Photoviscoelastic stress analysis of a plate with a central hole

An epoxy resin containing excessive plasticizer was developed and characterized. The material, which deforms viscously at room temperature, has optical properties that depend on stress and strain. A tensile specimen was prepared from the epoxy resin so that the mechanical and optical properties of the epoxy resin could be characterized. The elastic and plastic behavior was determined at 37°C using tensile stresses between 4 and 26 MPa. The birefringence was also recorded as a function of time and stress. From these results, a photoviscoelastic constitutive equation was constructed to describe the dependence of the birefringence on stress and strain. The constitutive equation was then applied to study the deformation of a tensile specimen containing a central circular hole. By using the isochromatic fringes in combination with the isoclinic, the time-dependent variation of the stress field in the specimen was solved.     

两个相等圆孔板弯曲时的三维应力集中

根据Hellinger-Reissner原理建立了具有一个无外力圆柱表面的三维八节点杂交应力元,其假设应力场严格满足柱坐标下三维平衡方程及圆柱面上无外力边界条件;当元退化为二维时也满足协调方程。数值算例表明,这种特殊杂交应力元可高效地分析具有两个圆孔薄板和厚板的应力集中,特别是三维应力集中。     

Wall shear stress characterization of a 3D bluff-body separated flow

Efficient flow control strategies aimed at reducing the aerodynamic drag of road vehicles require a detailed knowledge of the reference flow. In this work, the flow around the rear slanted window of a generic car model was experimentally studied through wall shear stress measurements using an electrochemical method. The mean and fluctuating wall shear stress within the wall impact regions of the recirculation bubble and the main longitudinal vortex structures which develop above the rear window are presented. Correlations allow a more detailed characterization of the recirculation phenomenon within the separation bubble. In the model symmetry plane the recirculation structure compares well with simpler 2D configurations; specific lengths, flapping motion and shedding of large-scale vortices are observed, these similarities diminish when leaving the middle plane due to the strong three-dimensionality of the flow. A specific attention is paid to the convection processes occurring within the recirculation: a downstream convection velocity is observed, in accordance with 2D recirculations from the literature, and an upstream convection is highlighted along the entire bubble length which has not been underlined in some previous canonical configurations.     

考虑土-结构相互作用效应的三维桩基结构动力有限元分析

结合简化阻抗法建立了三维相互作用结构的动力有限元分析模型,导出了考虑群桩刚体、惯性效应作用时的结构相互作用时程积分方程式,以近乎纯结构有限元的建模途径合理地反映出桩-土-上部结构在水平地震作用下的动力相互作用特性。模型中引入具有桩(筏)-土阻抗特性的弹阻单元来描述不同群桩布置、土层状况因素对体系反应的参与作用,而在动力方程中竖向SV剪切波经桩土刚体相互作用产生的水平、摇摆分量对体系的影响亦得以体现。20层桩承刚框架结构的动力分析表明:较柔的桩、土基础使得体系的SSI效应增强,但其参与程度与群桩效应相关,而结构构件内力较不考虑相互作用时有较大折减;应用该法可精确、快速地进行复杂上、下部结构时程反应分析。     

3D phase field modeling of electrohydrodynamic multiphase flows

A 3D phase field model is developed to investigate the electrohydrodynamic (EHD) two phase flows. The explicit finite difference method, enhanced by parallel computing, is employed to solve the coupled nonlinear governing equations for the electric field, the fluid flow field and free surface deformation. Numerical tests indicate that an appropriate interpolation of densities within the interface is critical in ensuring numerical stability for highly stratified flows. The 3D phase field model compares well with the Taylor theory for the deformation of a single dielectric droplet in an electric field. Computed results show that the deformation of a leaky dielectric droplet in an electric field undergoes various stages before it reaches the final oblate shape. This is caused by the free charge relaxation near the fluid–fluid interface. The coalescence of four droplets in an electric field illustrates a truly 3D deformation behavior and a complex evolving fluid flow field associated with the participating droplets. The coalescence is a result of combined actions produced by the global electric force, the circulatory flows generated by the local electrohydrodynamic stress and the electrically-induced deformation. The 3D phase field model is also applied in modeling of an electrohydrodynamic patterning process for manufacturing nanoscaled structures, in which complex 3D flow structures develop as the electrically-induced deformation evolves.     

