Time stepping schemes for coupled displacement and pore pressurē analysis

 The paper investigates the performance of various time stepping schemes for coupled displacement and pore pressure analysis. A number of alternative forms of the automatic time stepping method proposed by Sloan and Abbo (1999a) are also presented. These alternative schemes use different updates for the displacements and pore pressures and also adopt different starting conditions for the iterations. The automatic schemes are compared with an implicit θ-method, as well as an explicit method, through analysis of a variety of problems involving undrained loading, drained loading, and consolidation for Mohr-Coulomb and critical state models. As expected, the numerical results confirm that the explicit scheme is neither accurate nor robust. Although the implicit θ-method is accurate and fast, it fails to give a solution in a number of cases where the time step is large. The automatic schemes are shown to be accurate, fast and generally robust. Two of the automatic schemes proposed never fail to furnish a solution for the cases considered. In addition, all the automatic schemes are able to constrain the time-stepping (temporal integration) error in the displacements and pore pressures to lie near a prescribed tolerance, provided the iteration error tolerance is properly chosen. For complex soil models, it is important that the latter is set sufficiently small in order for the schemes to be able to constrain the time-stepping error to lie within a prescribed tolerance. Dedicated to the memory of Prof. Mike Crisfield, for his cheerfulness and cooperation as a colleague and friend over many years.     

An equation of state for pure fluids describing the critical region

Density fluctuations of a pure nuid are treated by a cell model, in which the fluid is divided into cells containing different numbers of particles. A probability function for the particle number is derived. This function, after convolution with a classical (mean field) equation of state, leads to an improved equation of state which is valid in the critical region. The equation of state is analytical, hence not exact in the immediate vicinity of the critical point. As an example, the convolution is applied to the Carnahan-Starling/van der Waals equation of state; the resulting equation of state is used to correlate thermodynamic properties of several simple fluids.     

A scaled equation of state for real fluids in the critical region

A scaled equation of state is proposed for real fluids in the critical region which incorporates asymmetry with respect to the critical isochore. In the range of reduced densities 0.65(/ _c)1.4 and for reduced temperatures (T/T _c)1.2, the equation represents P-V-T data for steam within the experimental accuracy.     

Erratum to the ‘Load stepping schemes for critical state models’ International Journal for Numerical Methods in Engineering 2001; 50:67–93

The original article to which this Erratum refers was published in Interntational Journal for Numerical Methods in Engineering 2001; 50 :67–93.     

Step size adjustment and extrapolation for time‐stepping schemes in non‐smooth dynamics

In this paper we use step size adjustment and extrapolation methods to improve Moreau's time‐stepping scheme for the numerical integration of non‐smooth mechanical systems, i.e. systems with impact and friction. The scheme yields a system of inclusions, which is transformed into a system of projective equations. These equations are solved iteratively. Switching points are time instants for which the structure of the mechanical system changes, for example, time instants for which a sticking friction element begins to slide. We show how switching points can be localized and how these points can be resolved by choosing a minimal step size. In order to improve the integration of non‐smooth systems in the smooth parts, we show how the time‐stepping method can be used as a base integration scheme for extrapolation methods, which allow for an increase in the integration order. Switching points are processed by a small time step, while time intervals during which the structure of the system does not change are computed with a larger step size and improved integration order. The overall algorithm, which consists of a time‐stepping module, an extrapolation module and a step size adjustment module, is discussed in detail and some examples are given. Copyright © 2008 John Wiley & Sons, Ltd.     

Noise-free Determination of Isochromatic Fringe Order by Load Stepping

The traditional ambiguity in the sign of fractional retardation in certain zones of the model by phase shifting technique has been overcome with the development of load stepping in digital photoelasticity. However, the existing methodology of load stepping introduces several points in the model domain that are subjected to excessive noise. A new methodology has been proposed that combines the merits of load stepping and phase shifting to obtain fractional retardation free of noise and ambiguity over the model domain.     

