Analysis Of Nonlinear Behavior Research Articles

Back analysis for prediction and behavior of laterally loaded single piles in sand

The purposes of this paper are to estimate the behavior of laterally loaded single piles by the back analysis and the effects of non-homogeneity consisted of two layers, constraint condition of pile head, relative density, and embedded length of pile on the behavior of single pile in sand. These effects can be quantified only by the results of model tests. Also, the model tests were compared with the results of the numerical methods (p-y method, modified Vlasov method; new γ parameter, Characteristic Load Method;CLM). In this study, the modulus of soil resistance and ultimate soil resistance are assumed to exponential function with depth for Nak-Dong River sand. Therefore, a new γ parameter equation based on the Vlasov method was derived to calculate the modulus of soil resistance (E h =n hi Z n ) of exponential function with depth. Thep-y method of nonlinear behavior analysis is relatively effective method of designing deep foundations subjected to lateral loads for only the reasonable of the modulus of soil resistance (E h ) and ultimate soil resistance (P u ). Therefore, the back analysis is used to determineE h andP u in this study. For this, theE h(DST) andP u(DST) are obtained from the stress-strain relationship of direct shear test (DST). TheE h andP u applicable to predict lateral behavior are obtained from back analysis usingp-y curve with hyperbolic function. The coefficients used to modify ofE h(DST) andP u(DST) are obtained with the range of 0.014–0.05 and 0.2–0.4, respectively. The predict of modified Vlasov method usedE h andP u suggested in this study is very good agreement with measured results blow y/D=0.06–0.14 and the predict ofp-y method used the recommend values of Terzaghi (1955) forE h and Reese et al.(1974) forP u is more under-estimated than the model test results.

Prediction to nonlinear behavior of steel frames subjected to fire

Abstract A new approach is presented for analysis of nonlinear behavior of steel frames subjected to fire. The material and geometrical nonlinearity as well as the non-uniform profile of temperature across section of frame members are taken into account. Thermal forces induced by temperature variation are also considered. The elasto-plastic stiffness equation of elements is established by using the generalized Clough model. The analysis of strutures subjected to fire is converted to analysis of structures subjected to unbalanced forces induced by temperature increment. Then a procedure to calculate the nonlinear response and ultimate load of steel frames exposed to fire is proposed. For verifying the validity of the approach proposed, tests on two large-scale models of single-story two-bay steel frames are conducted in gas furnace to simulate fire. The temperature elevation and deformation response of the models due to fire are measured. Good agreements between the results measured and calculated are demonstrated on the behavior of the models exposed to fire.

Experiment and Nonlinear Behavior Analysis of CFRP Laminated Plates with a Hole

Experiment and Nonlinear Behavior Analysis of CFRP Laminated Plates with a Hole

A refined R.C. beam element including bond–slip relationship for the analysis of continuous beams

In this paper a refined fibre model is proposed for analysis of R.C. beams that include an explicit formulation of bond–slip relationship. The model is introduced in a matrix formulation developing a computational method for statically indeterminate beams. The method takes into account detailed models of materials and their interaction so that a reliable analysis of non-linear behaviour of the R.C. beams can be obtained including debonding of rebars, width of cracks, tension stiffening effect and so on. The capability and the reliability of the procedure have been tested by means of a large theoretical–experimental comparison and a meaningful case is described as an example in the paper. The procedure is very efficient in terms of computational effort and convergence velocity, moreover it is general and allows a refined non-linear analysis to be effected for a design purpose without simplified hypothesis in the rotational capacity of the element. The model requires only the introduction of the geometrical characteristics of the element and the constitutive properties of the materials and allows the local behaviour of R.C. beams to be studied in details due to the bond interaction between steel and concrete.

