二步法三维编织变截面薄壁壳体RTM 工艺数值模拟与试验研究

采用分段-集合计算方法, 对二步法三维编织变厚度变截面薄壁壳体RTM 充模工艺过程进行了较深入的理论研究。提出了较准确的树脂流动速度、树脂充模时间和树脂流动压力计算方程。数值预测值与充模试验结果具有良好的一致性, 所推导理论方程为合理设计RTM 充模工艺参数提供了理论依据。      

板材软模成形数值模拟研究现状

分析了板材软模成形数值模拟的特点,对目前主要采用的软模成形数值模拟方法进行了阐述和评价,并对三类典型软模成形(液压成形,橡皮成形及粘性介质压力成形)过程数值模拟应用进行了综述,最后对板材软模成形数值模拟发展趋势进行了展望.     

三维有限元并行EBE方法

采用Jacobi预处理,推导了基于EBE方法的预处理共轭梯度算法,给出了有限元EBE方法在分布存储并行机上的计算过程,可以实现整个三维有限元计算过程的并行化。编制了三维有限元求解的PFEM(ParallelFiniteElementMethod)程序,并在网络机群系统上实现。采用矩形截面悬臂梁的算例,对PFEM程序进行了数值测试,对串行计算和并行计算的效率进行了分析,最后将PFEM程序应用于二滩拱坝-地基系统的三维有限元数值计算中。结果表明,三维有限元EBE算法在求解过程中不需要集成整体刚度矩阵,有效地减少了对内存的需求,具有很好的并行性,可以有效地进行三维复杂结构的大规模数值分析。     

非结构运动网格下的三维机翼颤振数值分析

利用非结构运动网格技术,考虑三维机翼弹性变形求解三维跨音速非定常流场,同时耦合多自由度结构运动方程进行跨音速标模算例AGARD445.6机翼的颤振数值分析。采用的流动控制方程为三维非定常Euler方程。用中心有限体积法进行空间离散,用双时间隐式方法进行时间推进。数值分析获得的颤振临界速度与马赫数关系曲线明显反映了跨音速颤振临界速度随马赫数变化出现“凹坑”的物理特征。同时,数值分析结果与风洞实验结果一致性较好验证了所使用的方法。     

基于ANSYS CFX的注塑成型充填过程三维模拟

注塑成型中,熔体在模腔内的流动为非牛顿流体在复杂型腔内的非等温、非稳态流动。充填过程的三维数值模拟能更真实地模拟熔体在型腔内的三维流动状态。本文采用有限元分析软件ANSYS CFX进行二次开发,实现注塑成型充填过程的三维模拟,可求解熔体前沿、压力场、温度场等一系列模拟结果。模拟结果与注塑成型软件MOLDFLOW结果进行对比,验证了该方法的有效性。算例分析结果表明,对于薄壁制品,基于中面模型的注塑成型模拟方法是适用的,但对于非薄壁制品,采用三维模拟方法可以得到更合理更全面的信息。     

基于遗传算法的低压铸造铝合金车轮工艺优化

为解决低压铸造铝合金车轮质量控制难度大的问题,采用遗传算法对工艺参数进行优化.基于铸造数值模拟结果,利用BP人工神经网络建立了铸造工艺参数与质量控制目标缩松缺陷和凝固时间的非线性关系,采用遗传算法实现了铸造工艺参数的优化.以某型低压铸造A356铝合金车轮为例,对浇注温度、上模温度、下模温度、侧模温度、模芯温度5个参数进行优化,得到的最佳工艺组合,可有效控制缩松缺陷和凝固时间.利用数值模拟结果、建立神经网络模型,采用遗传算法优化的方法,获得近似最优解,有助于优化低压铸造工艺.     

