Optimal bounded control of first-passage failure of quasi-integrable Hamiltonian systems with wide-band random excitation

The optimal bounded control of quasi-integrable Hamiltonian systems with wide-band random excitation for minimizing their first-passage failure is investigated. First, a stochastic averaging method for multi-degrees-of-freedom (MDOF) strongly nonlinear quasi-integrable Hamiltonian systems with wide-band stationary random excitations using generalized harmonic functions is proposed. Then, the dynamical programming equations and their associated boundary and final time conditions for the control problems of maximizinig reliability and maximizing mean first-passage time are formulated based on the averaged It$\ddot{\rm o}$ equations by applying the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraints. The relationship between the dynamical programming equations and the backward Kolmogorov equation for the conditional reliability function and the Pontryagin equation for the conditional mean first-passage time of optimally controlled system is discussed. Finally, the conditional reliability function, the conditional probability density and mean of first-passage time of an optimally controlled system are obtained by solving the backward Kolmogorov equation and Pontryagin equation. The application of the proposed procedure and effectiveness of control strategy are illustrated with an example.

A Viscoelastic Constitutive Model with Nonlinear Evolutionary Internal Variables

Based on the internal variable theory, a viscoelastic constitutive model of a highly deformable continuous medium is proposed. A set of second rank tensorial internal state variables corresponding to Biot's strain is introduced, and a nonlinear evolution

Contingent sensitivity to configuration in a nonlinear evolution system

A trans-scopic sensitivity of macroscopic failure to slight differentiation in the meso-scopic structure of a system with nonlinear evolution is reported. A periodical chain following a non-local load-sharing evolution was applied as a propotype in failure study. The results demonstrate that there is a transition region composed of globally stable (GS) and evolution induced catastrophic (EIC) modes. That is different from a critical threshold as predicted by percolation and renormalization group theories. Moreover, the EIC mode shows a distinctive sample specific behaviour. For instance, some neighbouring initial states may evolve into completely different final states, though different initial states can evolve into the same final states. As an example, a marginal configuration of EIC mode, a quasi-Fibonacci skeleton, is constructed.

Evolution induced catastrophe in a nonlinear dynamical model of material failure

In order to study the failure of disordered materials, the ensemble evolution of a nonlinear chain model was examined by using a stochastic slice sampling method. The following results were obtained. (1) Sample-specific behavior, i.e. evolutions are different from sample to sample in some cases under the same macroscopic conditions, is observed for various load-sharing rules except in the globally mean field theory. The evolution according to the cluster load-sharing rule, which reflects the interaction between broken clusters, cannot be predicted by a simple criterion from the initial damage pattern and even then is most complicated. (2) A binary failure probability, its transitional region, where globally stable (GS) modes and evolution-induced catastrophic (EIC) modes coexist, and the corresponding scaling laws are fundamental to the failure. There is a sensitive zone in the vicinity of the boundary between the GS and EIC regions in phase space, where a slight stochastic increment in damage can trigger a radical transition from GS to EIC. (3) The distribution of strength is obtained from the binary failure probability. This, like sample-specificity, originates from a trans-scale sensitivity linking meso-scopic and macroscopic phenomena. (4) Strong fluctuations in stress distribution different from that of GS modes may be assumed as a precursor of evolution-induced catastrophe (EIC).

Nonlinear Analysis of Oscillatory Indentation in Elastic and Viscoelastic Solids

Determining the mechanical properties at micro- and nanometer length scales using nanoindentation or atomic force microscopy is important to many areas of science and engineering. Here we establish equations for obtaining storage and loss modulus from oscillatory indentations by performing a nonlinear analysis of conical and spherical indentation in elastic and viscoelastic solids. We show that, when the conical indenter is driven by a sinusoidal force, the square of displacement is a sinusoidal function of time, not the displacement itself, which is commonly assumed. Similar conclusions hold for spherical indentations. Well-known difficulties associated with measuring contact area and correcting thermal drift may be circumvented using the newly derived equations. These results may help improve methods of using oscillatory indentation for determining elastic and viscoelastic properties of solids.