Performance of time‐stepping schemes for discrete models in fracture dynamic analysis

In this work we present a critical evaluation of different time integration schemes within the setting of non‐linear dynamic analysis of brittle fracture problem represented by a discrete model. The discrete model of this kind consists of Voronoi cells representing the grains of a heterogeneous structure, which are interconnected by cohesive forces modelled by beam‐like links capable of taking properly into account both brittle dynamic fracture and large displacement of a still connected pack of grains that might split from the structure. The brittle behaviour of cohesive links requires that the dynamic analysis of such a model be treated with care, and the best possible integration scheme be selected. Four different schemes are explored and compared in application to a dynamic traction test, including Newmark explicit and implicit schemes, HHT‐α scheme and energy‐decaying scheme. Copyright © 2005 John Wiley & Sons, Ltd.     

Equation of state and critical point of cesium

Equation-of-state measurements for cesium at temperatures from 350 to 2200 K and pressures from 1 to 60 MPa by means of a hermetically sealed two-zone dilatometer are presented. The experimental range includes the liquid and gaseous phases together with the coexistence curve up to critical point and supercritical region. The critical parameters are 1938 K, 9.4 MPa, 0.39 g · cm^–3. The data were used for the calculation of tables of the density and its derivatives for cesium. The results are discussed.     

Complete Isochromatic Fringe-order Analysis in Digital Photoelasticity by Fourier Transform and Load Stepping

Abstract:  In this paper, a new fully automated photoelastic technique based on both the Fourier transform and the envelope of the fringe centres, is presented. Using two images of the isochromatics acquired with different loads and a simple calculation routine, the method allows the user the complete determination of the isochromatic fringe retardation on any arbitrary line chosen over the model domain, without the need for supplementary external information or calibration. Various experiments have corroborated the accuracy of the method, estimated theoretically to about 0.07 fringe orders. As a result of its simplicity and sufficient accuracy, the method can be used in the industrial field also by a non-expert user.     

Crossover equation of state for the thermodynamic properties of mixtures of methane and ethane in the critical region

We present an equation of state for the thermodynamic properties of mixtures of methane and ethane in the critical region that incorporates the crossover from singular thermodynamic behavior near the locus of vapor-liquid critical points to regular thermodynamic behavior outside the critical region. The equation of state yields a satisfactory representation of the thermodynamic-property data for the mixtures in a large range of temperatures and densities.     

球磨机负荷检测的现状与发展趋势

根据球磨机负荷的检测在球磨过程自动控制中的重要作用 ,论述了球磨机负荷检测的现状 ,指出了未来的发展趋势     

A generalized scaled equation of state for n-alkanes (methane to n-nonane) in the critical region

A generalized scaled equation of state has been developed to calculate thermodynamic properties of n-alkanes from methane (CH₄) to n-nonane (C₉H₂₀) in the critical region. The equation is valid in the reduced density range 0.7 _c1.3 at T=T _c and up to 1.2T _c at = _c.     

Probability of the critical state of glue joints of a shallow laminated shell with random irregularities

Relations have been obtained for the determination of the probability of the dangerous (critical) state of the glue joints of a shallow laminated shell in the case of the presence of initial irregularities of the elastic plies with known probabilistic characteristics. An example of calculation of the probability of the critical state of the glue joint of a two-ply shell with known mathematical expectation and correlation function of random initial deflection of the upper ply is considered. __________ Translated from Problemy Prochnosti, No. 1, pp. 138–149, January–February, 2006.     

Nonconforming rotated Q1 tetrahedral element with explicit time stepping for elastodynamics

In this paper, we apply a rotated bilinear tetrahedral element to elastodynamics in . This element performs superior to the constant strain element in bending and, unlike the conforming linear strain tetrahedron, allows for row‐sum lumping of the mass matrix. We study the effect of different choices of approximation (pointwise continuity versus edge average continuity) as well as lumping versus consistent mass in the setting of eigenvibrations. We also use the element in combination with the leapfrog method for time domain computations and make numerical comparisons with the constant strain and linear strain tetrahedra. Copyright © 2012 John Wiley & Sons, Ltd.     

