非均质复合材料力学性能分析的多边形有限元方法

有限元方法是材料力学性能分析的主要工具.对于颗粒增强复合材料,其增强相或夹杂多为不规则的多边形,共采用经典有限元分析,需划分稠密的计算网格,降低分析效率.本文以多边形为有限元计算单元,采用Wachspress作为试函数,建立分析非均质材料力学性能的多边形有限元方法,给出形函数计算的简化公式.多边形单元的位移插值采用Wachspress插值,能自动满足不同形状单元间的协调性.计算网格按照材料分布的真实结构划分为若干多边形单元.数值算例验证了多边形有限元在模拟非均质材料力学性能方面的有效性和计算精度.     

埋管流化床颗粒流动行为的数值模拟

提出区域覆盖法,实现了正交结构化网格(DEM网格)与非规则网格(Fluent网格)的快速耦合,通过减少颗粒搜索量的方法,提高计算效率;采用向量法高效、精确定位颗粒在非规则网格内的位置,进而形成基于非规则网格的CFD-DEM数值模拟平台。在宽和高分别为250 mm和800 mm的二维多埋管流化床内对颗粒流动行为进行了数值模拟研究。结果表明:基于区域覆盖法建立的CFD-DEM模型能够模拟具有复杂几何结构流化床内的气固流动行为;多埋管流化床内的颗粒上升流磨损埋管的迎风面,在背风面形成颗粒浓度较低的区域;而颗粒下降流对埋管的影响与上升流的影响相反;多埋管流化床内的颗粒行为可划分为颗粒上升流、颗粒下降流、颗粒循环流和无颗粒区。     

用无网格伽辽金法模拟流场中的颗粒运动

采用无网格伽辽金法对多相流动中的颗粒运动进行了直接数值模拟.颗粒的受力通过积分颗粒表面压力和黏性力获得,颗粒运动用牛顿运动定律表示.在模拟两个颗粒一前一后的下落过程中,两颗粒呈现出文献中所观察到的拖曳、亲和、翻滚的现象.在处理颗粒碰撞上,无网格法显示了其优越性,实现了颗粒真正碰撞,解决了困扰多相流直接数值模拟发展的一个重要问题.最后,还模拟了6个颗粒在管道内的下落过程.这些计算都表明,由于无网格法不需要单元的连接,适合于推广到大型的气固两相流的直接数值模拟计算中,从而为多相流直接数值模拟的广泛开展奠定坚实的基础.     

外载荷作用下大开孔接管应力计算精度的影响因素分析

以在内压与外载荷作用下的圆柱壳上一大开孔接管为例,基于ANSYS软件中APDL语言建立了其有限元模型,研究了单元类型、单元技术、网格密度、施加外载荷方法等因素对计算的应力与位移的影响,同时将计算结果与薄壳理论解进行了对比。计算结果表明,以上4种因素对有限元分析结果影响较大。在网格划分密度较大情况下,优先选择Solid186单元全积分单元技术或Solid185单元增强应变单元技术;外载荷施加应采用RBE3命令。模拟结果可为外载荷作用下接管应力分析提供一定参考依据。     

基于模态应变能的复合材料板层间损伤定位研究

应用基于模态应变能的损伤识别方法对复合材料层合板的层间损伤进行定位研究,并基于单元模态应变能变化率提出了改进的损伤指标。通过有限元软件方法模拟复合材料板层与层之间的损伤(如残留气泡等缺陷引起的损伤),提取受损模型的各阶模态振型,将改进的单元模态应变能变化率作为复合材料层合板的损伤定位指标。通过有限元数值模拟,验证了模态应变能方法在复合材料层合板定位层间损伤的有效性,从而在保证损伤定位精度的前提下,大大减小后期分析的工作量。     

