Microstructure characterization of austenitic Fe–25Mn–22Cr–2Si–0.7N alloy processed by twin roll strip casting

Near net shape casting of austenitic stainless steel containing high Mn and N was explored by using a twin roll strip caster. Microstructural observation and analysis of the as-cast strip by XRD, SEM, and TEM demonstrated that the formation of δ-ferrite and carbides had been prohibited due to the high solidification cooling rate of more than 14,000 K/s during strip casting. Tensile tests indicated that the as-cast strip possessed reasonably good mechanical properties, with a yield strength of 500 MPa and elongation of about 15%. The elastic modulus of the as-cast strip was higher than that of solution treated steel by about one order of magnitude. From the TEM observations, it was found that the as-cast strip contained more dislocations and numerous interstitial elements (N and C) dissolved in grains than the solution treated material, in which dislocations were scarcely observed and precipitates were formed along grain boundaries. Fracture morphology indicates that the as-cast strip has undergone ductile rupture during tensile testing. Deformation twins were observed in the deformed region of the sample by the in-situ tensile test under SEM and TEM observations. The formation of deformation twins were believed to be responsible for high plasticity of the as-cast strip.     

Transient analysis of a piezoelectric strip with a permeable crack under anti-plane impact loads

The problem of a through permeable crack situated in the mid-plane of a piezoelectric strip is considered under anti-plane impact loads for two cases. The first is that the strip boundaries are free of stresses and of electric displacements, and the second is that the strip boundaries are clamped rigid electrodes. The method adopted is to reduce the mixed initial-boundary value problem, by using integral transform techniques, to dual integral equations, which are further transformed into a Fredholm integral equation of the second kind by introducing an auxiliary function. The dynamic stress intensity factor and energy release rate in the Laplace transform domain are obtained in explicit form in terms of the auxiliary function. Some numerical results for the dynamic stress intensity factor are presented graphically in the physical space by using numerical techniques for solving the resulting Fredholm integral equation and inverting Laplace transform.     

高速铁路路基的动力响应分析方法

基于一致粘弹性人工边界建立了有砟轨道高速铁路在动荷载作用下的三维轨道路基有限元模型,模型考虑列车荷载、钢轨、轨枕、道床及路基的接触关系,采用移动轮载单元模拟列车通过时的动力作用。分析了四种机车车辆的一个轮对荷载引起的动应力在路基中的传播特性,包括路基面动应力与轴重、车速的关系,动应力沿路基纵向、横向及深度方向的变化。通过计算结果与秦沈客运专线综合试验实测结果的比较,验证了有限元分析的可靠性。三维一致粘弹性人工边界及单元的的成功应用,对缩小计算模型、缩短计算时间和提高计算精度提供了解决方案,有利于高速铁路尤其是无砟轨道路基动力特性的进一步研究。     

Boundary integral equations from Hamilton's principle for surface acoustic waves under periodic metal gratings

The procedure describes the derivation of boundary integral equations for surface acoustic waves propagating under periodic metal strip gratings with piezoelectric films. It takes into account the electrical and mechanical perturbations, including the effects of mass loading caused by the gratings with an arbitrary shape. First, an integral equation is derived with line integrals on the boundaries within one period. This derivation is based on Hamilton's principle and uses Lagrange's method of multipliers to alleviate the continuous conditions of the displacement and the electric potential on the boundaries. Second, boundary integral equations corresponding to each substrate, piezoelectric film, metal strip, and free space region are obtained from the integral equation using the Rayleigh-Ritz method for admissible functions. With this procedure, it is not necessary to make any assumptions for separation of the boundary conditions between two neighboring regions. Consequently, we clarify the theoretical basis for the analytical procedure using boundary integral equations for longitudinal LSAW modes.     

