Use Of Nonlinear Analysis Research Articles

Sensitivity to Constitutive Modeling in Fiber-Based Discretization of Reinforced Concrete Members for Performance-Based Seismic Evaluation

Accurate constitutive models of the constituent materials in a reinforced concrete (RC) section, namely, unconfined concrete, confined concrete and reinforcing steel are necessary in fiber-based discretization of RC components for use in nonlinear analysis of RC structures. This paper examines the sensitivity to different constitutive models in predicting the inelastic seismic behavior of RC frame structures. In particular, the importance of incorporating confinement effects in modeling concrete behavior and including degrading effects in modeling the behavior of reinforcing steel bars so as to predict the monotonic, cyclic and seismic response of RC columns and frames is investigated. At the component level, it is shown that the inelastic response is controlled predominantly by the behavior of reinforcing steel. At the system level, the response of non-ductile structures is less sensitive to confined concrete models while the modeling of reinforcing steel is shown to influence the inelastic response of both non-ductile and ductile structures.

Usefulness of Nonlinear Analysis of ECG Signals for Prediction of Inducibility of Sustained Ventricular Tachycardia by Programmed Ventricular Stimulation in Patients with Complex Spontaneous Ventricular Arrhythmias

The aim of our study was to assess the effectiveness of the nonlinear analysis (NLA) of ECG in predicting the results of invasive electrophysiologic study (EPS) in patients with ventricular arrhythmias. We evaluated 25 patients with history of cardiac arrest, syncope, sustained, or nonsustained ventricular tachycardia (VT). All patients underwent electrophysiologic study (EPS) and nonlinear analysis (NLA) of ECG. The study group was compared with a control group of 25 healthy subjects, in order to define the normal range of NLA. ECG was processed in order to obtain numerical values, which were analyzed by nonlinear mathematical functions. Patients were classified through the application of a clustering procedure to the whole set of functions, and the correlation between the results of nonlinear analysis of ECG and EPS was tested. NLA assigned all patients with negative EPS to the same class of healthy subjects, whereas the patients in whom VT was inducible had been correctly and clearly isolated into a separate cluster. In our study, the result of NLA with application of the clustering technique was significantly correlated to that of EPS (P < 0.001), and was able to predict the result of EPS, with a negative predictive value of 100% and a positive predictive value of 100%. NLA can predict the results of EPS with good negative and positive predictive value. However, further studies are needed in order to verify the usefulness of this noninvasive tool for sudden death risk stratification in patients with ventricular arrhythmias.

Magnetosensory evoked potentials: Consistent nonlinear phenomena

Electromagnetic fields (EMFs) having strengths typically found in the general environment can alter brain activity, but the reported effects have been inconsistent. We theorized that the problem arose from the use of linear methods for analyzing what were actually nonlinear phenomena, and therefore studied whether the nonlinear signal-processing technique known as recurrence quantification analysis (RQA) could be employed as the basis of a reliable method for demonstrating consistent changes in brain activity. Our primary purpose was to develop such a method for observing the occurrence of evoked potentials in individual subjects exposed to magnetic fields (2 G, 30 and 60 Hz). After all conditions that affected the analysis of the EEG were specified in advance, we detected magnetosensory evoked potentials (MEPs) in all 15 subjects ( P < 0.05 in each experiment). The MEPs, which occurred within the predicted latency interval of 109–504 ms, were independent of the frequency and the direction of the field, and were not detected using the traditional linear method of analysis, time averaging. When the results obtained within subjects were averaged across subjects, the evoked potentials could not be detected, indicating how real nonlinear phenomena can be averaged away when the incorrect method of analysis is used. Recurrence quantification analysis, but not linear analysis, permitted consistent demonstration of MEPs. The use of nonlinear analysis might also resolve apparent inconsistencies in other kinds of brain studies.

Selection of ground motion time series and limits on scaling

A procedure to select time series for use in non-linear analyses that are intended to result in an average response of the non-linear system is proposed that is not based simply on magnitude, distance, and spectral shape. A simple model of a yielding system is used as a proxy for the non-linear behavior of a more complicated yielding system. As an example, Newmark displacements are used as a proxy for more complex slope-stability models. The candidate scaled time series are evaluated to find those that yield a response of the simple non-linear system that is near the expected response for the design event. Those scaled time series with responses near the expected value are selected as the optimum time series for defining average response even if the scale factors are larger than commonly accepted (e.g. scale factors >factor of 2).

Density waves in the full velocity difference model

Density waves are investigated in the full velocity difference model (FVDM) analytically and numerically. By the use of nonlinear analysis, the Burgers, Korteweg–de Vries (KdV) and Modified KdV equations are derived for the triangular shock wave, the soliton wave and the kink–antikink wave, respectively, appearing in the stable region out of the coexisting curve, near the spinodal line, and in the unstable region within the spinodal line. It is shown, numerically, that the triangular shock wave and the soliton wave are determined by the initial perturbation configuration and different initial perturbations will produce different waveforms in the stable region or near the spinodal line.

