Estimation of dry road braking distance considering frictional energy of patterned tires

This paper is concerned with the braking distance estimation of tire controlled by anti-lock brake system (ABS) according to a numerical–analytical method. While the frictional heat dissipation at disc pad is derived analytically, the tire frictional energy loss is computed by the 3D dynamic rolling analysis of patterned tire. Since the tire rolling analysis to obtain the time history of the frictional energy rate for the entire braking period is impractical, we alternatively seek the tire frictional energy rate curve versus the lapse of time by interpolating the discretized frictional energy rates computed at intervals of 10 km/h. The effect of ABS is numerically implemented by specifying the corresponding tire angular velocity to the dynamic rolling analysis. Applying the energy conservation law to each speed interval determines the interval-wise braking times and distances from which the total braking time and distance are predicted. Illustrative numerical experiment is presented together with the comparison with the experimental estimation.     

三维弹塑性结构下限分析的边界元方法

基于极限分析的下限定理,建立了用常规边界元方法进行三维理想弹塑性结构极限分析的求解算法.下限分析所需的弹性应力场可直接由边界元方法求得.所需的自平衡应力场由一组带有待定系数的自平衡应力场基矢量的线性组合进行模拟,这些自平衡应力场基矢量由边界元弹塑性迭代计算得到.下限分析问题最终被归结为一系列未知变量较少的非线性数学规划子问题并通过复合形法进行求解.给出的计算结果表明该算法有较高的精度和计算效率.     

Optimization of Euclidean distance threshold in the application of recurrence quantification analysis to heart rate variability studies

An integrated approach is proposed to solve the optimization problem of the Euclidean distance threshold ε in recurrence quantification analysis (RQA), which is increasingly applied in the study of heart rate variability (HRV). In this paper, ε is inversely computed from a given recurrence rate (REC), the percentage of recurrence points. From the inversely computed ε, two other RQA output variables: determinism (DET), the percentage of recurrence points forming diagonal line structures, and laminarity (LAM), the percentage of recurrence points forming vertical and horizontal structures, are computed out as well. The trend of DET, LAM values at different REC levels (DLR trend) is introduced to comprehensively represent the dynamic properties of a time series. Based on the DLR trend, the variation of discrimination power, represented by the average loss (or Bayes risk), of DET and LAM, at different REC values is analyzed. Surrogate techniques are used to generate reliable test data sets for the discrimination evaluation. In particular, the results show that (1) the optimal REC can be much higher than the widely used 1% REC, and (2) after the optimization, the average loss can be reduced compared to 1% REC. It is also demonstrated that the optimal ε depends on the dynamic source and RQA variables, and the DLR trend based ε optimization method can improve RQA discrimination analysis especially for the short term HRV analysis.     

The Tikhonov regularization method in elastoplasticity

The numerical simulation of the mechanical behavior of industrial materials is widely used for viability verification, improvement and optimization of designs. Elastoplastic models have been used to forecast the mechanical behavior of different materials. The numerical solution of most elastoplastic models comes across problems of ill-condition matrices. A complete representation of the nonlinear behavior of such structures involves the nonlinear equilibrium path of the body and handling of singular (limit) points and/or bifurcation points. Several techniques to solve numerical problems associated to these points have been disposed in the specialized literature. Two examples are the load-controlled Newton–Raphson method and displacement controlled techniques. However, most of these methods fail due to convergence problems (ill-conditioning) in the neighborhood of limit points, specially when the structure presents snap-through or snap-back equilibrium paths. This study presents the main ideas and formalities of the Tikhonov regularization method and shows how this method can be used in the analysis of dynamic elastoplasticity problems. The study presents a rigorous mathematical demonstration of existence and uniqueness of the solution of well-posed dynamic elastoplasticity problems. The numerical solution of dynamic elastoplasticity problems using Tikhonov regularization is presented in this paper. The Galerkin method is used in this formulation. Effectiveness of Tikhonov’s approach in the regularization of the solution of elastoplasticity problems is demonstrated by means of some simple numerical examples.     