条层法及其对板带轧制三维变形的仿真

提出一种模拟板带轧制过程三维变形的新的数值方法——条层法。首先沿高向将变形区均匀地划分为若干层,然后再沿着金属的流动轨迹将变形区内的每层带材划分为若干流线条元,为了方便分析和计算,又将流线条元映射为矩形条元。横向位移的纵向分布被构造为四次曲线,横向分布用三次样条插值函数表示,高向分布用二次曲线拟合。根据塑性力学流动理论,分析推导了变形区三维变形和应力的数学模型。与作者曾经提出的流线条元法相比,考虑了应力与变形沿高向的不均匀分布,实现了精确的三维分析和计算。关于热带钢连轧和厚板轧制的仿真实例表明,提出的方法和模型符合实际,为板带轧制过程的三维力学仿真提供了一个新的实用工程数值方法。     

Simplified BEM/FEM model for dynamic analysis of structures on piles and pile groups in viscoelastic and poroelastic soils

A simplified model for the analysis of the dynamic response of structures on piles and pile groups under time harmonic excitation is presented in this paper. It is a coupled boundary element–finite element model able to take into account dynamic pile–soil–pile interaction in a rigorous manner. Piles and pile groups in viscoelastic or poroelastic soils are considered. Two-node cylindrical boundary elements are used to represent the interface between soil and pile. These elements are connected to beam-type finite elements representing the concrete pile which can be connected to a pile cap and to any superstructure modeled by beam elements. The model is rather simple: two-node beam elements along the pile are directly connected to the BE nodes along the soil hole, and the uppermost node to the soil surface and to the FE nodes of any superstructure. Thus, large structures founded on piles in viscoelastic or poroelastic soils can be represented using a reasonable number of unknowns. In order to validate the procedure, single piles and pile groups in viscoelastic and poroelastic soils are analyzed. The obtained results are compared with those obtained by other authors using more complex or less general approaches. There is a good agreement between the present results and those reported in the literature.     

Initial response of a micro-polar hypoplastic material under plane shearing

The behavior of an infinite strip of a micro-polar hypoplastic material located between two parallel plates under plane shearing is investigated. The evolution equation of the stress tensor and the couple-stress tensor is described using tensor-valued functions, which are nonlinear and positively homogeneous of first order in the rate of deformation and the rate of curvature. For the initial response of the sheared layer an analytical solution is derived and discussed for different micro-polar boundary conditions at the bottom and top surfaces of the layer. It is shown that polar quantities appear within the shear layer from the beginning of shearing with the exception of zero couple stresses prescribed at the boundaries.     

Initial response of a micro-polar hypoplastic material under plane shearing

The behavior of an infinite strip of a micro-polar hypoplastic material located between two parallel plates under plane shearing is investigated. The evolution equation of the stress tensor and the couple-stress tensor is described using tensor-valued functions, which are nonlinear and positively homogeneous of first order in the rate of deformation and the rate of curvature. For the initial response of the sheared layer an analytical solution is derived and discussed for different micro-polar boundary conditions at the bottom and top surfaces of the layer. It is shown that polar quantities appear within the shear layer from the beginning of shearing with the exception of zero couple stresses prescribed at the boundaries.     

Earthquake response analysis in the time domain for 2D soil–structure systems using analytical frequency‐dependent infinite elements

This paper presents a time domain method for soil–structure interaction analysis under seismic excitations. It is based on the finite element formulation incorporating analytical frequency‐dependent infinite elements for the far‐field soil region. Equivalent earthquake input forces are calculated based on the free‐field responses along the interface between the near‐ and far‐field soil regions using the fixed exterior boundary method in the frequency domain. Then, the input forces are transformed into the time domain by using inverse Fourier transform. The dynamic stiffness matrices of the far‐field soil region formulated using the analytical frequency‐dependent infinite elements in the frequency domain can be easily transformed into the corresponding matrices in the time domain. Hence, the response can be analytically computed in the time domain. A recursive procedure is proposed to compute the interaction forces along the interface and the responses of the soil–structure system in the time domain. Earthquake response analyses have been carried out on a multi‐layered half‐space and a tunnel embedded in a layered half‐space, and results are compared with those obtained by the conventional method in the frequency domain. Copyright © 2003 John Wiley & Sons, Ltd.     