Stochastic analysis of time-variant nonlinear dynamic systems. Part 1: The Fokker-Planck-Kolmogorov equation approach in stochastic mechanics

The probabilistic description and analysis of the response of time-invariant nonlinear dynamic systems driven by stochastic processes is usually treated by means of evaluation of statistical moments and cumulants of the response. The background of these methods is the Fokker-Planck-Kolmogorov (FPK) equation for a probability density function or the Pugachev equation for a characteristic function, respectively. The exact solutions of these equations are obtained only for isolated cases. For engineering probabilistic analysis of a complex nonlinear systems, different mixed (hybrid) methods in these cases are used. In this study a ‘benchmark’ solution is obtained on the basis of the FPK equation in conjunction with the method of statistical moments for nonlinear mechanical system with colored parametric excitations. In Part 1 (this part), an exact solution of FPK equation on the basis of asymptotic analysis of nonlinear dynamic behavior of parametric excitation system is discussed. In Parts 2 and 3, applications of this method to stochasticity and stability analysis of nonlinear time-variant systems are considered. A comparison with the accuracy of different statistical methods is discussed. In Parts 4 and 5, a method of stochastic analysis of relativistic and quantum dynamic systems is described on the basis of a generalized stochastic Hamilton-Jacobi equations on a differential manifold as Riemanian geometry. This involves the task of relativistic navigation and dissipative quantum models of a nonlinear parametric oscillator in the presence of stochastic excitations on a differential manifold with different metric tensors of the space-time continuum.

Numerical conversion of transient to harmonic response functions for linear viscoelastic materials

Viscoelastic material behavior is often characterized using one of the three measurements: creep, stress-relaxation or dynamic sinusoidal tests. A two-stage numerical method was developed to allow representation of data from creep and stress-relaxation tests on the Fourier axis in the Laplace domain. The method assumes linear behavior and is theoretically applicable to any transient test which attains an equilibrium state. The first stage numerically resolves the Laplace integral to convert temporal stress and strain data, from creep or stress-relaxation, to the stiffness function, G( s), evaluated on the positive real axis in the Laplace domain. This numerical integration alone allows the direct comparison of data from transient experiments which attain a final equilibrium state, such as creep and stress relaxation, and allows such data to be fitted to models expressed in the Laplace domain. The second stage of this numerical procedure maps the stiffness function, G( s), from the positive real axis to the positive imaginary axis to reveal the harmonic response function, or dynamic stiffness, G( jω). The mapping for each angular frequency, s, is accomplished by fitting a polynomial to a subset of G( s) centered around a particular value of s, substituting js for s and thereby evaluating G( jω). This two-stage transformation circumvents previous numerical difficulties associated with obtaining Fourier transforms of the stress and strain time domain signals. The accuracy of these transforms is verified using model functions from poroelasticity, corresponding to uniaxial confined compression of an isotropic material and uniaxial unconfined compression of a transversely isotropic material. The addition of noise to the model data does not significantly deteriorate the transformed results and data points need not be equally spaced in time. To exemplify its potential utility, this two-stage transform is applied to experimental stress relaxation data to obtain the dynamic stiffness which is then compared to direct measurements of dynamic stiffness using steady-state sinusoidal tests of the same cartilage disk in confined compression. In addition to allowing calculation of the dynamic stiffness from transient tests and the direct comparison of experimental data from different tests, these numerical methods should aid in the experimental analysis of linear and nonlinear material behavior, and increase the speed of curve-fitting routines by fitting creep or stress relaxation data to models expressed in the Laplace domain.

自自関節を持つ平面アームのカオス的挙動と非線形制御 ドリフトを持つ非ホロノミック機械の制御

The nonholonomic systems considered in robotics are mechanical systems with nonintegrable constraints. These systems have the property that the dimension of the reachable space is larger than the number of degree-of-freedom. A two-joint planar manipulator with the second joint free is one of such systems. Chaos, on the other hand, is another major topic in nonlinear dynamics and has the property that a dynamical system is sensitive in the initial conditions. The two phenomena have the same mathematical background from integrability point of view. In this paper, we study when and how the manipulator exhibits the chaotic behavior. We propose a control strategy for simultaneous positioning of the two joints, based on the analysis of nonlinear behavior. Its effectiveness is to be shown by experiments.

On the bifurcations of nonautonomous systems with compound critical points

A systematic perturbation technique, combining selected features of the intrinsic harmonic balancing and multiple time scaling, is presented. Attention here is focused on more general nonlinear nonautonomous systems, bifurcation behaviour, and stability analysis in the vicinity of a compound critical point of interest. A symbolic computer language, MAPLE, has been used extensively, and a nonlinear nonautonomous circuit is analyzed as an application.

