预成形体渗透率预测及剪切变形的影响

准确预测预成型体渗透率对复合材料液态成型工艺过程仿真有重要意义,铺覆过程中织物发生的剪切变形对局部渗透率有很大影响。本工作考虑纱线的可渗透性,对织物单胞内的树脂流动建立了统一的流动控制方程,同时建立了逼真的正交单胞几何模型,基于Adams-Bashforth差分格式和Chorin投影法构造了数值求解树脂流动控制方程的高分辨率TVD格式,利用达西定律预测了单胞的渗透率,算例表明该算法预测值与实验值有较好的吻合,验证了算法的准确性。在正交单胞渗透率求解的基础上,采用贴体坐标法完成了单胞剪切变形后流动控制方程从物理域到计算域的转换,进而实现了剪切单胞渗透率的数值预测,考察了单胞主渗透率比与剪切角的关系,通过与文献中数据对比证明了该剪切单胞渗透率预测算法的合理性。     

预成型体渗透率预测及其受压缩变形的影响

建立了织物预成型体单胞内纱线间细观流动和纱线内部微观流动的统一的数学模型。基于最小势能原理建立了织物松弛状态下的单胞几何模型,同时对在模具压缩下的单胞变形进行了分析,并建立了不同压缩状态下的单胞几何模型。通过对单胞内树脂流动数学模型的数值求解,获得了流动速度场及压力场,进而预测了预成型体的渗透率。预测1组不同压缩状态下的单胞渗透率,研究了预成型体压缩变形对渗透率的影响。结果显示:随着压缩量的增加,其渗透率逐渐降低。通过实验测量及数据分析,验证了建模和预测方法的正确性。     

结合改进单胞模型的单钉双剪层合板螺栓连接结构挤压性能的多尺度表征分析

为提高螺栓连接层合板结构的可靠性和承载能力,基于ABAQUS软件及用户子程序(USDFLD),结合改进的单胞模型,建立了考虑组分材料失效的多尺度数值模型。利用该模型表征分析了单钉双剪层合板螺栓连接结构的力学性能,研究了铺层形式及几何尺寸对连接结构性能的影响。该模型的预报结果与试验结果吻合较好。结果表明:准各向同性层合板螺栓连接结构的挤压强度高于正交各向异性层合板连接结构的挤压强度,前者的失效模式为挤压失效,后者为剪出失效,该模式导致结构承载能力降低,设计中应避免。层合板边径比大于3时,不同宽径比连接结构的挤压强度趋近稳定值;但相同边径比的连接结构,其挤压强度随宽径比的增大而增大,连接结构设计时应给予考虑。      

复合材料液体模塑成型工艺中预成型体渗透率张量的数值预测

结合均匀化理论和计算流体动力学技术, 实现了对复合材料液体模塑工艺中预成型体渗透率张量的预测。首先, 采用均匀化理论分析了流体在多孔介质内的流动问题, 推导出广义达西定律, 证明以施加周期性边界条件的单胞为研究对象, 可以预测预成型体的渗透率张量, 并以单向纤维织物为例, 对该方法进行了验证。对于复杂结构的预成型体, 渗透率的预测分为两步, 首先分别确定预成型体中流道和纤维束的渗透率, 然后计算其整体宏观渗透率。对于二维平面织物, 该方法与其他预测方法及实验的结果吻合较好。本文还考察了单胞的微观结构对渗透率的影响, 微观结构相似的预成型体如果孔隙率相同, 但束间流道的结构不同, 其整体宏观渗透率也存在很大差别。      

跨尺度预测非屈曲织物增强复合材料的刚度和强度

为了预测非屈曲织物增强复合材料的力学性能, 建立了纤维束的正六边形单胞和非屈曲织物复合材料的长方形单胞, 并重点推导了正六边单胞的方程边界条件。通过跨尺度逐级计算这两个单胞的有效弹性常数, 得到了非屈曲碳纤维织物增强环氧树脂基复合材料的宏观有效弹性性能和强度。对该非屈曲织物复合材料在拉伸载荷下的累计失效进行了有限元损伤分析。结果表明: 初始损伤发生在富树脂区或横向纤维束, 损伤在富树脂区与横向纤维束内逐步扩展, 最后向纵向纤维束扩展并迅速导致整体失效; 非屈曲织物增强复合材料的面内拉伸模量的计算预测值非常接近实验值, 面内拉伸强度计算值略小于实验值。     

基于多尺度方法的纤维织物增强柔性复合材料拉伸模量预测

以超高分子量聚乙烯（UHMW-PE）纤维织物增强-聚乙烯（PE）涂层柔性复合材料作为研究对象,首先,通过离子抛光仪对复合材料横截面进行处理;然后,使用SEM和光学显微镜测量复合材料细观结构,获得复合材料细观几何参数;最后,基于均匀化方法和连续介质假设,建立单胞力学模型,计算单胞的拉伸载荷-应变曲线,将理论值与实验值进行比较。结果表明:基于多尺度方法的复合材料单胞力学模型所得拉伸载荷-应变曲线与实验所得曲线能较好吻合,该理论模型能够较好地预报纤维织物增强柔性复合材料的拉伸模量。      