Computation of 3D vortex flows past a flat plate at incidence through a variational approach of the full steady euler equations

A variational method for solving directly the full steady Euler equations is presented. This method is based on both Newton's linearization and a least squares formulation. The validity of the Euler model and boundary conditions to capture the vortex sheet is discussed. A finite element approximation of the groups of conservative variables is described and results are given for 3D subsonic flows as well as supersonic flows past a flat plate at high angle of attack.     

Boundary element elastic stress analysis of 3D generally anisotropic solids using fundamental solutions based on Fourier series

The authors have very recently proposed an efficient, accurate alternative scheme to numerically evaluate etc. Green’s function, U(x), and its derivatives for three-dimensional, general anisotropic elasticity. These quantities are necessary items in the formulation of the boundary element method (BEM). The scheme is based on the double Fourier series representation of the explicit, exact, algebraic solution derived by Ting and Lee (1997) [Ting, T.C.T., Lee, V.G., 1997. The three-dimensional elastostic Green’s function for general anisotropic linear elastic solid. Q. J. Mech. Appl. Math. 50, 407–426] expressed in terms of Stroh’s eigenvalues. By taking advantage of some its characteristics, the formulations in this double Fourier series approach are revised and several of the analytical expressions are re-arranged in the present study. This results in significantly fewer terms to be summed in the series thereby improving further the efficiency for evaluating the Green’s function and its derivatives. These revised Fourier series representations of U(x) and its derivatives are employed in a BEM formulation for three-dimensional linear elastostatics. Some numerical examples are presented to demonstrate the veracity of the implementation and its applicability to the elastic stress analysis of generally anisotropic solids. The results are compared with known solutions in the literature where possible, and with those obtained using the commercial finite element code ANSYS. Excellent agreement is obtained in all cases.     

Linear spatial instability analysis in 3D boundary layers using plane-marching 3D-LPSE

It is widely accepted that a robust and efficient method to compute the linear spatial amplified rate ought to be developed in three-dimensional (3D) boundary layers to predict the transition with the e ^N method, especially when the boundary layer varies significantly in the spanwise direction. The 3D-linear parabolized stability equation (3D-LPSE) approach, a 3D extension of the two-dimensional LPSE (2D-LPSE), is developed with a plane-marching procedure for investigating the instability of a 3D boundary layer with a significant spanwise variation. The method is suitable for a full Mach number region, and is validated by computing the unstable modes in 2D and 3D boundary layers, in both global and local instability problems. The predictions are in better agreement with the ones of the direct numerical simulation (DNS) rather than a 2D-eigenvalue problem (EVP) procedure. These results suggest that the plane-marching 3D-LPSE approach is a robust, efficient, and accurate choice for the local and global instability analysis in 2D and 3D boundary layers for all free-stream Mach numbers.     

三维机织复合材料的弹性性能预报模型

建立了基于等效响应比拟技术的三维机织复合材料弹性性能预报模型．首先将三维机织物的结构单元分解为4个子元(经纱、纬纱、填充纱和接结纱),用几何模型去估算这些子元的体积分数．然后依据不同的外载形式,将复合材料的应力-应变关系等效地表达为3组诸子元所组成的三维弹簧网络．根据刚度系数的物理意义,采用不同的弹簧网络连接形式,并按体积平均化方法获得材料总体刚度矩阵中相应的刚度系数,进而计算得到三维机织复合材料的9个弹性系数．该模型考虑了层内交织经纱、层间交织接结纱的弯曲以及材料内部纯树脂区对三维机织复合材料弹性性能的影响．试验结果与模型的理论预测值进行比较,表明这个模型是有效的。     

The deformation of the front of a 3D interface crack propagating quasistatically in a medium with random fracture properties

One studies the evolution in time of the deformation of the front of a semi-infinite 3D interface crack propagating quasistatically in an infinite heterogeneous elastic body. The fracture properties are assumed to be lower on the interface than in the materials so that crack propagation is channelled along the interface, and to vary randomly within the crack plane. The work is based on earlier formulae which provide the first-order change of the stress intensity factors along the front of a semi-infinite interface crack arising from some small but otherwise arbitrary in-plane perturbation of this front. The main object of study is the long-time behavior of various statistical measures of the deformation of the crack front. Special attention is paid to the influences of the mismatch of elastic properties, the type of propagation law (fatigue or brittle fracture) and the stable or unstable character of 2D crack propagation (depending on the loading) upon the development of this deformation.     