Streamline strip element method for analysis of the three‐dimensional stresses and deformations of strip rolling

This paper puts forward a new method—the streamline strip element method (SSEM) for simulating the three‐dimensional stresses and deformations of strip rolling process. The rolling deformation zone is divided into a number of streamline strip elements along metal flow traces, and the streamline strip elements are mapped onto the corresponding rectangle strip elements for computation. The longitudinal distribution model of the metal lateral displacement is constructed to be a quartic plus cubic curve. The three‐dimensional deformations and stresses of the deformation zone are formulated. For the cold strip rolling on a 300 mm wide four‐high mill, the computed results of the transverse distributions of the rolling pressure and the front and back tension stresses are close to the experimental ones. For the cold strip rolling on a 1850 mm wide six‐high CVC mill, the computed results of the transverse distributions of the front tension stress are also close to the experimental ones. This proves that the streamline strip element is a reliable engineering–computation method, and of great importance to developing the mathematical model of the shape control of strip rolling. Copyright © 2001 John Wiley & Sons, Ltd.     

Dynamic Stress-Intensity Factors for an Orthotropic Infinite Strip with a Semi-Infinite Crack

A clamped infinite strip of an orthotropic material and containing a semi-infinite crack is considered. The strip is loaded by time-dependent translations of the boundaries and the dynamic stress-intensity factor is obtained using a path independent integral. The solution is found to be of the same form as for the corresponding isotropic case.     

Quasiparticle Edge Losses in Double STJs Strip X-Rays Detectors

The 2D diffusion model of the strip X-ray detector was developed. The detector consists of a long superconducting strip, which is ended by the trapping layers and superconducting tunnel junctions at each end. The model takes into account the diffusion of the excess quasiparticles, quasiparticle trapping at the tunnel junctions and quasiparticle losses in the volume of the strip and at the strip boundaries. The analytical solution was obtained. It has been shown that quasiparticle losses at the strip boundaries caused the dependence of the signals on the photon absorption site in transverse direction. The latter worsens the energy resolution and transforms the spectral line of the detector to nongaussian shape.      

下卧刚性基岩条件下场地土-结构体系地震反应分析方法研究

下卧刚性基岩条件下的土-结构体系地震反应分析模型是一个能量“半开放-半封闭”系统。它与完全的能量“开放”系统土-结构体系地震反应分析模型的不同之处是其采用了域内惯性力的地震动输入方式,这与刚性基岩-结构体系地震反应分析模型的地震动输入方式是相同的。不同于刚性基岩上的结构地震反应分析模型,下卧刚性基岩条件下的土-结构体系地震反应分析模型需要考虑半无限土层对截断边界处的影响。就笔者-所见,目前有许多研究者和工程技术人员对这一问题有错误的理解,认为截断边界的影响只是一个人工边界处理问题,分析中仅采用人工边界条件模拟了截断边界对辐射能量的影响,而忽略了一个更重要的影响因素--下卧刚性基岩条件下场地土的自由场效应。为澄清这一问题,基于土-结构体系地震反应的直接分析模型,严格推导了下卧刚性基岩条件下的土-结构体系地震反应分析方法,指出在通常的工程经验尺度内遗漏自由场运动效应将得不到正确的计算结果。     

Kosterlitz-Thouless Transition in Finite-Size BEC Systems

The Kosterlitz-Thouless (KT) transition in two-dimensional BEC systems is calculated taking into account the fact that in experiments these are finite-size systems. The outer boundaries of the condensate effectively act as hard walls, and this has a polarizing effect on the vortex pairs of the KT transition, causing the superfluid fraction to become strongly anisotropic. The decreased pair energy near the walls results in a strongly enhanced vortex density near the boundaries. Since the pair density can now be directly measured, we extend here our previous calculations to include the vortex density as a function of the distance from the boundaries. Possible experiments using sound propagation in the gases are proposed to probe the anisotropic properties of the superfluid density, including an unusual sharp dip in the superfluid density that is predicted to occur down the middle of a long superfluid strip.      