Modeling Nonlinear Peeling of Ductile Thin Films-Critical Assessment of Analytical Bending Models Using FE Simulations

Three analytical double-parameter criteria based on a bending model and a two-dimensional finite element analysis model are presented for the modeling of ductile thin film undergoing a nonlinear peeling process. The bending model is based on different governing parameters: (1) the interfacial fracture toughness and the separation strength, (2) the interfacial fracture toughness and the crack tip slope angle, and (3) the interfacial fracture toughness and the critical Mises effective strain of the delaminated thin film at the crack tip. Thin film nonlinear peeling under steady-state condition is solved with the different governing parameters. In addition, the peeling test problem is simulated by using the elastic-plastic finite element analysis model. A critical assessment of the three analytical bending models is made by comparison of the bending model solutions with the finite element analysis model solutions. Furthermore, through analyses and comparisons for solutions based on both the bending model and the finite element analysis model, some connections between the bending model and the finite element analysis model are developed. Moreover, in the present research, the effect of different selections for cohesive zone shape on the ductile film peeling solutions is discussed.

Time-Frequency Analysis of Nonlinear Systems: The Skeleton Linear Model and the Skeleton Curves

The joint time-frequency analysis method is adopted to study the nonlinear behavior varying with the instantaneous response for a class of S.D.O.F nonlinear system. A time-frequency masking operator, together with the conception of effective time-frequency region of the asymptotic signal are defined here. Based on these mathematical foundations, a so-called skeleton linear model (SLM) is constructed which has similar nonlinear characteristics with the nonlinear system. Two skeleton curves are deduced which can indicate the stiffness and damping in the nonlinear system. The relationship between the SLM and the nonlinear system, both parameters and solutions, is clarified. Based on this work a new identification technique of nonlinear systems using the nonstationary vibration data will be proposed through time-frequency filtering technique and wavelet transform in the following paper.

Nonlinear Analysis of m Method for Single Pile Under Lateral Loading

通过对大量模型试验结果的分析,提出了简便合理的水平荷载作用下单桩的计算方法。该方法将常用m法中单一m值与位移建立指数关系,并由b_m及K两参数来描述。将这一关系引入常用单桩m法计算中,则计算结果可考虑单桩非线性响应的影响。

Modelling nonlinear vehicle dynamics with neural networks

The nonlinear modelling ability of neural networks has been widely recognised as an effective tool to identify and control dynamic systems, with applications including nonlinear vehicle dynamics which this paper focuses on using multi-layer perceptron networks. Existing neural network literature does not detail some of the factors which effect neural network nonlinear modelling ability. This paper investigates into and concludes on required network size, structure and initial weights, considering results for networks of converged weights. The paper also presents an online training method and an error measure representing the network's parallel modelling ability over a range of operating conditions. Copyright © 2010 Inderscience Enterprises Ltd.

A Nonlinear Threshold Model Applied to Spallation Analysis

Spallation in heterogeneous media is a complex, dynamic process. Generally speaking, the spallation process is relevant to multiple scales and the diversity and coupling of physics at different scales present two fundamental difficulties for spallation modeling and simulation. More importantly, these difficulties can be greatly enhanced by the disordered heterogeneity on multi-scales. In this paper, a driven nonlinear threshold model for damage evolution in heterogeneous materials is presented and a trans-scale formulation of damage evolution is obtained. The damage evolution in spallation is analyzed with the formulation. Scaling of the formulation reveals that some dimensionless numbers govern the whole process of deformation and damage evolution. The effects of heterogeneity in terms of Weibull modulus on damage evolution in spallation process are also investigated.

An incremental micromechanical scheme for nonlinear particulate composites

A general incremental micromechanical scheme for the nonlinear behavior of particulate composites is presented in this paper. The advantage of this scheme is that it can reflect partly the effects of the third invariant of the stress on the overall mechanical behavior of nonlinear composites. The difficulty involved is the determination of the effective compliance tensors of the anisotropic multiphase composites. This is completed by making use of the generalized self-consistent Mori-Tanaka method which was recently developed by Dai et al. (Polymer Composites 19(1998) 506-513; Acta Mechanica Solida 18 (1998) 199-208). Comparison with existing theoretical and numerical results demonstrates that the present incremental scheme is quite satisfactory. Based on this incremental scheme, the overall mechanical behavior of a hard-particle reinforced metal matrix composite with progressive particle debonding damage is investigated.