Triple-region structure for turbulent-flow in a square duct - a finite-element approach

The Reynolds-averaged Navier-Stokes equations for describing the turbulent flow in a straight square duct are formulated with two different turbulence models. The governing equations are then expanded as a multi-deck structure in a plane perpendicular to the streamwise direction, with each deck characterized by its dominant physical forces as commonly carried out in analytical work using triple-deck expansion. The resulting equations are numerically integrated using higher polynomial (H-P) finite element technique for each cross-sectional plane to be followed by finite difference representation in the streamwise direction until a fully developed state is reached. The computed results using the two different turbulence models show fair agreement with each other, and concur with the vast body of available experimental data. There is also general agreement between our results and the recent numerical works anisotropic k-epsilon turbulence model.

Collapsed isoparametric element as a singular element for a crack normal to the bi-material interface

It is shown that the variable power singularity of the strain field at the crack tip can be obtained by the simple technique of collapsing quadrilateral isoparametric elements into triangular elements around the crack tip and adequately shifting the side-nodes adjacent to this crack tip. The collapsed isoparametric elements have the desired singularity at crack tip along any ray. The strain expressions for a single element have been derived and in addition to the desired power singularity, additional singularities are revealed. Numerical examples have shown that triangular elements formed by collapsing one side lead to excellent results.

A finite-element analysis of viscoelastically damped sandwich plates

A finite element analysis associated with an asymptotic solution method for the harmonic flexural vibration of viscoelastically damped unsymmetrical sandwich plates is given. The element formulation is based on generalization of the discrete Kirchhoff theory (DKT) element formulation. The results obtained with the first order approximation of the asymptotic solution presented here are the same as those obtained by means of the modal strain energy (MSE) method. By taking more terms of the asymptotic solution, with successive calculations and use of the Padé approximants method, accuracy can be improved. The finite element computation has been verified by comparison with an analytical exact solution for rectangular plates with simply supported edges. Results for the same plates with clamped edges are also presented.

A new formulated method of a quasi-compatible finite-element and its application in fracture-mechanics

Based on the local properties of a singular field, the displacement pattern of an isoparametric element is improved and a new formulated method of a quasi-compatible finite element is proposed in this paper. This method can be used to solve various engineering problems containing singular distribution, especially, the singular field existing at the tip of cracks. The singular quasi-compatible element (SQCE) is constructed. The characteristics of the elements are analysed from various angles and many examples of calculations are performed. The results show that this method has many significant advantages, by which, the numerical analysis of brittle fracture problems can be solved.

Ductile crack propagation with the strain-energy density criterion

The strain energy density criterion is used to characterize subcritical crack growth in a thin aluminum alloy sheet undergoing general yielding. A finite element analysis which incorporates both material and geometrical nonlinear behaviors of the cracked sheets is developed to predict fracture loads at varying crack growth increments. The predicted results are in excellent agreement with those measured experimentally, thus confirming the validity of the strain energy density criterion for characterizing ductile crack propagation.

Elastic-plastic finite element analyses of short cracks

Stress and strain distributions and crack opening displacement characteristics of short cracks have been studied in single edge notch bend and centre cracked panel specimens using elastic–plastic finite element analyses incorporating both a non strain hardening and a power law hardening behaviour. J contour integral solutions to describe stress strain conditions at crack tips for short cracks differ from those for long cracks. The analyses show that (i) short cracks can propagate at stress levels lower than those required for long cracks and (ii) a two-parameter description of crack tip fields is necessary for crack propagation.

A Finite Element Analysis of a Crack Penetrating or Deflecting into an Interface in a Thin Laminate

The crack tip driving force of a crack growing from a pre-crack that is perpendicular to and terminating at an interface between two materials is investigated using a linear fracture mechanics theory. The analysis is performed both for a crack penetrating the interface, growing straight ahead, and for a crack deflecting into the interface. The results from finite element calculations are compared with asymptotic solutions for infinitesimally small crack extensions. The solution is found to be accurate even for fairly large amounts of crack growth. Further, by comparing the crack tip driving force of the deflected crack with that of the penetrating crack, it is shown how to control the path of the crack by choosing the adhesion of the interface relative to the material toughness.

微尺度压痕实验的数值模拟及相关问题研究

目前国际上占主导地位的纳米压痕技术是由Oliver与Pharr提出并发展,目前的纳米压痕可以给出整个加、卸载过程的载荷—位移曲线以及硬度与弹性模量随压痕深度变化的曲线,从而提供了丰富的、比较精确的信息,为利用它探索材料比较完整的力学特性提供了可能.为达到该目的,就必须对压痕实验的加、卸过程进行较为深入的研究.作为主要的研究工具,有限元方法模拟微压痕过程在探讨通过实验数据得到更多、更准确的材料表层力学性能参数以及解释实验现象等方面发挥着重要作用.基于计算机速度与容量的原因,较早进行微压痕过程有限元模拟的BhattacharyaandNix、LaursenandSino都使用圆锥压头模拟维氏显微硬度标准正四棱锥Vicker压头与纳米压痕仪标准正三棱锥Berkovich压头,因为圆锥压头具有旋转对称性,可用二维旋转对称单元(二维实体单元)进行计算从而降低计算规模.即便如此,以当时大型计算机的水平,对规模为400~2000个四节点矩形单元的有限元模型进行一次完整的加、卸载过程也需要1~2天.到目前为止,微尺度压痕实验的数值模拟沿用二维模型.事实上,由于加工工艺的限制,微尺度压痕仪的压头如Berkovich与Vicker压头均不个旋转对称性;就微观尺度而言,实际的表层材料都是非均匀的.这些特征均不能由二维模拟体现,所以该文首先建立三维有限元模型,模拟带滑动接触的微尺度压痕加、卸载过程.在此基础上重点讨论了压头几何效应的问题,如二维模拟与三维模拟的关系、显微硬度与纳米的压痕硬度的关系、不同压头下材料的应力应变场、压痕间距与压痕边界的效应等,最后针对微尺度压痕实验中出现的压痕硬度随压痕深度减小而升高的现象,讨论了影响不同压痕深度硬度值的因素.