基于单胞解析模型的单向复合材料强度预报方法

基于单胞解析模型,建立一种从复合材料细观组分到宏观单向板的强度预报方法。根据连续介质力学和均匀化方法构建细-宏观关联矩阵,通过该关联矩阵将细观组分材料的弹性和损伤性能传递到宏观单向板中。考虑复合材料细观损伤状态,当纤维和基体满足各自强度准则时失效,并通过失效因子折算成刚度的衰减。在此基础上,结合有限元分析,实现复合材料单向板纵横向拉伸模拟,从而预报单向板的拉伸强度。结果表明:该方法预报的模量和强度与实验值基本一致,验证了该方法的有效性与高效性。     

二维半线性抛物方程的二重网格差分算法

针对二维半线性抛物方程,本文提出了两种二重网格差分算法,并给出了误差估计。该算法能够在粗网格和细网格上线性地求解半线性问题。若重复算法的最后几步可以按粗网格步长任意阶地逼近细网格上的非线性解。     

考虑磁导率非线性的铁磁材料脉冲涡流检测仿真研究

长期以来,脉冲涡流检测中铁磁材料的磁导率多被视为常数,但这种简化的合理性及其影响尚缺乏充分的证明.本文基于有限元法,建立了探头置于Q235钢板上方的脉冲涡流检测模型,研究了钢板磁导率的空间分布和时间变化规律及其对探头信号的影响,并进行了实验验证.结果表明:钢板中瞬态磁场的工作点与激励电流幅值有关,增大激励电流,磁场可能超出磁化曲线的起始磁化区而进入到瑞利区甚至陡峭区;由于磁导率非线性的影响,激励方波高、低电平段的感应电压信号不成奇谐对称,高电平段的晚期感应电压比低电平段的大;钢板浅层磁导率的变化显著,不能简化为常数,而深层的磁导率变化很小,可视为常数.     

A Numerical Comparison of Finite Difference and Finite Element Methods for a Stochastic Differential Equation with Polynomial Chaos

A numerical comparison of finite difference (FD) and finite element (FE) methods for a stochastic ordinary differential equation is made. The stochastic ordinary differential equation is turned into a set of ordinary differential equations by applying polynomial chaos, and the FD and FE methods are then implemented. The resulting numerical solutions are all non-negative. When orthogonal polynomials are used for either continuous or discrete processes, numerical experiments also show that the FE method is more accurate and efficient than the FD method.     

周期性单胞复合材料有效弹性性能的边界力方法

均匀化方法是一种适应于周期性构造复合材料有效性能预测的有效方法。然而均匀化方程数学表达形式复杂, 均匀化方法很难直接应用通用有限元软件进行计算, 因此本文中提出一种便于求解均匀化方程的边界力方法, 利用高斯定理将原均匀化问题转化为普通的三维应力问题, 给出了单胞中不同材料交界面上作用的面分布力形式。运用有限元软件求解了均匀化系数, 预报了单向复合材料和三维四向编织复合材料的有效性能, 计算结果与实验吻合很好。      

Solution of Fokker-Planck equation by finite element and finite difference methods for nonlinear systems

The response of a structural system to white noise excitation (deltacorrelated) constitutes a Markov vector process whose transitional probability density function (TPDF) is governed by both the forward Fokker-Planck and backward Kolmogorov equations. Numerical solution of these equations by finite element and finite difference methods for dynamical systems of engineering interest has been hindered by the problem of dimensionality. In this paper numerical solution of the stationary and transient form of the Fokker-Planck (FP) equation corresponding to two state nonlinear systems is obtained by standard sequential finite element method (FEM) using C⁰ shape function and Crank-Nicholson time integration scheme. The method is applied to Van-der-Pol and Duffing oscillators providing good agreement between results obtained by it and exact results. An extension of the finite difference discretization scheme developed by Spencer, Bergman and Wojtkiewicz is also presented. This paper presents an extension of the finite difference method for the solution of FP equation up to four dimensions. The difficulties associated in extending these methods to higher dimensional systems are discussed. This paper is dedicated to Prof R N Iyengar of the Indian Institute of Science on the occasion of his formal retirement.     

$H^1$-Stability and Convergence of the FE,FV and FD Methods for an Elliptic Equation

We obtain the coefficient matrices of the finite element (FE), finite volume (FV) and finite difference (FD) methods based on $P_1$-conforming elements on a quasi-uniform mesh, in order to approximately solve a boundary value problem involving the elliptic Poisson equation. The three methods are shown to possess the same $H^1$-stability and convergence. Some numerical tests are made, to compare the numerical results from the three methods and to review our theoretical results.     