三维Stokes方程的一个低阶非协调混合元格式收敛性分析

本文对三维Stokes方程提出一个新的低阶稳定的非协调混合元格式。首先,将该低阶Crouzeix-Raviart型非协调矩形元用于逼近速度空间,压力空间选取分片常数进行逼近,然后得到了关于速度能量模,压力和速度L2-模的最优误差估计。最后,数值算例验证了方法的有效性,并支持了本文的理论分析。     

连接块温挤压模具强度校核及结构优化

目的解决铝合金连接块温挤压成形过程中出现的模芯开裂和上模载荷过大的问题。方法基于有限元软件Deform-3D进行了三维有限元模拟,研究了连接块成形过程和模芯的受力状态。结果结果表明,局部应力过大是导致模芯开裂的主要原因。通过优化上模结构、增设溢流槽等措施以增大金属流动面积,可以显著降低模芯内腔局部应力和上模载荷。结论采用理论计算验证了2层组合凹模的安全性,有利于提高连接块的成形质量和凹模模芯的使用寿命。     

裂缝孔隙介质中驱动问题的特征交替方向有限元方法及分析

本文考虑裂缝孔隙介质中驱动问题的数值方法及理论分析。我们分别对压力方程采用混合元方法,对裂缝系统上的浓度方程采用特征线交替方向有限元方法,对岩块系统上的浓度方程采用交替方向有限元方法,证明了交替方向有限元格式具有最优L~2-模和H~1-模误差估计。     

帘线在肘形芯模上的缠绕模型

设计了帘线在肘形芯模上的缠绕模式,推导出帘线在肘形芯模上的缠绕轨迹微分方程,采用自适应步长四阶Runge-Kutta数值方法得到微分方程的数值解。理论分析结果表明:直管段缠绕时,如果芯模对中良好,即芯模轴线与纱盘旋转中心重合,则帘线缠绕角是一常数,若芯模与纱盘未对中,则帘线缠绕角是一个变化值;弯管段缠绕时,帘线缠绕角始终是一个变化值,在弯管的两个侧面出现极值,这与实际缠绕角线形基本一致。      

Adaptive mesh generation for mould filling problems in resin transfer moulding

In injection moulding processes such as Resin Transfer Moulding (RTM) for example, numerical simulations are usually performed on a fixed mesh, on which the numerical algorithm predict the displacement of the flow front. Error estimations can be used in the numerical algorithm to optimise the mesh for the finite element analysis. The mesh can be also adapted during mould filling to follow the shape of the moving boundary. However, in order to minimize computer time, it is preferable to optimise the mesh before carrying out the filling calculation. In this paper, these ideas are adapted to 3D shells, which represent the most common type of composite parts manufactured by RTM. An error estimator generally used in planar or solid geometries is extended for curved 3D surfaces in the specific case of RTM calculations. The extension consists of a projection of the solution field in the tangent plane to avoid problems related to the curvature of the part. Some other issues specific to shell geometries are pointed out and the results of a filling simulation made on a real part are presented. Non-isothermal filling simulations are also carried out in a rectangular mould to illustrate the stability conditions that arise from the convective heat transfer problem. Finally, an analytical study of radial injections is carried out to illustrate issues related to four types of different mesh refinement procedures: (1) a constant time step, (2) constant radial density (to allow a regular progression of the flow front at each time step), (3) a constant Courant number (to ensure stable thermal simulations); and (4) finally, a constant interpolation error.     

Simulation of the three-dimensional non-isothermal mold filling process in resin transfer molding

Numerical simulation of resin transfer molding (RTM) is known as a useful method to analyze the process before the mold is actually built. In thick parts, the resin flow is no longer two-dimensional and must be simulated in a fully three-dimensional space. This article presents numerical simulations of three-dimensional non-isothermal mold filling of the RTM process. The control volume/finite element method (CV/FEM) is used in this study. Numerical formulation for resin flow is based on the concept of nodal partial saturation at the flow front. This approach permits to include a transient term in the working equation, removing the need for calculation of time step to track the flow front in conventional scheme. In order to compare the results of the nodal partial saturation concept with the conventional method, a numerical scheme based on the quasi-steady state formulation is also presented. The computer codes developed based on both numerical formulations, allow the prediction of flow front positions; and pressure, temperature and conversion distributions in three-dimensional molds with complicated geometries. The validity of the two schemes is evaluated by comparison with analytical solutions of simple geometries. In all instances excellent agreement is observed. Numerical case studies are provided to demonstrate the effectiveness of the developed computer codes. The results show that the numerical procedure based on the nodal partial saturation concept, developed in this study, provides numerically valid and reasonably accurate predictions.     

