Modeling Of Nonlinear Behavior Research Articles

Finite Element Simulation of a Full-Scale Crash Test of a Composite Helicopter

Finite Element Simulation of a Full-Scale Crash Test of a Composite Helicopter

Selecting nonlinear model structures for computer control

Many authors have noted the difficulty of developing the models required for nonlinear model predictive control (NMPC) and other nonlinear, model-based control strategies. One reason this task is difficult is that success depends strongly on initially selecting a reasonable structure for this nonlinear model. Unfortunately, this selection is extremely difficult because most of our intuition about structure/behavior relations (e.g., if the step response exhibits overshoot, a model of at least second order is required) is based on experience with relatively low-order linear models and often fails completely when confronted with comparably simple nonlinear models. To help bridge this chasm between nonlinear model behavior and our linear intuition, this paper describes some broad classes of nonlinear model structures, which may be approximately characterized as mildly nonlinear, strongly nonlinear, or of intermediate nonlinearity, depending on the different ways they violate linear intuition. It is hoped that these results will be useful in selecting simple nonlinear model structures for use in model-based control.

Solution strategies for FEM analysis with nonlinear viscoelastic polymers

The Schapery model is a very common model for nonlinear viscoelastic behaviour of polymers. Therefore this model has been implemented with a user subroutine into the FEM package MARC. Since explicit integration is relatively fast but is often accompanied by numerical instabilities and implicit integration is relatively slow but numerically stable, combined strategies have been programmed. Results show that the viscoelastic response of complex products can be calculated without numerical instabilities and with short calculation times. Full viscoelastic calculations and calculations using creep isochrones on dead weight loading of an HDPE bottle crate only differ from the onset of creep buckling.

Development of adaptive modeling techniques for non-linear hysteretic systems

Adaptive estimation procedures have gained significant attention by the research community to perform real-time identification of non-linear hysteretic structural systems under arbitrary dynamic excitations. Such techniques promise to provide real-time, robust tracking of system response as well as the ability to track time variation within the system being modeled. An overview of some of the authors’ previous work in this area is presented, along with a discussion of some of the emerging issues being tackled with regard to this class of problems. The trade-offs between parametric-based modeling and non-parametric modeling of non-linear hysteretic dynamic system behavior are discussed. Particular attention is given to (1) the effects of over- and under-parameterization on parameter convergence and system output tracking performance, (2) identifiability in multi-degree-of-freedom structural systems, (3) trade-offs in setting user-defined parameters for adaptive laws, and (4) the effects of noise on measurement integration. Both simulation and experimental results indicating the performance of the parametric and non-parametric methods are presented and their implications are discussed in the context of adaptive structures and structural health monitoring.

Whole learning algorithm of the neural network for modeling nonlinear and dynamic behavior of RC members

A new sort of learning algorithm named whole learning algorithm is proposed to simulate the nonlinear and dynamic behavior of RC members for the estimation of structural integrity. A mathematical technique to solve the multi-objective optimization problem is applied for the learning of the feedforward neural network, which is formulated so as to minimize the Euclidean norm of the error vector defined as the difference between the outputs and the target values for all the learning data sets. The change of the outputs is approximated in the first-order with respect to the amount of weight modification of the network. The governing equation for weight modification to make the error vector null is constituted with the consideration of the approximated outputs for all the learning data sets. The solution is neatly determined by means of the Moore-Penrose generalized inverse after summarization of the governing equation into the linear simultaneous equations with a rectangular matrix of coefficients. The learning efficiency of the proposed algorithm from the viewpoint of computational cost is verified in three types of problems to learn the truth table for exclusive or, the stress-strain relationship described by the Ramberg-Osgood model and the nonlinear and dynamic behavior of RC members observed under an earthquake.

Application of a model of nonlinear history-dependent magnetic behavior for inductance estimation of a microinductor

This paper presents a method for the numerical inductance calculation of a passive electromagnetic inductive device using cores made of a nonlinear magnetic material. The material model used for this purpose describes the nonlinear magnetic behavior by a set of differential equations. The coupled implicit system of Maxwell equations and material model equations is solved by a simplified algorithm which shall be explained while applied to a new design of a microinductor, the so called I-inductor.

Genetic evolution of nonlinear material constitutive models

Material constitutive model is highly nonlinear and multimodal in the large parameter space. A genetic evolution algorithm is thus proposed for its recognition. The nonlinear stress–strain relationship presented by several added multinomials, whose structure is not simplified, is automatically recognized from global response information, e.g., load vs. reflection data, obtained from a structure test through genetic evolution in global space. Nonlinear finite element analysis is used as a bridge to build a relationship between stress–strain data and load–deflection information. The potential of the proposed method is demonstrated by applying it to the macro-mechanical modeling of nonlinear behavior in advanced composite materials. A nonlinear material model for the ply is recognized using experimental results on a lamina plate [(±45)6]s to be a modification of Hahn–Tsai model [H.T. Hahn, S.W. Tsai, J. Compos. Mater. (1973) (7) 102]. The obtained nonlinear constitutive model is subsequently used to predict nonlinear behaviors of the [(±30)6]s and [(0/±45)4]s plates. The results are satisfying. This modeling procedure can be used as a method to guide to improve analysis of nonlinear behavior and damage of composite materials.