Implementation and performance of the time integration of a 3D transport model

The total solution of a three-dimensional model for computing the transport of salinity, pollutants, suspended material (such as sediment or mud), etc. in shallow seas involves many aspects, each of which has to be treated in an optimal way in order to cope with the tremendous computational task involved. In this paper we focus on one of these aspects, i.e. on the time integration, and discuss two numerical solution methods. The emphasis in this paper is on the performance of the methods when implemented on a vector/parallel, shared memory computer such as a Cray-type machine. The first method is an explicit time integrator and can straightforwardly be vectorized and parallelized. Although a stabilizing technique has been applied to this method, it still suffers from a severe time step restriction. The second method is partly implicit, resulting in much better stability characteristics; however, as a consequence of the implicitness, it requires in each step the solution of a large number of tridiagonal systems. When implemented in a standard way, the recursive nature would prevent vectorization, resulting in a very long solution time. Following a suggestion of Golub and Van Loan, this part of the algorithm has been tuned for use on the Cray C98/4256. On the basis of a large-scale test problem, performance results will be presented for various implementations.     

复杂形状及开孔功能梯度板的三维分析

In this paper, the basic formulae for the semi-analytical graded FEM on FGM members are derived. Since FGM parameters vary along three space coordinates, the parameters can be integrated in mechanical equations. Therefore with the parameters of a given FGM plate, problems of FGM plate under various conditions can be solved. The approach uses 1D discretization to obtain 3D solutions, which is proven to be an effective numerical method for the mechanical analyses of FGM structures. Examples of FGM plates with complex shapes and various holes are presented.     

3D Numerical heat transfer and fluid flow analysis in plate-fin and tube heat exchangers with electrohydrodynamic enhancement

Three-dimensional laminar fluid flow and heat transfer over a four-row plate-fin and tube heat exchanger with electrohydrodynamic (EHD) wire electrodes are studied numerically. The effects of different electrode arrangements (square and diagonal), tube pitch arrangements (in-line and staggered) and applied voltage (V_E=0–16 kV) are investigated in detail for the Reynolds number range (based on the fin spacing and frontal velocity) ranging from 100 to 1,000. It is found that the EHD enhancement is more effective for lower Re and higher applied voltage. The case of staggered tube pitch with square wire electrode arrangement gives the best heat transfer augmentation. For V_E=16 kV and Re = 100, this study identifies a maximum improvement of 218% in the average Nusselt number and a reduction in fin area of 56% as compared that without EHD enhancement.     

Interpolation of Scattered 3D PTV Data to a Regular Grid

The velocity data obtained by many 3D measurement methods such as particle tracking velocimetry (PTV) are not regularly distributed in3D space. We revised three numerical schemes to interpolate the scattered velocity vectors to a regularly spaced grid. Additionally, two techniques were examined to smooth the resulting flow field. The different algorithms were tested for a synthetic data set based on the analytical solution of Burgers' vortex. To study the impact of measurement errors a Gaussian noise was superimposed on the exact solution. It was found that an interpolation scheme of higher order does not necessarily perform better than one of lower order. The most‘robust’ algorithm was used to process 3D PTV data, which were obtained from measurements of a separating flow in a forward facing step configuration. Information on the 3D streamlines and vortex structures was obtained. This revised version was published online in July 2006 with corrections to the Cover Date.     