A study of fiber orientation in short fiber-reinforced composites with simultaneous mold filling and phase change effects

Most of the properties of injection molded short fiber-reinforced composites are highly dependent on the patterns of their fiber orientation, which are induced by the flow. On the other hand, in most practical injection molding processes, both filling and solidification of the molten suspension takes place simultaneously. This behavior indicates that both filling and phase change for solidification can occur at the same time and therefore affect the flow behavior of the suspension, hence the fiber orientation. The aim of the current work is to present a numerical analysis of fiber orientation prediction in a three-dimensional rectangular cavity considering simultaneous mold filling and phase change of the suspending polymer. To trace the flow front during the filling process, the volume of fluid method (VOF) has been used, while an enthalpy-based approach was used to model the solidification. The standard Hybrid closure model of Advani and Tucker was applied to approximate the evolved fourth order orientation tensor during the fiber orientation calculation. To validate the developed numerical model, the results of the simulation model were compared with available experimental data for the rectangular cavity. The simulation results showed that they are in good agreement with the experimental data. Hence, the numerical model could assist in decisions regarding the design of polymer composite products.     

Application of the level set method to the simulation of resin transfer molding

A new methodology is presented to simulate mold filling in resin transfer molding (RTM) using a combination of the level set and boundary element methods (BEMs). RTM is a composite manufacturing process where a liquid resin is injected in a closed rigid mold containing a dry fibrous reinforcement. Process simulation is motivated by the importance of tracking accurately the motion of the flow front during the mold filling stage. The BEM solves the equation governing the resin flow and the level set method is implemented to track the resin front in the mold. This formulation opens up new opportunities to improve RTM flow simulations and optimize injection molds. The present paper focuses on isothermal resin flow in undeformable porous medium. The implementation of the numerical algorithm is described and several examples of two-dimensional filling with single or multiple injection gates are presented. The robustness of the coupling and the ability to predict accurately the position of the front by this new model are discussed. It is also shown how dry spot formation can be tracked precisely during the simulation and how a generalization of this approach allows predicting resin flow across obstacles.     

注射模充模流动和传热过程的理论与算法

从粘性流体力学的质量、动量和能量方程出发，针对塑料注射成型特点，基于量纲分析，建立了适合于充模分析的数学模型。控制方程的求解主要包括三个阶段：压力场、温度场和流动前沿位置的确定。数值求解采用有限元法求解压力场、有限差分法求解温度场、控制体积法确定流动前沿位置，并详细讨论了数值算例的分析结果。     

NUMERICAL SOLUTION OF TRANSIENT,FREE SURFACE PROBLEMS IN POROUS MEDIA

The focus of this paper is the development of numerical schemes for tracking the moving fluid surface during the filling of a porous medium (e.g., polymer injection into a porous mold cavity). Performing a mass balance calculation on an arbitrarily deforming control volume, leads to a general governing filling equation. From this equation, a general, fully time implicit, numerical scheme based on a finite volume space discretization is derived. Two numerical schemes are developed: (1) a fully deforming grid scheme, which explicitly tracks the location of the filling front, and (2) a fixed grid scheme, that employs an auxiliary variable to locate the front. The validity of the two schemes is demonstrated by solving a variety of one- and two-dimensional problems; both approaches provide predictions with similar accuracy and agree well with available analytical solutions.     

Variation of stress intensity factor along the front of a 3D rectangular crack by using a singular integral equation method

In this paper a singular integral equation method is applied to calculate the distribution of stress intensity factor along the crack front of a 3D rectangular crack. The stress field induced by a body force doublet in an infinite body is used as the fundamental solution. Then, the problem is formulated as an integral equation with a singularity of the form of r ^–3. In solving the integral equation, the unknown functions of body force densities are approximated by the product of a polynomial and a fundamental density function, which expresses stress singularity along the crack front in an infinite body. The calculation shows that the present method gives smooth variations of stress intensity factors along the crack front for various aspect ratios. The present method gives rapidly converging numerical results and highly satisfied boundary conditions throughout the crack boundary.     