An implementation of solution strategies for the analysis of complex non-linear equilibrium behavior

An implementation of solution strategies for controlling the analysis of the non-linear equilibrium behavior of elastic structures is presented. The automated procedure guides the solution-stepping process in the vicinity of critical stability points, including limit points, and bifurcation points of multiplicity one or two. The procedure was developed for use with analysis methods in which the total potential energy of a structure is expressed as a power series of finite order in an arbitrary number of generalized coordinates. Aspects of both the Riks-Wempner arc-length control method and the equivalence-transformation method of Thurston are incorporated. The procedure is applied to several plate and stiffened-panel problems in order to demonstrate key features, and to illuminate difficulties that arise in some situations.

Direct Analysis of Slender Columns with P‐Delta Effects

A numerical method is introduced for direct analysis of nonlinear behavior of slender beam‐columns. A strain control technique in conjunction with the quasi‐Newton's method was developed to obtain the updated flexural stiffness directly for lateral deflection estimation. Numerical difficulties such as singular problems or softening behavior could be detected beforehand and overcome. This algorithm may also be formulated to trace the M‐P‐Φ curve and to calculate the current flexural stiffness for sections from very small strain to extremely large strain. Details about the principles and the formulations are given in this paper. Examples include step‐by‐step calculation results for biaxially loaded sections and analyses of slender reinforced concrete and steel columns including uniform or nonuniform cross sections. Further applications can be made to uniaxially or biaxially loaded columns constructed with most engineering materials or to enhance the performance of nonlinear frame analyses.

Analysis of non-linear behaviour of reinforced concrete diaphragm walls under horizontal load : Mazzucato, A; Natali, A Proc 1st International Geotechnical Seminar on Deep Foundations on Bored and Auger Piles, Ghent, 7–10 June 1988P239–244. Publ Rotterdam: A A Balkema, 1988

Analysis of non-linear behaviour of reinforced concrete diaphragm walls under horizontal load : Mazzucato, A; Natali, A Proc 1st International Geotechnical Seminar on Deep Foundations on Bored and Auger Piles, Ghent, 7–10 June 1988P239–244. Publ Rotterdam: A A Balkema, 1988

White-noise analysis of nonlinear behavior in an insect sensory neuron: kernel and cascade approaches.

A functional expansion was used to model the relationship between a Gaussian white noise stimulus current and the resulting action potential output in the single sensory neuron of the cockroach femoral tactile spine. A new precise procedure was used to measure the kernels of the functional expansion. Very similar kernel estimates were obtained from separate sections of the data produced by the same neuron with the same input noise power level, although some small time-varying effects were detectable in moving through the data. Similar kernel estimates were measured using different input noise power levels for a given cell, or when comparing different cells under similar stimulus conditions. The kernels were used to identify a model for sensory encoding in the neuron, comprising a cascade of dynamic linear, static nonlinear, and dynamic linear elements. Only a single slice of the estimated experimental second-order kernel was used in identifying the cascade model. However, the complete second-order kernel of the cascade model closely resembled the estimated experimental kernel. Moreover, the model could closely predict the experimental action potential train obtained with novel white noise inputs.

Newton-raphson procedure for the sensitivity analysis of nonlinear structural behavior

A method is developed that evaluates the gradients of displacements and stresses with respect to structural parameters in a nonlinear finite element analysis. The nonlinearity in the material's behavior is accounted for in the analysis. In the Newton-Raphson procedure, the equilibrium equation is differentiated in each iteration and then solved to obtain incremental gradients. Incremental gradients are updated to obtain total gradients. This procedure is presented as an algorithm for the general case and is demonstrated for plane truss elements. The method is tested by comparing the results with the exact answers in four examples.

An analysis of nonlinear behavior in delta - sigma modulators

This paper introduces a new method of analysis for deltasigma modulators based on modeling the nonlinear quantizer with a linearized gain, obtained by minimizing a mean-square-error criterion [7], followed by an additive noise source representing distortion components. In the paper, input signal amplitude dependencies of delta-sigma modulator stability and signal-to-noise ratio are analyzed. It is shown that due to the nonlinearity of the quantizer, the signal-to-noise ratio of the modulator may decrease as the input amplitude increases prior to saturation. Also, a stable third-order delta-sigma modulator may become unstable by increasing the input amplitude beyond a certain threshold. Both of these phenomena are explained by the nonlinear analysis of this paper. The analysis is carried out for both dc and sinusoidal excitations.