颗粒形状为任意的多相颗粒增强复合材料有效本构关系

引进夹杂形状函数（ISF）来描述夹杂的形状与大小,假设夹杂与基体之间完全接触,通过弹性力学的方法与等效夹杂法求解夹杂（颗粒）形状为任意的多相颗粒增强复合材料的有效本构张量,并利用Maple编程计算对其进行数值验证,从而为求解夹杂形状为各向异性的多相颗粒增强复合材料的有效弹性张量提供一种方法,具有很强的应用价值。     

TNT爆炸的数值计算及其影响因素

应用LS-DYNA有限元程序建立了模拟TNT爆炸的数值计算模型并进行了空爆冲击波超压等数值计算。通过数值计算结果与经验公式和试验数据的对比分析,验证了计算模型和参数取值的可信性。基于数值计算结果,分析了炸药材料参数、TNT药量、单元网格密度、建模方式、空气域形状和炸药形状等参数变化对爆炸冲击波超压的影响。结果表明,与试验结果相比,数值计算结果可以作为爆炸冲击波超压的下限值,而Henrych公式、Sadovskyi公式和GB6722-2003公式给出的是超压的中位和下位值;炸药材料参数的取值、单元网格密度和炸药形状对数值模拟结果的影响与比例距离相关,比例距离小于2.0时,不能忽视其影响;冲击波超压会随TNT药量的增加而小幅度增加,但建模方式和空气域形状对数值计算结果的影响可以忽略不计。     

复合材料结构耐撞性能的数值模拟研究

本文研究了复合材料结构耐撞性能数值模拟的策略和方法,包括接触-碰撞有限元理论、复合材料层板缓冲吸能模型和薄弱单元,并在DYNA3D(研究版)软件中加入了复合材料板缓冲吸能模块.采用改进后的程序对波纹梁盒段的坠毁过程进行了数值模拟,并将正面坠毁的数值模拟结果与试验结果进行了比较.结果表明本文采用的理论和有限元模型是合理可行的,同时还对波纹梁盒段斜碰撞的情况进行了数值模拟.本文所提出的方法为复合材料结构的耐撞性设计分析提供了一种有效的工具.     

复合材料层合板雷击损伤数值模拟研究

复合材料导电性差,雷击损伤严重危及到复合材料飞机结构安全。研究建立了复合材料层合板雷击损伤数值模拟的三维有限元模型。首先给出雷击电流作用下复合材料层合板的热-电耦合控制方程,然后建立基于层合板温度分布的单元失效和材料热电性能衰减准则,通过ABAQUS有限元软件的热电耦合分析模块中添加用户子程序USDFLD实现复合材料层合板雷击损伤数值模拟。预测结果与试验结果对比表明,该模型可准确预测复合材料层合板雷击损伤的损伤形状、面积和深度。     

埋管流化床内不同粒径颗粒传热行为的欧拉-拉格朗日模拟研究

将有限元方法、基于非结构化网格的计算流体力学方法与离散单元法结合,建立了CFD-DEM-FEM耦合方法,并在此基础上采用k-ε湍流模型及考虑颗粒间及气固间作用的多向耦合传热模型,对埋管流化床内的流动和传热行为进行了模拟和分析.通过计算结果从微观尺度探讨了埋管流化床内的传热机制,分析了影响床内传热的关键因素,得到了换热管道周围固含率和传热系数的分布规律,考察了颗粒直径对埋管周围传热系数的影响.数值模拟结果与实验数据基本一致,证实了CFD-DEM-FEM耦合方法模拟复杂气固流动和传热的可行性和准确性.     