注射条件对LCM工艺非饱和流动特性影响

双尺度多孔纤维预制体填充过程中延迟浸润的非饱和流动现象,对基于树脂流过区域为完全饱和区域的充模理论及模拟方法提出了挑战。通过控制体/有限单元（CV/FE）法结合沉浸函数实现了液体模塑成型工艺（LCM）中非饱和填充浸润的数值模拟,并对比了恒压下的实验结果,验证了其可靠性。分析讨论了注射口压力、流量和液体黏度对双尺度多孔纤维织物非饱和填充浸润特性的影响。结果表明:在允许误差内,该数值模拟结果可靠,可用于分析讨论各因素对双尺度多孔织物非饱和流动特性的影响;填充浸润过程中,纤维织物内部非饱和区域长度并非保持不变,而是随着填充浸润的进行经历了4个变化过程;不同注射条件下,压力、流量及黏度对非饱和流动特性影响不同。研究结果对合理控制注射条件及流体特性实现双尺度多孔纤维预制件的完全浸润具有指导意义。      

漂浮式光伏电站方阵环境载荷计算方法研究

针对我国建成的全球首个单体容量达到40 MW的漂浮式光伏电站方阵进行了环境载荷数值预报研究,在与风洞模型试验结果对比验证的基础上,基于计算流体力学（computational fluid dynamics,CFD）方法对该大规模方阵的整体风载荷和流载荷进行了数值研究。CFD计算的数值考察验证了采用简化浮体模型进行研究的可行性,单体模型的计算结果与风洞试验结果吻合良好;对方阵进行实尺度建模及3D简略计算,得到了整体风载荷在不同风向角下的变化规律;通过对最大载荷风向的北风条件下的载荷分布规律的分析,提出了2.5D计算的策略,得到了数值验证;根据计算结果设计并实施了18行×11列单元模块的缩尺方阵风洞试验,试验结果和CFD计算结果吻合良好,据此构建了完整的数值计算方法;对2.5D进行高精度计算,确定了针对3D简略计算的修正系数,得到较为准确的整体风载荷结果。流载荷计算方法与风载荷相同。采取势流计算方法开展了波浪载荷数值分析研究,得到了在单位波幅规则波作用下漂浮方阵波浪载荷随行和列的变化规律;根据此规律获得了整体漂浮方阵的波浪载荷,并据此计算了50年一遇的极端条件下漂浮方阵所受的波浪载荷。该研究为漂浮式光伏电站的风、流、波浪等环境载荷的数值预报提供了方法,为漂浮方阵的锚泊计算及水上光伏电站的系统设计提供了技术支持。     

Multiscale Optimization of 3D-Printed Beam-Based Lattice Structures through Elastically Tailored Unit Cells

Herein, a numerical multiscale tool is developed to design 3D periodic lattice structures. The work is motivated by the high design freedom of additive manufacturing technologies, which enable complex multiscale lattice structures to be printed. A finite-element-based free-material optimization method is used to determine the ideal orthotropic material properties of a 3D macrostructure space. Subsequently, a population-based algorithm is established to design optimized microscopic lattice unit cells with the desired structural properties. The design variables are the coordinates of lattice skeleton nodes defined within the 3D lattice unit cell space, and the connectivities between them resulting in a truss skeleton. For the calculation of the mechanical properties of the individual lattice cells, an effective Timoshenko beam-based finite element calculation method is developed. The macroscale structure can be constructed by periodically filling the domain with the customized unit cell representing a metamaterial. The method is demonstrated by 3D beam problems with compliance constraints. These macroscopic demonstrators of the developed lattice structures were also 3D-printed. The benefit regarding the weight-specific structural performance is validated through benchmarking with periodic lattice design solutions using well-known standard lattice cells.