Numerical study on heavy rigid particle motion in a plane wake flow by spectral element method

Experimental particle dispersion patterns in a plane wake flow at a high Reynolds number have been predicted numerically by discrete vortex method (Phys. Fluids A 1992; 4:2244-2251; Int. J. Multiphase Flow 2000; 26:1583-1607). To address the particle motion at a moderate Reynolds number, spectral element method is employed to provide an instantaneous wake flow field for particle dynamics equations, which are solved to make a detail classification of the patterns in relation to the Stokes and Froude numbers. It is found that particle motion features only depend on the Stokes number at a high Froude number and depend on both numbers at a low Froude number. A ratio of the Stokes number to squared Froude number is introduced and threshold values of this parameter are evaluated that delineate the different regions of particle behavior. The parameter describes approximately the gravitational settling velocity divided by the characteristic velocity of wake flow. In order to present effects of particle density but preserve rigid sphere, hollow sphere particle dynamics in the plane wake flow is investigated. The evolution of hollow particle motion patterns for the increase of equivalent particle density corresponds to that of solid particle motion patterns for the decrease of particle size. Although the thresholds change a little, the parameter can still make a good qualitative classification of particle motion patterns as the inner diameter changes.

A Hybrid Scheme Based on Finite Element/Volume Methods for Two Immiscible Fluid Flows

We have successfully extended our implicit hybrid finite element/volume (FE/FV) solver to flows involving two immiscible fluids. The solver is based on the segregated pressure correction or projection method on staggered unstructured hybrid meshes. An intermediate velocity field is first obtained by solving the momentum equations with the matrix-free implicit cell-centered FV method. The pressure Poisson equation is solved by the node-based Galerkin FE method for an auxiliary variable. The auxiliary variable is used to update the velocity field and the pressure field. The pressure field is carefully updated by taking into account the velocity divergence field. This updating strategy can be rigorously proven to be able to eliminate the unphysical pressure boundary layer and is crucial for the correct temporal convergence rate. Our current staggered-mesh scheme is distinct from other conventional ones in that we store the velocity components at cell centers and the auxiliary variable at vertices. The fluid interface is captured by solving an advection equation for the volume fraction of one of the fluids. The same matrix-free FV method, as the one used for momentum equations, is used to solve the advection equation. We will focus on the interface sharpening strategy to minimize the smearing of the interface over time. We have developed and implemented a global mass conservation algorithm that enforces the conservation of the mass for each fluid.

On The Thermally Induced Cracking Of A Segmented Coating Deposited On The Outer Surface Of A Hollow Cylinder

In this work, the thermally induced cracking behavior of a segmented coating has been investigated. The geometry under consideration is a hollow cylinder with a segmented coating deposited onto its outer surface. The segmentation cracks are modeled as a periodic array of axial edge cracks. The finite element method is utilized to obtain the solution of the multiple crack problem and the Thermal Stress Intensity Factors (TSIFs) are calculated. Based on dimensional analysis, the main parameters affecting TSIFs are identified. It has been found that the TSIF is a monotonically increasing function of segmentation crack spacing. This result confirms that a segmented coating exhibits much higher thermal shock resistance than an intact counterpart, if only the segmentation crack spacing is narrow enough. The dependence of TSIF on some other parameters, such as normalized time, segmentation crack depth, convection severity as well as material constants, has also been discussed. (C) 2008 Elsevier B.V. All rights reserved.

Micromodification of element distribution in glass using femtosecond laser irradiation

We report micromodification of Eu element distribution in a silicate glass with femtosecond laser irradiation. Elemental analysis shows that the content of Eu decreased at the focal point and increased in a ring-shaped region around the focal point, which indicates migration of Eu ions has been induced by the femtosecond laser irradiation. Confocal fluorescence spectra demonstrate that the fluorescence intensity of Eu3+ ions increased by 20% in the laser-induced, Eu-enriched, ring-shaped region compared with that for nonirradiated glass. The mechanism for the laser induced change in fluorescence properties of Eu3+ has been investigated. (C) 2009 Optical Society of America

Inter-stage line ratio of He- and Li-like Ti emissions for the electron temperature measurement

Under coronal conditions, the steady state rate-equations are used to calculate the inter-stage line ratios between Li-like Is(2)2p(P-2(3/2))-> 1s(2)2s -> ((2) S-1/2) and He-like 1s2p (P-1(1))-> 1s(2) (S-1(0)) transitions for Ti in the electronic temperature ranges from 0.1 keV to 20 keV. The results show that the. temperature sensitivities are higher at the electronic temperature less than 5000 eV and the temperature sensitivities will decrease with the increase of electronic temperature.

大型干涉仪镜子的支承设计与温度变形分析

在星间激光通信中，涉及对大口径衍射极限激光波面的检测，为保证测量精度，必须严格控制波面十涉仪镜子的自重和温度变形。采用有限元方法对大型干涉仪镜子在不同支承方式下的表面变形进行了分析，结果表明，接触角为180°的钢带支承是较好的支承方式，反射镜表面变形峰-谷(P-V)值仅为1．35nm，均方根(RMS)值为0．363nm根据这一结论，设计了一个同定支承点与浮动支承相结合的超静定钢带支承结构。在该结构下，分析了镜子轴向、径向、周向的温度梯度效应，分析数据表明，镜子的热弹性变形远大于自重变形，建议采取一定的温控