车辆悬架零部件载荷谱提取方法研究

优选载荷谱提取方法是提高汽车悬架零部件疲劳性能分析精度的关键.基于此,以某紧凑型SUV和某中级轿车为测试车型,通过实车试验场强化路面和室内振动台架试验采集得到轮心六分力和悬架多个监测部位的加速度、位移响应信号;实测整车参数并在ADAMS软件中建立整车刚柔耦合动力学模型;采用虚拟迭代法和约束加载法对多种振动台工况进行仿真...     

Estimating the critical time‐step in explicit dynamics using the Lanczos method

The goal of our paper is to demonstrate the cost‐effective use of the Lanczos method for estimating the critical time step in an explicit, transient dynamics code. The Lanczos method can provide a significantly larger estimate for the critical time‐step than an element‐based method (the typical scheme). However, the Lanczos method represents a more expensive method for calculating a critical time‐step than element‐based methods. Our paper shows how the additional cost of the Lanczos method can be amortized over a number of time steps and lead to an overall decrease in run‐time for an explicit, transient dynamics code. We present an adaptive hybrid scheme that synthesizes the Lanczos‐based and element‐based estimates and allows us to run near the critical time‐step estimate provided by the Lanczos method. Copyright © 2006 John Wiley & Sons, Ltd.     

Adaptive backward Euler time stepping with truncation error control for numerical modelling of unsaturated fluid flow

An automatic time stepping scheme with embedded error control is developed and applied to the moisture‐based Richards equation. The algorithm is based on the first‐order backward Euler scheme, and uses a numerical estimate of the local truncation error and an efficient time step selector to control the temporal accuracy of the integration. Local extrapolation, equivalent to the use of an unconditionally stable Thomas–Gladwell algorithm, achieves second‐order temporal accuracy at minimal additional costs. The time stepping algorithm also provides accurate initial estimates for the iterative non‐linear solver. Numerical tests confirm the ability of the scheme to automatically optimize the time step size to match a user prescribed temporal error tolerance. An important merit of the proposed method is its conceptual and computational simplicity. It can be directly incorporated into existing or new software based on the backward Euler scheme (currently prevalent in subsurface hydrologic modelling), and markedly improves their performance compared with simple fixed or heuristic time step selection. The generality of the approach also makes possible its use for solving PDEs in other engineering applications, where strong non‐linearity, stability or implementation considerations favour a simple and robust low‐order method, or where there is a legacy of backward Euler codes in current use. Copyright © 2001 John Wiley & Sons, Ltd.     

喷雾冷却临界传热特性试验研究

为了进行极限热工况下的喷雾冷却传热特性研究,设计并搭建采用蒸馏水及乙醇溶液喷雾冷却试验台,分析结构参数、喷雾流量、喷雾腔内压力等对喷雾冷却临界热流密度的影响。试验结果表明:临界热流密度随槽道深度增加先增大后减小,最佳槽道深度为0.8 mm,此时临界热流密度达到326 W/cm^2;随着喷雾流量的增加,临界热流密度始终增大;喷雾腔内压力对临界热流密度基本没有影响。计算结果表明,喷雾冷却效率随槽道深度增加而提升,随喷雾流量的增加而减弱。     

Theory of the universal and nonuniversal quantities of fluids at the critical point

We show that the hierarchical reference theory is an accurate global theory of fluids at least above the critical temperatureT _c. The hierarchy is truncated at the first equation, the one connecting the free energy to the pair correlation function, with an Ornstein-Zernike ansatz. In this approximation the theory can be considered as a sophisticated generalization of the optimized random phase approximation which has genuine nonclassical critical exponents and for which scaling is satisfied. We study the system of hard spheres plus the Lennard-Jones attractive well and find a good agreement with measuredPVT, specific heat, correlation length, and structure factor in rare gases. The accuracy of the theory remains very good up to freezing density.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Indirect measurement of state variables for the diagnostics of electromechanical systems

A method of estimating the actual state of electromechanical systems based on the use of a model, connected in parallel with the diagnosed equipment, and an indirect measurement of the state variables is considered. A diagnostic system structure is proposed and also versions of models which take the operating features into account. __________ Translated from Izmeritel’naya Tekhnika, No. 7, pp. 43–46, July, 2007.