考虑桩土耦合作用时弹性支承桩纵向振动特性分析及应用

从三维轴对称角度对弹性支承桩与均质土耦合作用时的纵向振动特性进行了研究分析。假定桩为竖直弹性均匀截面桩,土为线性粘弹性体,其材料阻尼为滞回阻尼,首先通过对土层进行求解得到其振动位移形式解,然后利用该解并以小应变条件下桩土接触界面位移连续来考虑桩土的耦合作用,来分析基桩的动力反应,研究得到了弹性支承桩在谐和荷载作用下频域响应函数解析解,并利用所得解对土层动力反应特性以及桩土体系的振动特性进行了分析,得到了一些新的结论,最后将该理论解与桩顶实测导纳曲线进行了拟合比较,两者较为一致。     

Development and validation of a 3D computational tool to describe concrete behaviour at mesoscale. Application to the alkali-silica reaction

A finite element analysis of the large deformation of three-dimensional polycrystals is presented using pixel-based finite elements as well as finite elements conforming with grain boundaries. The macroscopic response is obtained through volume-averaging laws. A constitutive framework for elasto-viscoplastic response of single crystals is utilized along with a fully-implicit Lagrangian finite element algorithm for modeling microstructure evolution. The effect of grain size is included by considering a physically motivated measure of lattice incompatibility which provides an updated shearing resistance within grains. A domain decomposition approach is adopted for parallel computation to allow efficient large scale simulations. Conforming grids are adopted to simulate flexible and complex shapes of grains. The computed mechanical properties of polycrystals are shown to be consistent with experimental results for different grain sizes.     

Boundary element solution of the transonic integro-differential equation

The transonic integro-differential equation for two-dimensional flows is solved by boundary element methods. In addition to constant and quadrilateral elements we develop hybrid elements based on constant elements in the streamwise direction and variable elements in the transverse direction. Computation is carried out for parabolic-arc and NACA0012 airfoils and the results, which converge fast, compare favourably with finite-difference solutions. The hybrid elements are to be preferred because they yield results which are more accurate than constant elements without the computational complexity associated with quadrilateral elements. Moreover, they can be applied with a small number of nodes by using only one strip of rectangular elements.     

Transient response of a functionally graded piezoelectric strip with a penny-shaped crack under electric time-dependent loading

Summary The dynamic fracture problem for a functionally graded piezoelectric material (FGPM) strip containing a penny-shaped crack parallel to the free boundaries is considered in this study. It is assumed that the electroelastic properties of the strip vary continuously along the thickness direction of the strip, and that the strip is under time-dependent electric load. Integral transform techniques and dislocation density functions are employed to reduce the problem to the solutions of a system of singular integral equations. The stress and electric displacement intensity factors versus time are presented for various values of dimensionless parameters representing the crack size, the crack location and the material nonhomogeneity.     

Flatness measurement system based on a nonlinear opticaltriangulation technique

This paper describes the development of a flatness measurement system, integrated in the control process of a hot strip mill in the steel industry. The objective of the system is to calculate flatness indexes for every rolled strip, comparing the length of its lateral profiles with the central length. The reconstruction of the profiles is based on a nonlinear triangulation technique. Images of laser spots over the steel strip, at high temperature and high speed, are sampled every two milliseconds at five different points and are processed online in order to calculate height displacement values of the strip, so that final flatness indexes for the steel strip can be calculated. The measurement method developed introduces an innovative geometry in the disposition of the optic elements which increases the measurement range of the system without reducing its accuracy. It also includes a tracking system to compensate for the effects of lateral displacements of the strip. The flatness measurement system has been implemented using a heterogeneous distributed computer system     

Mixed isogeometric analysis of strongly coupled diffusion in porous materials

In this paper, we develop a mixed isogeometric analysis approach based on subdivision stabilization to study strongly coupled diffusion in solids in both small and large deformation ranges. Coupling the fluid pressure and the solid deformation, the mixed formulation suffers from numerical instabilities in the incompressible and the nearly incompressible limit due to the violation of the inf‐sup condition. We investigate this issue using subdivision‐stabilized nonuniform rational B‐spline (NURBS) elements, as well as different families of mixed isogeometric analysis techniques, and assess their stability through a numerical inf‐sup test. Furthermore, the validity of the inf‐sup stability test in poromechanics is supported by a mathematical proof concerning the corresponding stability estimate. Finally, two numerical examples involving a rigid strip foundation on saturated soil and a swelling hydrogel structure are presented to validate the stability and to demonstrate the robustness of the proposed approach.