utilized for stochastic dynamic (i.e., random vibration) analysis, because the latter analysis method requires a random process model of the earthquake ground motion. Synthetic ground motions are particularly useful for nonlinear dynamic analysis due to the scarcity of recorded motions for large-magnitude earthquakes that are capable of causing nonlinear responses. Two approaches are available for nonlinear dynamic analysis of structures subjected to earthquakes (1) nonlinear response-history analysis by the use of a selected set of ground motion time series and (2) nonlinear stochastic dynamic analysis by the use of a stochastic representation of the ground motion. 

The response sensitivity, probabilistic response and reliability analysis methods presented are based on nonlinear FE quasi-static pushover and time-history analyses, which are used extensively in earthquake engineering and referred to by structural design codes. 

The treatment of uncertainties requires the use of probabilistic methods, estimating the probability of exceeding response targets for the different performance requirements, for example, on an annual basis. The dynamic structural responses are highly nonlinear, and their time history must be found by numerical (e.g., finite elements) analysis for the duration of the earthquake. In a thorough analysis, the nonlinearity of the response is further increased when the interactions between the structure and the foundations are included. It is not possible to establish an explicit relationship between the intervening variables and the dynamic responses, and results can only be obtained in a discrete manner, given specific values of the structural variables and a particular earthquake record. Reliability calculations depend on simulations... 

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