Dense particulate flow model on unstructured mesh

A numerical method based on two-dimensional (2D) unstructured meshes is developed to solve the discrete particle model (DPM). Inter-particle interactions are taken into account for dense particulate flows, which are described by binary collisions in a hard-sphere model. The particle volume fraction is calculated accurately and physical scalars from the Eulerian grid to the Lagrangian particle positions are mapped through gradient interpolations. The governing equations for the continuous phase are discretized using a finite volume method on an unstructured grid and solved by the algebraic multi-grid (AMG) method. The SIMPLE algorithm employed to solve single-phase flows on unstructured meshes is extended to the pressure-velocity equations. Momentum coupling between the two phases is strongly implicit resulting in a very robust convergence of the AMG solver. Data structuring and mapping techniques for further enhancement of the flexibility and computational efficiency of the numerical model are introduced. Several test cases confirm that the numerical method can be applied to gas-solid and gas-liquid flows in irregular domains without regard to element types of the mesh. The numerical model presented in this paper partly overcomes the difficulties in simulating dense particulate flows using the DPM in 2D irregular domains.     

Numerical simulation of the resin transfer mold filling process using the boundary element method

A numerical simulation of the mold filling process during resin transfer molding with a heated die was performed using the boundary element method. The governing differential equation with a variable coefficient was rearranged into a system of Poisson equations using the perturbation technique. The boundary element method was employed to solve the resulting equations. The resin viscosity was calculated by introducing markers at the resin inlet and tracing them. As the calculation domain changes because of the proceeding resin front, numerical calculation nodes on the boundary were rearranged for each time step and integration was performed only for the meshes in the calculation domain among the fixed meshes over the mold. Sample calculations were performed for two molds with different shapes. To check the validity of the numerical scheme, the calculated mass flow rate at the resin front was compared with the mass flux at the inlet. Close agreement was observed.     

Viscoelastic flow past a confined cylinder: Instability and velocity inflection

The flow of the Oldroyd-B fluid past a circular cylinder in a channel is simulated by a parallelized finite volume method (FVM) using fine unstructured meshes. Convergent solutions are obtained up to a high Deborah number of De=1.6 with a high aspect ratio mesh, while it can only be obtained for De=0.6 with a more or less equi-lateral mesh. The governing equations are re-written using the discrete elastic viscous split stress formulation together with an independent interpolation of the vorticity (DEVSS-ω). The numerical procedure is based on the semi-implicit method for pressure-linked equations revised (SIMPLER) algorithm, using a collocated FVM discretization. To enhance the numerical accuracy, mixed meshes (structured and unstructured) are used and adapted to the geometry and the flow physics. The results show that an instability featuring stress oscillations on the top of the cylinder is produced at a critical De number (De≈0.6). This critical value is in agreement with the experiments in the literature. The oscillation generated in the shear layer on the cylinder surface at high De number is convected downstream into the wake behind the cylinder. This feature of flow oscillation agrees well with experiments reported in the literature. The mechanism of these phenomena can be explained reasonably by a boundary layer analysis. The key finding is that the instability is due to an inflectional velocity profile, near the cylinder, generated by normal stress on the cylinder surface at high De number, which can only be captured with fine meshes. According to a newly proposed theory (so called energy gradient theory), inflectional velocity profile leads to flow instability and consequently allows the convection of the oscillatory flow within the shear layer downstream of the wake and results in the flow pulsation in the spanwise direction. Therefore, the origin of the instability for the flow around a cylinder is in the shear layer on the cylinder and not in the wake itself. In addition, it seems that the increasing rate of numerical perturbation is related to the mesh aspect ratio. Computing using thin-long meshes could get convergence even if the flow is oscillatory, while the computing is prohibited by the inflectional instability when equi-lateral triangular meshes are used.     