Multiscale prediction of mechanical behavior of ferrite–pearlite steel with numerical material testing

Multiscale mechanical behaviors of ferrite–pearlite steel were predicted using numerical material testing (NMT) based on the finite element method. The microstructure of ferrite–pearlite steel is regarded as a two‐component aggregate of ferrite crystal grains and pearlite colonies. In NMT, the macroscopic stress–strain curve and the deformation state of the microstructure were examined by means of a two‐scale finite element analysis method based on the framework of the mathematical homogenization theory. The microstructure of ferrite–pearlite steel was modeled with finite elements, and constitutive models for ferrite crystal grains and pearlite colonies were prepared to describe their anisotropic mechanical behavior at the microscale level. While the anisotropic linear elasticity and the single crystal plasticity based on representative characteristic length have been employed for the ferrite crystal grains, the constitutive model of a pearlite colony was newly developed in this study. For that reason, the constitutive behavior of the pearlite colony was investigated using NMT on a smaller scale than the scale of the ferrite–pearlite microstructure, with the microstructure of the pearlite colony modeled as a lamellar structure of ferrite and cementite phases with finite elements. On the basis of the numerical results, the anisotropic constitutive model of the pearlite colony was formulated based on the normal vector of the lamella. The components of the anisotropic elasticity were estimated with NMT based on the finite element method, where the elasticity of the cementite phase was numerically evaluated with a first‐principles calculation. Also, an anisotropic plastic constitutive model for the pearlite colony was formulated with two‐surface plasticity consisting of yield functions for the interlamellar shear mode and yielding of the overall lamellar structure. After addressing the microscopic modeling of ferrite–pearlite steel, NMT was performed with the finite element models of the ferrite–pearlite microstructure and with the microscopic constitutive models for each of the components. Finally, the results were compared with the corresponding experimental results on both the macroscopic response and the microscopic deformation state to ascertain the validity of the numerical modeling. Copyright © 2011 John Wiley & Sons, Ltd.     

Compression modeling of plain weave textile fabric using finite elements

Textile composite are used extensively in aerospace as they offer a 3D reinforcement in a single layer providing better mechanical properties in both in‐plane and transverse directions. This paper reports on the mechanical behavior of a plain weave textile fabric under the compressive loading. Unit cell geometry of the plain weave fabric structure is identified and its model is created using TexGen geometric modeling scheme developed by the University of Nottingham (U.K.). Later on its mechanical behavior is predicted using finite element modeling (FEM) based simulation software ABAQUS^® incorporating a transversely isotropic material law. Strain energy of the developed model has been compared with that of the published results and shows very good agreement. The analysis indicated that transverse‐longitudinal shear (TLS) modulus plays an important role in characterizing the behavior of the woven fabric under compression, while the friction between the yarns and longitudinal stiffness has less significant influence on compaction behavior. In order to ascertain the effectiveness of the developed model, exhaustive parametric studies have also been conducted to investigate the effect of transverse‐longitudinal shear modulus on some of the important parameters such as artificial strain energy, external work, frictional dissipation, internal energy, kinetic energy, strain energy and total energy of the model. The developed model has the capacity to predict and simulate the behavior of variety of fabric architectures based on their constituent yarn properties under various regimes of service loads.     

Self-consistent one-particle 3D unit cell model for simulation of the effect of graphite aspect ratio on Young’s modulus of cast-iron

The graphite phase of ferritic cast-iron was assumed to consist of randomly oriented, rotationally symmetric, ellipsoidal inclusions of same dimensions. Accordingly, a self-consistent one-particle 3D unit cell model was developed to simulate the effect of graphite aspect ratio on cast-iron elastic constants. The cube shaped unit cell is made up of an inner rotational ellipsoid of graphite surrounded by Fe–2.5%Si matrix in a concentric outer ellipsoid of the same aspect ratio as the inner graphite ellipsoid in order to model the desired graphite content. The remainder of the unit cell is filled up by the cast-iron compound, the elastic behaviour of which is determined self-consistently. In order to obtain elastic properties, the unit cell was subjected to uniaxial loading. Calculations of stress and strain distributions, in dependence on the orientation of the graphite ellipsoid, were carried out by the finite element method using 3D elements. Finally, updated values of Young’s modulus and Poisson’s ratio were derived by employing Hooke’s law. This procedure was repeated, using the updated elastic constants as new input, to get a self-consistent convergent solution. The results are compared with finite element calculations using a conventional one-particle 3D unit cell model with multiphase elements, and an analytical solution given in the literature. Comparison with experimental data shows the relatively wide range of validity and the superiority of the self-consistent method.