Shakedown of an Elastic-Plastic Arch Under Moving Load

Abstract

The problem considered consists in calculating the maximum value of a shakedown load which moves slowly across an arch according to a prescribed loading program. Sandwich cross section of the arch and elastic-plastic material with linear strain-hardening and ideal Bauschinger effect are assumed. Both current residual stress distribution and yield limits are evaluated for selected cross sections and for every load crossing.

In most cases the first crossing is decisive, and shakedown loads can be computed on the basis of the results of the first and second crossing     

Spectral simulation and shock absorber identification

In vehicle dynamics shock absorbers are used for the optimization of driving comfort and driving safety. Therefore, it is necessary to identify characteristics of shock absorbers under real conditions. This paper introduces the use of hardware-in-the-loop simulations for the identification of shock absorbers involving stochastic models of the road roughness. For this purpose a dynamic hydraulic test stand is used replacing the classical mechanical test stands which allow only sinusoidal excitation. For the Monte Carlo simulation with a real shock absorber in the loop, the random excitation of ground roughness is generated using a modified spectral representation method based on the famous contributions of Shinozuka. Motion and force of the shock absorber are measured and fed back to the Monte Carlo simulation of a car model in real time. The characteristic of the shock absorber is identified using the classical least squares method and a correlation-based method. A piecewise linear model for the characteristic relating the damping force and the velocity of the piston is applied for the shock absorber identification.     

Optimization of LiMn2O4 electrode properties in a gradient- and surrogate-based framework

In this study, the effects of discharge rate and LiMn2O4 cathode properties (thickness, porosity, particle size, and solid-state diffusivity and conductivity) on the gravimetric energy and power density of a lithium-ion battery cell are analyzed simultaneously using a cell-level model. Surrogate-based analysis tools are applied to simulation data to construct educed-order models, which are in turn used to perform global sensitivity analysis to compare the relative importance of cathode properties. Based on these results, the cell is then optimized for several distinct physical scenarios using gradient-based methods. The comple-mentary nature of the gradient-and surrogate-based tools is demonstrated by establishing proper bounds and constraints with the surrogate model, and then obtaining accurate optimized solutions with the gradient-based optimizer. These optimal solutions enable the quantification of the tradeoffs between energy and power density, and the effect of optimizing the electrode thickness and porosity. In conjunction with known guidelines, the numerical optimization frame-work developed herein can be applied directly to cell and pack design.     

Aerodynamic analysis of circular plate-shaped and circular ring-shaped squeeze film bearings

Aerodynamics of circular plate-and circular ring-shaped squeeze film bearings isanalyzed in detail,yielding analytic expressions for the pressure distribution of thesebearings.Several formulae for these bearings are modified using the developed method.Thepaper also gives numerical results of pressure distribution and load-bearing capacities ofthese bearings.     

Simultaneous identification of stiffness and damping properties of isotropic materials from forced vibrating platesIdentification simultanée de rigidités et d'amortissements de matériaux isotropes à partir de plaques en vibrations forcées

This paper presents a novel methodology for the identification of damping of isotropic plates. It relies on forced inertial excitation of a clamped plate and full-field curvature measurements using a suitable optical technique. Using the Virtual Fields Method, it is shown that the damping parameter is easily related to the curvature field, even on a non-resonant plate. This paper opens a totally new field of investigation for damping identification. To cite this article: A. Giraudeau, F. Pierron, C. R. Mecanique 331 (2003).     