The Lyapunov–Movchan method in problems of the stability of flows and deformation processes

The extension of Lyapunov's method to continuous mechanical systems are discussed. An annotated bibliography of papers is given in which, based on the Lyapunov–Movchan method, with the construction of corresponding functionals, a direct analysis is carried out of the stability of motion (deformation) of continuous mechanical systems. The material is divided into sections, devoted to the following: (a) the extension of the mathematical apparatus as a whole to continuous and dynamic systems, (b) the stability of elastic, elastoplastic and viscoelastic deformable solids, (c) stability in aeroelasticity and hydroelasticity theory, (d) the linearized theory of hydrodynamic stability, and (e) the stability with reference to perturbations of material functions in the theory of constitutive relations.     

Application of the Sinc method to a dynamic elasto-plastic problem

This paper presents the application of Sinc bases to simulate numerically the dynamic behavior of a one-dimensional elastoplastic problem. The numerical methods that are traditionally employed to solve elastoplastic problems include finite difference, finite element and spectral methods. However, more recently, biorthogonal wavelet bases have been used to study the dynamic response of a uniaxial elasto-plastic rod [Giovanni F. Naldi, Karsten Urban, Paolo Venini, A wavelet-Galerkin method for elastoplasticity problems, Report 181, RWTH Aachen IGPM, and Math. Modelling and Scient. Computing, vol. 10, 2000]. In this paper the Sinc–Galerkin method is used to solve the straight elasto-plastic rod problem. Due to their exponential convergence rates and their need for a relatively fewer nodal points, Sinc based methods can significantly outperform traditional numerical methods [J. Lund, K.L. Bowers, Sinc Methods for Quadrature and Differential Equations, SIAM, Philadelphia, 1992]. However, the potential of Sinc-based methods for solving elastoplasticity problems has not yet been explored. The aim of this paper is to demonstrate the possible application of Sinc methods through the numerical investigation of the unsteady one dimensional elastic-plastic rod problem.     

Complexity analysis of spatial–temporal precipitation system by PCA and SDLE

In this paper, an ensemble technique combining the principal component analysis (PCA) with scale-dependent Lyapunov exponent (SDLE) is used to characterize complexity of precipitation dynamical system. The spatial–temporal precipitation data is decomposed by employing PCA method and then the SDLE for the first few principal components (PCs) time series are computed. The first few PCs time series are found to exhibit the different scaling laws on different time scales. The study illustrate that the spatial–temporal precipitation data is chaotic and the precipitation system is truly multiscaled and complex.     

Dynamic analysis of elastic beams under uncertainty

We consider minimax estimation of the state of semi-infinite elastic beams under uncertainty using initial, boundary, and external dynamic inputs (concentrated and distributed forces, bending and torsional moments) and state observations. The errors of all measurements and observations are assumed to be in a given ellipsoidal region. The problems are solved using standard classical solutions of elastoplastic beams, Lur'e's symbolic method, and the theory of minimax filtering of noise in linear dynamic systems.Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 75, pp. 64–70, 1991.     

A compact formulation of an elastoplastic analysis problem

Two important problems in the area of engineering plasticity are limit load analysis and elastoplastic analysis. It is well known that these two problems can be formulated as linear and quadratic programming problems, respectively (Refs. 1–2). In applications, the number of variables in each of these mathematical programming problems tends to be large. Consequently, it is important to have efficient numerical methods for their solution. The purpose of this paper is to present a method which allows the quadratic programming formulation of the elastoplastic analysis to be reformulated as an equivalent quadratic programming problem which has significantly fewer variables than the original formulation. Indeed, in Section 4, we will present details of an example for which the original quadratic programming formulation required 297 variables and for which the equivalent formulation presented here required only two variables. The method is based on a characterization of the entire family of optimal solutions for a linear programming problem.This research was supported by the Natural Science and Engineering Council of Canada under Grant No. A8189 and by a Leave Fellowship from the Social Sciences and Humanities Research Council of Canada. The author takes pleasure in acknowledging many stimulating discussions with Professor D. E. Grierson.     