Simpson数值积分在水平井井眼轨迹计算中的应用

本文把Simpson数值积分法与三次样条插值方法有机结合起来解决水平井井眼轨迹问题,避免了繁琐的递推公式推导,为水平井井眼轨迹的计算问题提供了一种行之有效的方法;并且引入计算点,通过求解计算点这个中间计算过程,应用经典公式,编制程序,方法简单可靠,易于实现及理解,为钻柱力学的有限元分析提供了必要的条件。     

注射成型充模流动模拟的边界元方法

有限差分法和有限元法用于注射成型充模过程数值模拟时，迭代过程和区域积分不可避免。本文通过对充模过程非线性压力控制方程的合理变换，将边界元方法引入充模过程的数值模拟，从而有效地避免复杂的迭代过程和区域积分。     

Finite element analysis for wavelike flow marks in injection molding

Wavelike flow marks are a kind of surface defect that can arise during the filling stage of the injection molding process. In this study, we performed a numerical analysis using a finite element method to predict the conditions under which flow marks are generated. To simplify the analysis, a two dimensional flow through a channel between two parallel plates was considered. The viscosity of the polymer melt was modeled by the Cross‐WLF equation. For the finite element analysis, a velocity–pressure formulation was used to simultaneously solve the continuity and momentum equations. The calculation domain for the numerical analysis keeps changing with time due to the advancing melt front. To handle the free surface more accurately, a moving grid method was employed. A numerical mesh was generated at each time step using an automatic mesh generation scheme. An analytical model was developed to correlate the effects of process variables to the flow mark geometry. Results of the numerical analysis were compared with the available experimental data. The estimated geometry of the flow marks were in good qualitative agreement with experimental observations. Parametric studies have been performed to examine the effects of various processing conditions and the material properties on flow mark size. POLYM. ENG. SCI., 47:922–933, 2007. © 2007 Society of Plastics Engineers     

Numerical prediction of fiber orientation in injection molding

We develop a numerical method for calculating fiber orientation in the midsurface of a molded part of small thickness. Two-dimensional fiber orientation is predicted on the basis of either Jeffery's equation or a constitutive equation for the orientation tensor. The calculation is fully transient; it is performed on a time-dependent flow domain. The method is based on finite elements. Updated finite element meshes are generated at every instant of filling and allow one to perform an accurate calculation of the orientation even along the boundary of the flow domain. The method is applied to several examples in plane and three-dimensional geometries.     

基于八叉树自适应网格技术的LevelSet运动界面追踪方法

Level Set方法因能有效地处理界面处复杂的拓扑结构变化以及大变形问题,广泛应用于界面追踪领域。在Level Set方法追踪运动界面时引入八叉树网格技术,通过八叉树网格的细化和粗化技术减少计算网格数量和计算内存并提高计算效率和计算精度。因为八叉树网格为非均匀网格,其相邻网格的层数值可能不相同,所以不能直接采用WENO格式离散Level Set函数得到网格处的函数值,进而提出八叉树网格离散模型解决这一问题,并提出基于八叉树网格距离场重新初始化方法减少Level Set方法的质量损失,最后将基于八叉树网格技术的Level Set方法应用于两个给定速度场的运动界面模拟算例以及基准件方腔的铸造充型过程的模拟。模拟结果表明该方法可以提高界面的精度,同时改善质量守恒性。     

Numerical modeling of thermal effects in turbulent mixing of large flows

A numerical approach for the modeling of thermal effects in turbulent mixing of large flows with uniform eddy viscosities and eddy diffusivities is presented. The distinctive features of this approach are the simultaneous compliance of mass and momentum equations, and accurate predictions of the surface waves and pressure distribution in flow fields with arbitrary bottom geometry. The numerical approach employs centered three-point finite difference expressions for the first and second spatial derivatives with unequal mesh size and a forward time integration. Numerical stability analysis of the governing equations is utilized to select optimum space and time increments for numerical integration.     

Finite element solution for gas–solid reactions: Application to the moving boundary problems

Gas–solid reactions are very important in the chemical and metallurgical process industries. Several models described these reactions such as volume reaction model, grain model, and nucleation model. These models give two coupled partial differential equations (CPDEs). In this work an integral transformation and subsequent finite element method is used for solving the coupled partial differential equations of these reactions. In each mesh the Rayleigh–Ritz method is applied. Finally the results of this work are compared with the existing numerical solutions and experimental data successfully.