Nonlinear dynamic analysis

Many commercial finite element computer programs (for example ABAQUS, ADINA, ANSYS, DYNA, DYNA3D, LS-DYNA, NASTRAN and NONSAP) arc readily available for nonlinear dynamic analysis. Other computer codes, such as CBARCS, COSMOS/M, STABLE, ANSR 1 have been developed specifically for the design of structures to resist blast toads. All these computer programs possess nonlinear analysis capabilities to varying degrees. 

Nonlinear Dynamic Analysis of Cooling Tower Yeh, Chang-hua... 

However, as discussed in the introduction, living systems can exhibit much more complicated temporal behaviors. The purpose of the present section is to illustrate how different forms of complex dynamics can arise in the electrophysiological activity of pancreatic f) -cells, and to show how these phenomena can be accounted for in a simple nonlinear dynamic analysis. 

Karagueuzian, H., Kogan, B., Khan, S., Denton, T., Karplus, W., Man-del, W., and Diamond, G., Induction of cellular chaos during quinidine toxicity. Predictive power of nonlinear dynamic analysis for drug-induced proarrhythmia-A hypothesis, Journal of Electrocardiology, Vol. 24 Suppl, 1992, pp. 91-96. 

We then use the hypercube representation to carry out a nonlinear dynamical analysis of these networks. The key insight is that quantitative aspects of flows in phase space can be computed from linear fractional maps that represent the flows between boundaries on the hypercube. Analysis is possible because the composition of two linear fractional maps is a hnear fractional map. This analysis is useful for analyzing steady states, limit cycles, and chaotic dynamics in these networks. 

Using a model with lumped masses at two characteristic levels (top and level 1), a nonlinear dynamic analysis was performed with a complex hysteretic (IZIIS) model (Fig. 8.5, Shendova 1998). To calibrate the computations in defining the capacity degradation in hysteretic models, the results from seismic shaking table testing of the model were used. With this, an attempt was made to model the dynamic response in a simple way, suitable for everyday analyses, resulting however in satisfactory final results on the behavior at individual levels. 

A nonlinear dynamic analysis has been performed for the three monuments (Sect. 8.2.3), with the masses lumped at characteristic levels and applying a corresponding storey hysteretic model obtained by summing up the elastoplastic characteristics of each of the bearing walls, with the load-bearing capacity of each of them limited to the bending and shear capacity, whichever is less. 

Analysis of load-bearing and deformation capacity of the structure and nonlinear dynamic analysis for maximum expected actual earthquake effects with intensity of Umax = 0.24g with a return period of 1,000 years. 

Dynamic analysis With the masses lumped at two characteristic levels, a nonlinear dynamic analysis has been performed with storey hysteretic model obtained by summing up the elastoplastic characteristics of each of the bearing walls, whereas the load-bearing capacity of each of them has been limited to the lower value of bending and shear capacity (according to Sect. 8.3.3). To obtain the dynamic response, three different types of earthquake (Petrovac 1979, Ulcinj 1979 and El Centro 1940) with maximum input acceleration of 0.24g and return period of 1,000 years have been applied. Obtained as the results from the dynamic analysis are the storey displacements and ductility ratios required by the earthquake that have to comply with the design criteria defined in Sect. 8.3.4. 

If the footing s safety factor for vertical loads is high, i.e., N N, there is very little hysteresis in cyclic loading and the cyclic M-0 relation is nonlinear-elastic, returning to about zero displacement at zero moment or force and dissipating very little energy. Then Eqs. (15.7) may be applied also in nonlinear dynamic analysis, with the twin springs taken as nonlinear elastic. 

The major computational effort is transferred to the development of a deterministic response database for neural network training. The networks, acting as a substitute for the nonlinear dynamic analysis, make feasible the reliability estimation through direct Monte Carlo simulation, at a small computational cost. 

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

Fig. 4 Hysteretic behavior of a nonlinear viscous damper from nonlinear dynamic analysis (Karavasilis et al. 2012b)...

Figure 6 shows the hysteretic behavior of a typical viscoelastic damper from nonlinear dynamic analysis conducted in Fan (1998). 

In general, the nonlinear dynamic analysis procedure is the most robust procedure available for evaluating the behavior of structures with passive dampers. It allows explicit modeling of individual devices, the elements connecting the devices to the structure, and the structure itself. If the connecting elements or the structural framing yields during the response, this behavior must be incorporated into the analytical model. 

When nonlinear dynamic analysis is used, it is often beneficial to investigate the sensitivity of the stmcture response to one or more systemic parameters. Examples of parameters to vary include ground motion scaling parameters and parameters of the passive dampers (Symans et al. 2008). 

Lin et al. (2013 a) for the first time used the term conditional spectrum which was used to represent an analytical distribution of response spectra in the manner described here. The CS builds upon the CMS (which focuses on the mean) and includes a measure of the variance in addition to the mean. Figure la depicts the analytical distribution of the conditional spectrum with conditional mean spectrum as the thick solid line as well as conditional mean +/— conditional standard deviation as the thick dashed lines. Lin et al. (2013b, c) utilized the conditional spectrum to select ground motions for nonlinear dynamic analysis (also known as response history... 

The conditional spectrum (CS) is a target response spectrum (with mean and variance) for ground motion selection to perform nonlinear dynamic analysis. The computation of the CS requires (1) input earthquake parameters of magnitude, distance, relevant seismological and site characteristics (e.g., fault type and soil type) ... 

Performing IDA is conceptually simple. One only needs to take one record at a time, incrementally scale it at constant or variable IM steps, and perform a nonlinear dynamic analysis each time. Start from a low IM value where the structure behaves elastically, and stop when global collapse is encountered. The latter is defined as the occurrence of a nonsimulated failure mode or the appearance of a global dynamic instability as a collapse mechanism showing infinite EDP values at a given IM level. For a well-executed analysis and robust structural model, global dynamic instabihty manifests itself as numerical nonconvergence. 

The structural analysis involves the definition of the model and selection of the analysis type. The model should represent the stiffness, the mass, and the loads of the structure. The structures can be represented using simplified models, such as the lumped mass models, and advanced models resorting the finite element method (FEM) and discrete element method (DEM). Depending on the characteristics of the structure, different types of analysis can be used such as limit analysis, linear and nonlinear static analysis, and linear and nonlinear dynamic analysis. 

In comparison with the nonlinear static analysis, the nonlinear dynamic analysis, which has attracted more attention in recent years, exhibits a broader range of apphcations. Because nonlinear dynamic analysis is directly based on the structural dynamic equation, the displacement, velocity, and acceleration of each story of a building and the internal forces, cracking, and yielding of the individual structural components of a building can be obtained... 

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