Effect of non-linearities in the identification and fault detection of gear-pair systems

This study investigates issues related to parametric identification and health monitoring of dynamical systems with non-linear characteristics. In the first part, a gear-pair system supported on bearings with rolling elements is selected as an example mechanical model and the corresponding equations of motion are set up. This model possesses strongly non-linear characteristics, accounting for gear backlash and bearing stiffness non-linearities. Then, the basic steps of the parametric identification and fault detection procedure employed are outlined briefly. In particular, a Bayesian statistical framework is adopted in order to estimate the optimal values of the gear and bearing model parameters. This is achieved by combining experimental information from vibration measurements with theoretical information built into a parametric mathematical model of the system. In the second part of the study, characteristic numerical results are presented. First, based on the effect of the system parameters on its dynamics, a solid basis is created for explaining some of the peculiar results obtained by applying classical gradient-based optimization methodologies for the strongly non-linear system examined. Some serious difficulties, associated with the existence of irregular response or the coexistence of multiple motions, are first pointed out. A solution to some of these problems, through the application of a suitable genetic algorithm, is then presented. Special problems, related to more classical identification issues associated with the presence of measurement noise and model error, are also investigated.     

R_滤子的谱及几何性质

By applying the Fourier analysis, we study the spectral properties of R- filters. Further, we prove that R-filters are a generalization of least squares polynomial adjustment, and we give the geometric interpretation of R-filters.     

On the use of neural networks for identification of linear and nonlinear systems

A procedure based on neural networks for the classification of linear and nonlinear systems is presented, using excitation and response data under swept sine excitation. Special attention is paid to the classification and identification of linear and bilinear systems, the latter being considered since they exhibit typical characteristics of cracked systems. The computer simulations show that: (1) using the procedure presented in this paper the trained classification network can reliably classify a linear system and different nonlinear systems; (2) the output of the trained identification neural network for a linear system and a bilinear system can be used as a quantitative indicator of characteristics of bilinear systems having different stiffness ratios (k _(x>0)/k _(x<0)) with respect to the bilinear system used in the training stage; (3) for two-degree-of-freedom systems, the trained network can not only determine the existence of a bilinear stiffness and the magnitude of its stiffness ratio, but also specify which stiffness is bilinear, i.e. indicate its position. These results provide a possibility of using the trained neural networks to detect and locate structural cracks which have the characteristics of bilinear systems.Visiting scholar, from People's Republic of China.     

Stiffness relations for piezoelectric indentation of flat and non-flat punches of arbitrary planform: Applications to probing nanoelectromechanical properties of materials

Stiffness relations for voltage-dependent contact mechanics of piezoelectric material are derived for an indenter of arbitrary planform under normal force, centrally or non-centrally applied, and electric charge distribution at the base. Relations between indentation depth, indentation force, electric potential and electric charge are explicitly given in terms of indenter's geometry and piezoelectric material constants. The analysis covers indenters with non-flat base approximated by a second-order surface; elliptic paraboloid is considered as an example. In the case of the elliptic non-flat planform, the derived stiffness relations are exact; otherwise, they are approximate and are shown to have good accuracy. The stiffness relations are given in elementary functions and are obtained by utilizing the recently established principle of correspondence between the piezoelectric and purely elastic problems. Besides contributing to extension of Hertzian mechanics to piezoelectric materials, these results are essential for quantitative interpretation of the scanning probe microscopy and piezoelectric nanoindentation data on piezoelectric, ferroelectric, and multiferroic materials.     

Application of plane wave expansion and stiffness matrix methods to study transmission properties and guided mode of phononic plates

Numerical procedure based on plane wave expansion and stiffness matrix method is developed to calculate the transmission factor of a micro two-dimensional phononic plate. Calculations of the dispersion curve have been achieved by introducing particular functions which transform motion equations into an eigenvalue problem. The state vector has been generalized to a phononic material, it leads to a comparatively convenient matrix formulation. The influence of the layer number on the transmission factor is studied. In addition, our interest is focused on the observed gap and how it behaves when phononic structure undergoes a slight change. The result shows that if the central phononic layer is replaced by one or two homogeneous layers, guided modes originate inside the frequency band gaps.     