Coupled FEM-BEM for elastoplastic contact problems using Lagrange multipliers

The coupling of the elastoplastic finite element and elastic boundary element methods for two-dimensional frictionless contact stress analysis is presented. Interface traction matching (boundary element approach), which involves the force terms in the finite element analysis being transformed to tractions, is chosen for the coupling method. The analysis at the contact region is performed by the finite element method, and the Lagrange multiplier approach is used to apply the contact constraints. Since the analyses of elastoplastic problems are non-linear and involve iterative solution, the reduced size of the final system of equations introduced by combining the two methods is very advantageous, especially for contact problems where the nature of the problem also involves an iterative scheme.     

Stability of hydrostatic-pressured FGM thick rings with material nonlinearity

Buckling behaviors of elastoplastic ceramic/metallic functionally graded material (FGM) rings are investigated by using the first order shear deformation theory. The hydrostatic-pressured rings are assumed to be in both the plane-stress case and the plane-strain case, which lead respectively to a uniaxial and a biaxial elastoplastic stress states in prebuckling stage. A uniform strain hypothesis helps to deal with the elastoplastic stress states. By introducing in the graded material properties, the constitutive model of FGMs is formulated under the framework of J₂ deformation theory. By considering the kinetic relations of von-Kárman type and employing the principle of virtual displacement, the equilibrium equations and the buckling governing equations of FGM circular rings are formulated, and the analytical solution of the anisotropic rings is obtained. Finally, the elastoplastic buckling problem is numerically solved through a semi-analytical method, which is proposed to seek the real circumferential strain of FGM rings at the buckling point and determinate the elastoplastic buckling critical hydrostatic pressure. The effects of the inhomogeneous and geometrical parameters on the buckling critical load and the position of the elastoplastic interface are discussed. Results show that, in both the plane-stress and the plane-strain cases, the elastoplastic critical loads are generally lower than their elastic counterparts due to material flow, and the plane-strain critical load is generally larger than the plane-stress one. The elastoplastic critical load does not always decrease monotonously with the increase of the inhomogeneous parameters, which is quite different from their elastic counterparts.     

Numerical method for solving a boundary-value problem of thermoelasticity

We consider the problem of determining the stress-strain state of an elastoplastic layer under impulse heating. The theory of small elastoplastic strains with linear hardening is used. A boundary-value problem is obtained for the equations of thermoelasticity whose coefficients at any time are functionals of strain history. A method is developed for solving this problem, based on discretization by space and time variables and application of an appropriate difference scheme. This scheme constructs a recursive evolution process for the state column at the nodes of the space grid. Numerical implementation of the method has demonstrated its reliability and efficiency.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 58, pp. 66–71, 1986.     

Aeroelastic analysis of large horizontal wind turbine baldes?

A nonlinear aeroelastic analysis method for large horizontal wind turbines is described. A vortex wake method and a nonlinear ?nite element method (FEM) are coupled in the approach. The vortex wake method is used to predict wind turbine aero-dynamic loads of a wind turbine, and a three-dimensional (3D) shell model is built for the rotor. Average aerodynamic forces along the azimuth are applied to the structural model, and the nonlinear static aeroelastic behaviors are computed. The wind rotor modes are obtained at the static aeroelastic status by linearizing the coupled equations. The static aeroelastic performance and dynamic aeroelastic responses are calculated for the NH1500 wind turbine. The results show that structural geometrical nonlinearities signi?cantly reduce displacements and vibration amplitudes of the wind turbine blades. Therefore, structural geometrical nonlinearities cannot be neglected both in the static aeroelastic analysis and dynamic aeroelastic analysis.     

An efficient backcalculation algorithm of time domain for large-scale pavement structures using Ritz vectors

This paper describes a backcalculation algorithm to determine the layer moduli and damping coefficients in the time domain for large-scale pavement structures. Pavement is modeled by three-dimensional finite element (3D FE). The parameter identification procedure makes use of Ritz vectors to reduce the size of matrices involved in the forward dynamic response analysis and the deflection sensitivity analysis. An exact complex mode superposition technique is used to obtain the dynamic response of the reduced equation system in the time domain. This method is more efficient, accurate and stable. The parameter estimates are improved iteratively by means of an algorithm that calls the finite element program of dynamic response analysis as a subroutine combining truncated singular value decomposition (TSVD) method. Simulation of a numerical solution validates the efficiency of the proposed method. Finally, the method is implemented for two experimentally tested sections of semiflexible pavement. All parameters are determined using the surface deflections of pavement experimentally recorded at the sensor locations of falling weight deflectometer (FWD).     