Case studies on the use of neural networks in eutrophication modeling

Artificial neural networks are becoming more and more common to be used in development of prediction models for complex systems as the theory behind them develops and the processing power of computers increase. A three layer Levenberg–Marquardt feedforward learning algorithm was used to model the eutrophication process in three water bodies of Turkey (Keban Dam Reservoir, Mogan and Eymir Lakes). Despite the very complex and peculiar nature of Keban Dam, a relatively good correlation (correlation coefficient between 0.60 and 0.75) was observed between the measured and calculated values. For Mogan and Eymir, which are much smaller and more homogenous lakes compared to Keban Dam Reservoir, correlation values as high as 0.95 were achieved between the measured and calculated values. Neural network models were able to model non-linear behavior in eutrophication process reasonably well and could successfully estimate some extreme values from validation and test data sets which were not used in training the neural network.

Assessment of the non-linear behaviour of plastic ankle foot orthoses by the finite element method

The stiffness characteristics of plastic ankle foot orthoses (AFOs) are studied through finite element modelling and stress analysis. Particular attention is given to the modelling and prediction of non-linear AFO behaviour, which has been frequently observed in previous experimental studies but not fully addressed analytically. Both large deformation effects and material non-linearity are included in the formulation and their individual influence on results assessed. The finite element program is subsequently applied to the simulation of a series of tests designed to investigate the relation between AFO trimline location and stiffness for moderate and large rotations. Through careful consideration and identification of key modelling parameters, the developed finite element solution proves to be a reliable and effective alternative means of assessing variations of a typical plastic AFO design so that particular patient requirements could be met, in the long term.

A new differential equations-based model for nonlinear history-dependent magnetic behaviour

The paper presents a new kind of numerical model describing nonlinear magnetic behaviour. The model is formulated as a set of differential equations taking into account history dependence phenomena like the magnetisation hysteresis as well as saturation effects. The capability of the model is demonstrated carrying out comparisons between measurements and calculations.

Analytical modeling of nonlinear behavior of composite beams with deformable connection

A numerical procedure for the analysis of steel and concrete composite beams is herein presented. The program accounts for nonlinear behavior of concrete, steel and shear connectors. In particular the most refined stress–strain constitutive relationships available in the literature can be used in the procedure. For shear connectors an empirical nonlinear load–slip relationship is used. The accuracy and reliability of the program are demonstrated by the analysis of four composite beams over the entire loading range up to failure. The analytical results are compared with the corresponding experimental data with good agreement between them. The reported results demonstrate that the numerical approach is a valid tool for extensive parametric studies on composite beams with complete or partial shear connection.

Introduction to the Special Issue: Applications of Complexity Theory to Organization Science

The seven articles that appear in this special issue concerning applications of complexity theory to organizations push our field forward significantly, not simply by importing ideas from an emerging interdisciplinary area, but by using them to inform rich, theoretically-grounded depictions of how organizations operate. Each emphasizes how the interaction of elements in a system produces surprising, emergent behavior that can be understood through formal models, even if those models cannot necessarily predict how a given system will evolve. Together, they constitute a foundation for a new way of thinking about how to model nonlinear behavior in organizations.

Phenomenological Theory of Intermodulation in HTS Resonators and Filters.

Recent work on nonlinear effects in microwave resonators and filters from high temperature superconductors, focusing on intermodulations, is reviewed. We calculate the intrinsic nonlinear response of s-wave and d-wave superconductors. A phenomenological description of the lowest order nonlinear behavior in high-T-c films in terms of a single parameter, j(IMD), is proposed. We show how this description can be used to calculate the intermodulation power arising in realistic microstrip resonators. These calculations show good agreement with measurements on hairpin resonators. This description can also be used for the modeling of nonlinear behavior of complex microwave filters.

Regionalization scheme for the simulation of regional water balances using a physically based model system

The regional simulation of hydrological behaviour is often performed by applying simplified model approaches adapted from the local scale. This is done because averaging the input parameters is not feasible due to the non-linear model behaviour. A region is assumed to be an ensemble of a number of ecotopes (hydrologically homogenous areas). The simulation of all computational units of a region is not possible due to excessive computer cost. A regionalization scheme is presented which enables us to calculate regional water balances by simulating a limited number of representative ecotopes instead of all units using a physically based (not simplified) model system. This concept is based on a cluster analysis of simulation results of theoretical ecotopes (all reasonable combinations of model parameters). The link between these theoretical ecotopes and the real ecotopes, derived by overlaying digital maps, is accomplished by ‘characteristic values’ which are integral measures of the soil hydrological properties (e.g. water available for plants, travel time, height of capillary flux). Simulating selected representative instead of all ecotopes reduces the number of desired simulation runs up to 95% without affecting the quality of the simulation results and without losing the spatial distribution of hydrological properties.