Implementation and performance of the time integration of a 3D numerical transport model

The total solution of a three-dimensional model for computing the transport of salinity, pollutants, suspended material (such as sediment or mud), etc. in shallow seas involves many aspects, each of which has to be treated in an optimal way in order to cope with the tremendous computational task involved. In this paper we focus on one of these aspects, i.e. on the time integration, and discuss two numerical solution methods. The emphasis in this paper is on the performance of the methods when implemented on a vector/parallel, shared memory computer such as a Cray-type machine. The first method is an explicit time integrator and can straightforwardly be vectorized and parallelized. Although a stabilizing technique has been applied to this method, it still suffers from a severe time step restriction. The second method is partly implicit, resulting in much beter stability characteristics; however, as a consequence of the implicitness, it requires in each step the solution of a large number of tridiagonal systems. When implemented in a standard way, the recursive nature would prevent vectorization, resulting in a very long solution time. Following a suggestion of Golub and Van Loan, this part of the algorithm has been tuned for use on the Cray C98/4256. On the basis of a large-scale test problem, performance results will be presented for various implementations.     

扫描电镜下断口表面的三维重建及分形维数的测量

基于数字散斑相关方法,利用扫描电镜立体对技术和计算机视觉方法实现了物体表面的三维重建,讨论了影响其精度的原因,并且利用分形理论对表面的三维形貌进行了定量分析,由立方体覆盖法得到了三维形貌的分形维数.作为应用的实例,将该方法应用到岩石断口的三维重建中,得到了重建后的高度云图和分形维数.结果表明,利用扫描电镜立体对技术对断口表面进行三维重构并进行分形维数的计算是一种行之有效的断口定量分析方法.这为研究材料断裂的微观机理、断裂过程和断裂性质等问题提供了一种途径.     

An effective boundary element method for analysis of crack problems in a plane elastic plate

A simple and effective boundary element method for stress intensity factor calculation for crack problems in a plane elastic plate is presented. The boundary element method consists of the constant displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity elements proposed by YAN Xiangqiao. In the boundary element implementation the left or the right crack-tip displacement discontinuity element was placed locally at the corresponding left or right each crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. Test examples (i. e. , a center crack in an infinite plate under tension, a circular hole and a crack in an infinite plate under tension) are included to illustrate that the numerical approach is very simple and accurate for stress intensity factor calculation of plane elasticity crack problems. In addition, specifically, the stress intensity factors of branching cracks emanating from a square hole in a rectangular plate under biaxial loads were analysed. These numerical results indicate the present numerical approach is very effective for calculating stress intensity factors of complex cracks in a 2-D finite body, and are used to reveal the effect of the biaxial loads and the cracked body geometry on stress intensity factors.     

3D full-loop simulation and experimental verification of gas-solid flow hydrodynamics in a dense circulating fluidized bed

Because of their advantages of high efficiency and low cost, numerical research methods for large-scale circulating fluidized bed （CFB） apparatus are gaining ever more importance. This article presents a numer- ical study of gas-solid flow dynamics using the Eulerian granular multiphase model with a drag coefficient correction based on the energy-minimization multi-scale （EMMS） model. A three-dimensional, full-loop, time-dependent simulation of the hydrodynamics of a dense CFB apparatus is performed. The process parameters （e.g., operating and initial conditions） are provided in accordance with the real experiment to enhance the accuracy of the simulation. The axial profiles of the averaged solid volume fractions and the solids flux at the outlet of the cyclone are in reasonable agreement with experimental data, thereby verifying the applicability of the mathematical and physical models. As a result, the streamline in the riser and standpipe as well as the solids distribution contours at the cross sections is analyzed. Computational fluid dynamics （CFD） serves as a basis for CFB modeling to help resolve certain issues long in dispute but difficult to address experimentally. The results of this study provide the basis of a general approach to describing dynamic simulations of gas-solid flows.     

用三分量LDV测量壁湍流边界层

本文用三分量激光多普勒测速仪对壁湍流边界层进行了测量，经过数据处理后，给出了各湍流参数的分布曲线，并与Ｄｊｅｎｉｄｉ等的测量结果进行了比较，吻合得很好。结果表明，用３Ｄ－ＬＤＶ研究湍流是可行的