Behavior of Damaged Tubular Structural Members

An analytical model of dented tubular members is constructed. Using this model, an ultimate strength interaction relationship between axial force and biaxial bending moments is derived. The implementation of this interaction relationship to take account of denting and bending damage in the analysis of nonlinear behavior of tubular space frames by ISUM (the Idealized Structural Unit Method) is described. An experimental study of the behavior of dented members subjected to pure bending is reported. Comparison with theoretical predictions is presented.

New Efficient and Accurate Method of Nonlinear Analysis of Offshore Tubular Frames (the Idealized Structural Unit Method)

The Idealized Structural Unit Method [1, 2] is applied to the analysis of nonlinear behavior of three-dimensional offshore tubular frames. To this purpose the “tubular structural unit” is developed and used to analyze the entire behavior of the frame until final collapse. In this method large deflections, instability, plasticity and the effect of residual stresses and initial out of straightness are considered. Modeling of a structure is very simple since large structural units are regarded as elements. The required computer effort is very small while attaining a high degree of accuracy and reliability.

Numerical study of M=1 resistive internal kink mode in a cylindrical Tokamak

A numerical analysis of nonlinear behavior of m=1 resistive internal kink instability in a Tokamak is presented in a cylindrical approximation. A two-dimensional nonlinear code which solves incompressible resistive MHD equations with helical symmetry has been developed. For the case of small longitudinal wave number k, the magnetic axis moves outward until it reaches the critical surface where the value of helical magnetic flux has the same value as the one at the magnetic axis. On the other hand, as k is increased, the shift of the magnetic axis saturates before touching this critical surface. This result gives a possible explanation of suppression of internal disruptions observed in high power neutral beam injection experiment to Tokamaks.

Finite deformation and stability behaviour of cylindrical membranes subjected to symmetric line loads†

An ‘exact’ analysis of the complete non-linear load-deflection and stability behaviour of cylindrical membranes without end ‘shear walls’ subjected to longitudinal Symmetric line loads is presented. The analysis includes low as well as high profile structures. In order to determine the lateral stability behaviour, infinitesimal lateral displacements are superimposed on the symmetric finite deflection field. Results indicate that such structures may experience vertical and/or lateral instability depending on their initial geometry. Membranes with initial central angles, θ 0 ⩽ 90° are stable, both vertically and laterally, for all load values. For 42.23° < θ 0 < 90° the structure is laterally stable but becomes vertically unstable at a certain ‘limit load’ W̄ V while for θ 0< 42.23°, the structure becomes laterally unstable at a load value w̄ l < W̄ V . The analysis admits contact between vertical segments of the membrane to either side of the line load as well as between the membrane and the horizontal surface next to the supports.

El-plastic Behavior and Ultimate Strength of Damaged Tubular Members

An analytical model of dented tubular members is constructed. Using this model, an ultimate strength interaction relationship between axial force and biaxial bending moments is derived. The implementation of this interaction relationship to take account of denting and bending damage in the analysis of nonlinear behavior of tubular space frames by ISUM (the Idealized Structural Unit Method) is described. An experimental study of the behavior of dented members subjected to pure bending is reported. Comparison with theoretical predictions is presented.

Nonlinear behaviour and failure analysis of multicell reinforced concrete box girder bridges

A numerical method of analysis is developed to trace the nonlinear response of multicell reinforced concrete (RC) box girder bridges under stepwise increasing static loads. The nonlinearities considered are material nonlinearities inherent in reinforced concrete structural members, such as cracking of the concrete and yielding of the reinforcement due to flexure, shear, and torsion. The analytical model, based on a three-dimensional grillage, is developed for multicellular structures of arbitrary plan geometry and constant height. The analytical method can trace the complex nonlinear behaviour of the bridge beyond the working stress range up to ultimate failure and collapse of the structure. Collapse mechanisms and failure loads can both be determined. The proposed analytical scheme, which is based on a mixed model formulation, is demonstrated and tested on two numerical examples. The results are compared with experimental results obtained from large-scale tests on RC box girder bridge models and indicate excellent agreement. The behaviour of these bridge models under increasing overloads is discussed. Key words: box girder bridges, bridge design, multicell structures, reinforced concrete, analytical model, nonlinear analysis, mixed model, ultimate strength, failure modes.