Rheological properties of branched polystyrenes: nonlinear shear and extensional behavior

Nonlinear shear and uniaxial extensional measurements on a series of graft-polystyrenes with varying average numbers and molar masses of grafted side chains are presented. Step-strain measurements are performed to evaluate the damping functions of the melts in shear. The damping functions show a decreasing dependence on strain with an increase in mass fraction of grafted side chains. Extensional viscosities of the melts of graft-polystyrenes exhibit a growing strain hardening with increasing average number of grafted side chains as long as the side branches have a sufficient molar mass to be entangled. Graft-polystyrenes with side arms below the critical molar mass M _c for entanglements of linear polystyrene but above the entanglement molar mass M _e of linear polystyrene (M _e < M _w,br < M _c) still show a distinct strain hardening. With decreasing molar mass of the grafted side chains (M _w,br < M _e) the nonlinear-viscoelastic properties of the graft-polystyrene melts approach the behavior for a linear polystyrene with comparable polydispersity.Electronic Supplementary Material Supplementary material is available for this article at     

Hysteresis models of dynamic mode atomic force microscopes: analysis and identification via harmonic balance

A new class of models based on hysteresis functions is developed to describe the operation of dynamic mode atomic force microscopy. Such models can account for dissipative phenomena affecting the interaction between the probe and the sample. The model analysis, which is developed using frequency domain techniques, provides a insights into experimentally observed behavior. Experimental data corroborates the models developed.     

Experimental-theoretical study of the penetration of rigid projectiles and identification of soil properties

The parameters of the Grigoryan soil model are determined using an experimental-computational method previously proposed and the results of reversed experiments on penetration of projectiles with flat and hemispherical heads at impact velocities of 50–450 m/sec in sandy soil. It is shown that the quasistationary dependences of the resistance force on impact velocity obtained in the reversed experiment can be used to solve problems of deep penetration of projectile in soil with an error not exceeding the measurement error.     

Trace type functional differential equations and the identification of hydraulic properties of porous media

Summary The authors give four examples of inverse problems related to fluid flow in a porous media. These are the problems of identifying an unknown source term, and unknown diffusivity, an unknown porosity, and both an unknown diffusivity and porosity. The authors show how these problems can be recast into problems whoso equations are well-defined differential equations with trace type functional coefficients. The authors conclude with a discussion of the reformulated problems.     

Stochastic modeling and identification of an uncertain computational dynamical model with random fields properties and model uncertainties

This paper is devoted to the construction and to the identification of a probabilistic model of random fields in the presence of modeling errors, in high stochastic dimension and presented in the context of computational structural dynamics. Due to the high stochastic dimension of the random quantities which have to be identified using statistical inverse methods (challenging problem), a complete methodology is proposed and validated. The parametric–nonparametric (generalized) probabilistic approach of uncertainties is used to perform the prior stochastic models: (1) system-parameters uncertainties induced by the variabilities of the material properties are described by random fields for which their statistical reductions are still in high stochastic dimension and (2) model uncertainties induced by the modeling errors are taken into account with the nonparametric probabilistic approach in high stochastic dimension. For these two sources of uncertainties, the methodology consists in introducing prior stochastic models described with a small number of parameters which are simultaneously identified using the maximum likelihood method and experimental responses. The steps of the methodology are explained and illustrated through an application.     

Flat-jack tests and inverse analysis for the identification of stress states and elastic properties in concrete dams

In this paper an experimental-numerical method, centred on flat-jack tests, is presented for the identification of local stress states and possibly deteriorated elastic properties of concrete in existing dams. It is shown herein that the synergistic combination of new pattern of flat-jack experiment, computer simulation of the test (by conventional finite elements) and inverse analysis allows to exploit experimental data more effectively than by the traditional procedure, and to achieve more information on material properties. In fact, at suitably chosen locations on the free surface of the monitored dam, all the components of local (plane) stress state and the elastic moduli in two orthogonal directions (including shear stiffness) can be estimated by the proposed method. The inverse problem in point is formulated as a sequence of two parameter identifications, i.e. as a bilevel (in the sense of Stackelberg) mathematical programming problem. The solution in a stochastic context is achieved by means of a modified Bayes technique, allowing to obtain, in a “batch” (non sequential) way, parameter estimates endowed with a covariance matrix which quantifies their degrees of confidence and correlations. Dedicated to the memory of Professor Giulio Ceradini.