Recent advances in the numerical modeling of constitutive relations

In this paper we present an overview of the recent developments in the area of numerical and finite element modeling of nonlinear constitutive relations. The paper discusses elastic, hyperelastic, elastoplastic and anisotropic plastic material models. In the hyperelastic model an emphasis is given to the method by which the incompressibility constraint is applied. A systematic and general procedure for the numerical treatment of hyperelastic model is presented. In the elastoplastic model both infinitesimal and large strain cases are discussed. Various concerns and implications in extending infinitesimal theories into large strain case are pointed out. In the anisotropic elastoplastic case, emphasis is given to the practicality of proposed theories and its feasible and economical use in the finite element environment.     

Measuring rank correlation coefficients between financial time series: A GARCH-copula based sequence alignment algorithm

This paper presents a novel four-stage algorithm for the measurement of the rank correlation coefficients between pairwise financial time series. In first stage returns of financial time series are fitted as skewed-t distributions by the generalized autoregressive conditional heteroscedasticity model. In the second stage, the joint probability density function (PDF) of the fitted skewed-t distributions is computed using the symmetrized Joe–Clayton copula. The joint PDF is then utilized as the scoring scheme for pairwise sequence alignment in the third stage. After solving the optimal sequence alignment problem using the dynamic programming method, we obtain the aligned pairs of the series. Finally, we compute the rank correlation coefficients of the aligned pairs in the fourth stage. To the best of our knowledge, the proposed algorithm is the first to use a sequence alignment technique to pair numerical financial time series directly, without initially transforming numerical values into symbols. Using practical financial data, the experiments illustrate the method and demonstrate the advantages of the proposed algorithm.     

Elasticoplastic bending of rectangular plates reinforced with fibers of constant cross section

The problem on the elastoplastic transverse bending of Kirchhoff plates of variable thickness reinforced with fibers of constant cross section is formulated and its qualitative analysis is performed. An analytical solution to the problem is constructed in the case of cylindrical bending, and, by using the Bubnov-Galerkin method, an approximate solution for a rectangular plate is obtained. Based on calculations of plates reinforced with boron fibers and steel wire, it is shown that the load-carrying capacity of the structural member in elastoplastic bending is several times (or even by an order of magnitude) higher than in purely elastic one.Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 1, pp. 17–36, January–February, 2005.     

Nonsingular decoupled terminal sliding-mode control for a class of fourth-order nonlinear systems

This paper presents a nonsingular decoupled terminal sliding mode control (NDTSMC) method for a class of fourth-order nonlinear systems. First, the nonlinear fourth-order system is decoupled into two second-order subsystems which are referred to as the primary and secondary subsystems. The sliding surface of each subsystem was designed by utilizing time-varying coefficients which are computed by linear functions derived from the input–output mapping of the one-dimensional fuzzy rule base. Then, the control target of the secondary subsystem was embedded to the primary subsystem by the help of an intermediate signal. Thereafter, a nonsingular terminal sliding mode control (NTSMC) method was utilized to make both subsystems converge to their equilibrium points in finite time. The simulation results on the inverted pendulum system are given to show the effectiveness of the proposed method. It is seen that the proposed method exhibits a considerable improvement in terms of a faster dynamic response and lower IAE and ITAE values as compared with the existing decoupled control methods.     

New Applications of the Boundary Element Method in Dynamics of Solids

The boundary element method (BEM) is developed and applied in new fields of dynamic fracture mechanics, dynamics of composite, elasto–plastic and piezoelectric materials. The BEM results are compared with solutions computed by the finite element method (FEM) showing high accuracy of the BEM. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)