On a composite implicit time integration procedure for nonlinear dynamics

Transient analysis of nonlinear problems in structural and solid mechanics is mainly carried out using direct time integration of the equations of motion. For reliable solutions, a stable and efficient integration algorithm is desirable. Methods that are unconditionally stable in linear analyses appear to be a natural choice for use in nonlinear analyses, but unfortunately may not remain stable for a given time step size in large deformation and long time range response solutions. A composite time integration scheme is proposed and tested in some example solutions against the trapezoidal rule and the Wilson θ-method, and found to be effective where the trapezoidal rule fails to produce a stable solution. These example results are indicative of the merits of the composite scheme.

Predictions of the uplift response of model belled piles in geogrid-cell-reinforced sand

Breakout factors from a series of laboratory pullout tests on model-belled piles (or enlarged base footings) in geogrid-cell-reinforced sand, which included tests on various model geometries and sand densities, are examined. The concept of effective diameter and effective embedment ratio based on the diameters of both belled piles and geogrid-cell-reinforcement is introduced which provides a pattern of uplift behaviour consistent with previous findings for anchor-type foundations. A unique relationship between effective breakout factor and effective embedment ratio is derived for a given sand density. Experimental breakout factors compare well with predictions from some existing theories for anchor foundations, while a simple approach based on the vertical slip surface model incorporating an uplift coefficient K=0.8√ K P yields close overall agreement with the laboratory data. A hyperbolic relationship is established between pullout load and displacement, which can be used to determine soil stiffness for use in non-linear analyses.

Density waves in traffic flow.

Density waves are investigated in the car-following model analytically and numerically. This work is a continuation of our previous investigation of traffic flow in the metastable and unstable regions [Phys. Rev. E 58, 4271 (1998); 60, 180 (1999)]. The Burgers equation is derived for the density wave in the stable region of traffic flow by the use of nonlinear analysis. It is shown, numerically, that the triangular shock wave appears as the density wave at the late stage in the stable region. The decay rate of the shock wave is calculated and compared with the analytical result. It is shown that the density waves out of the coexisting curve, near the spinodal line, and within the spinodal line appear, respectively, as the triangular shock wave, the soliton, and the kink-antikink wave. The density waves are described, respectively, by the Burgers, Korteweg-de Vries, and modified Korteweg-de Vries equations.

Jamming transition in a two-dimensional traffic flow model.

Phase transition and critical phenomenon are investigated in the two-dimensional traffic flow numerically and analytically. The one-dimensional lattice hydrodynamic model of traffic is extended to the two-dimensional traffic flow in which there are two types of cars (northbound and eastbound cars). It is shown that the phase transition among the freely moving phase, the coexisting phase, and the uniformly congested phase occurs below the critical point. Above the critical point, no phase transition occurs. The value a(c) of the critical point decreases as increasing fraction c of the eastbound cars for c<or=0.5. The linear stability theory is applied. The neutral stability lines are found. The time-dependent Ginzburg-Landau (TDGL) equation is derived by the use of nonlinear analysis. The phase separation lines, the spinodal lines, and the critical point are calculated from the TDGL equation.

The use of non-linear analysis for differentiating the biomagnetic activity in ovarian lesions

In this study we investigated the biomagnetic activity measured with the superconducting quantum interference device (SQUID) in benign and malignant ovarian lesions using non-linear analysis. We used a single channel biomagnetometer SQUID in order to measure the magnetic field emitted from benign and malignant ovarian lesions. We can differentiate such biomagnetic activities using non-linear analysis. Using the application of non-linear analysis in the ovarian lesions together with the use of dimensional calculations we have observed a clear saturation value for the dimension of malignant ovarian lesions and non-saturation for benign ovarian lesions. The biomagnetic measurements with the SQUID and the application of non-linear analysis in benign and malignant ovarian lesions, is a promising procedure in assessing and differentiating ovarian tumours.

Prediction of shear strength of reinforced concrete beams by nonlinear finite element analysis

This paper describes the results of a nonlinear finite element analysis to predict the shear strength of rectangular reinforced concrete beams using a single material model for concrete. Over one hundred beams were analysed covering all important parameters governing shear strength. The results of the analysis enable one to predict ‘good’ lower bound to the experimental values. Unlike many investigations, emphasis was placed not only on good prediction of the ultimate shear strength, but also on the fact that the predicted mode of failure corresponded closely with the observed mode of failure. It is hoped that the investigation will encourage wide spread use of nonlinear analysis to predict the performance of unconventional structures.

The use of non-linear analysis of the primate ERG to detect retinal dysfunction

Serial ERG's were recorded from rhesus monkey eyes after a standard posterior penetrating ocular injury and simulated vitreous hemorrhage caused by the injection of 0·5 ml of autologous blood. As reported previously, this procedure resulted in a progressive reduction, to virtual extinction, of the ERG, followed by a remarkable recovery over a period of 8–10 weeks. In this study, the a- and b-waves of the flash evoked ERG were compared with similar features of the response to a rapid random flash stimulus. The first order kernel (KF) like the flash response underwent progressive changes, during the 12 week recovery period, in amplitude and waveform. Its a-wave, like the flash a-wave was substantially recovered by 126 days. Its b-wave, however, showed much less recovery than the flash b-wave. This b-wave depression in the KF reflects a defect in rapid adaptation of the retina. It is conveniently evaluated as the ratio of first to second order kernels, (-KS/KF), called the adaptation index. This measure was abnormal in the post-operative retina for the b-wave but not the a-wave permitting the conclusion that the defect is postsynaptic to the receptors.