Modeling and measurement of nonlinear dynamic behavior in piezoelectric ceramics with application to 1-3 composites

The nonlinear vibratory behavior of a 1-3 piezoceramic composite is characterized theoretically and experimentally. The developed theoretical model for the electroelastic behavior of the 1-3 composite follows conventional assumptions made by prior investigators but includes nonlinear terms to account for hysteresis in the embedded PZT phase. Experimental measurements of the quasistatic and dynamic mechanical response of the 1-3 with embedded PZT-4 or PZT-5H phases to harmonic electrical excitation over a range of excitation frequencies and two different mechanical loading conditions quantify the nature and level of nonlinearity and illustrate its dependence on the type of PZT material and the mechanical coupling conditions of the 1-3 to its surroundings. Good agreement exists between theoretical predictions and experimental measurements.

Application of parallel computation to material models with a large number of internal variables

Abstract.The finite element code ZeBuLoN has been parallelized using the FETI subdomain decomposition method for the use of non-linear mechanical behavior models which require a high number of inte...

A kinetic network model for nonlinear flow behavior of molten plastics in both shear and extension

The revised Berkeley kinetic network model is shown to accurately describe experimental data in many types of nonlinear deformation, including large amplitude oscillatory shear (LAOS), exponential shear, planar extension, step biaxial extension, uniaxial extension, and step strain, for the IUPAC X low density polyethylene (LDPE). It is shown that while LAOS is helpful in determining the approximate model parameters, a LAOS test is not sufficient to determine their precise values. Exponential shear, however, is more sensitive to the parameter values, and LAOS and exponential shear together are sufficient for precise parameter determination. Both of these experiments can be performed easily on a sliding plate rheometer incorporating a shear stress transducer.

Harmonic Balance Vibration Analysis of Turbine Blades With Friction Dampers

Although considerable effort has been devoted to the formulation of predictive models of friction damper behavior in turbomachinery applications, especially for turbine blades, the problem is far from being solved due to the complex nonlinear behavior of the contact surfaces. This paper primarily focuses on analytical and numerical aspects of the problem and addresses the problem in the frequency domain while exploring the viability of equivalent time-domain alternatives. The distinct features of this work are: (i) the modelling of nonlinear friction damper behavior as an equivalent amplitude-dependent complex stiffness via a first-order harmonic balance method (HBM), (ii) the use of sine sweep excitation in time-marching analysis, (iii) the application of the methodology to numerical test cases, including an idealised 3D turbine blade model with several friction dampers, (iv) the verification of the numerical findings using experimental data, and (v) a detailed assessment of the suitability of HBM for the analysis of structures with friction dampers.

A constitutive model for nonlinear viscoelastic behavior of polymers

AbstractA new constitutive model for the nonlinear behavior of noncrosslinked polymers with infinitesimal strains is derived. It generalizes a model of adaptive links for the viscoelastic behavior of crosslinked polymers. According to the model, a viscoelastic medium is treated as a set of elastic springs that replace each other. The springs model chemical links between polymer molecules, which arise and collapse because of the micro‐Brownian motion, a law for replacing the springs determines the stress relaxation in a viscoelastic medium. Unlike crosslinked polymers, noncrosslinked polymers demonstrate steady‐state creep flow after some transition period. To describe both the transition process and the steady creep, the model distinguishes two different types of adaptive links. Links of the first type are ruptured under loading, whereas links of the second type replace one another. Both these processes (destruction and replacement) are treated as kinetic, and equations of chemical kinetics are introduced for their description. The nonlinearity of the model arises because of a dependence of rates of kinetic processes on the stress intensity. The constitutive equations derived are testified by comparing theoretical results with data for polypropylene fibers. For the verification we use data presented by three independent sources. The results demonstrate good agreement between experimental observations and their theoretical predictions. Finally, the effect of molecular weight of polymers on parameters of the model is studied.

A model of nonlinear behavior of ice cracks

A work presented at the previous ASA meeting has demonstrated that the cracks may provide anomalously strong vibroacoustic nonlinearity in ice. Experimental data were obtained from the field experiments on a fresh‐water lake, where a strong subharmonic signal was, in particular, registered. Here, a theoretical model is suggested for the description of the effects observed and possible use of them for characterizing the crack parameters. The model is based on consideration of nonlinear flexural oscillations of the ice plate with a crack which may be ‘‘opened’’ from its upper or lower part due to flexural oscillations. Together with the added mass of the surrounding area of the plate, a nonlinear oscillator may be formed which admits both higher harmonic and subharmonic generation (a parametric effect). The oscillator has a strong nonlinearity and relatively low Q factor which may provide a possibility of parametric excitation if there is a rather wide frequency range. The model considered seems to be applicable for real sea conditions.