非均质材料动力分析的广义多尺度有限元法

自然界和工程中的大部分材料都具有多尺度特征,当考察尺度小到一定程度后,都将表现出非均质性.针对非均质材料的动力问题,提出了一种广义多尺度有限元方法,其基本思想是利用静态凝聚法以及罚函数法构造能够反映单元内部材料非均质特性的多尺度位移基函数.与传统扩展多尺度有限元法中的基函数构造方式不同,广义多尺度有限元法的基函数无需通过在子网格域上多次求解椭圆问题得到,而可直接通过矩阵运算获得.其主要步骤如下:利用数值基函数将一个非均质单胞等效为一个宏观单元,进而形成整个结构的等效刚度矩阵,并得到宏观网格的节点位移,最后再次利用数值基函数得到微观尺度上的位移结果.该广义多尺度有限元法是扩展多尺度有限元法的一种新的拓展,可模拟具有更加复杂几何的非均质单胞的力学行为.通过数值算例,模拟了非均质材料的静力问题、广义特征值问题以及瞬态响应问题,计算结果表明:在边界条件一样的情况下,广义多尺度有限元法的计算结果与传统有限元的计算结果保持高度一致.与传统有限元相比,该方法在保证计算精度的同时极大地提高了计算效率.研究结果表明,广义多尺度有限元法能够很好地模拟非均质单胞的力学行为,具有良好的工程应用潜力.      

功能梯度材料动力学问题的POD模型降阶分析

为了快速分析非均质材料结构在复杂载荷作用下的动态响应,提出一种模型降阶方法,只需计算结构在简单均质材料情况下的动力学问题,进而用其计算结果对非均质材料结构进行分析.首先,采用结构内部任意一点处的材料参数值作为整个结构的材料参数,利用有限元分析软件计算该均质材料结构在动态载荷作用下的位移场建立数据库,该数据库包含计算模型各个节点(自由度为N)在某时间段内L个时刻的位移;其次,对数据库中的信息按照时间离散的特定方式组集成瞬像矩阵,并利用特征正交分解方法对其进行分解,得到该模型的L个特征正交基底,选取其中能反应模型主要特征的H个(其中HL?N)作为一组最优基底,通过这组基底建立模型的低阶离散控制方程;最后,求解低阶离散微分方程组,得到功能梯度材料结构在复杂载荷作用下的位移场.文中分别给出二维和三维算例,比较了降阶模型和全阶模型计算结果,验证了该方法的有效性,并且计算效率能提高1～2个数量级.     

复合材料应力分析的均匀化方法

建立了基于均匀化理论的确定复合材料结构应力场的方法．其实质是用均质的宏观结构和非均质的具有周期性分布的细观结构描述原结构；将力学量表示成关于宏观坐标和细观坐标的函数，并用细观和宏观两种尺度之比为小参数展开，用摄动技术将原问题化为一细观均匀化问题和一宏观均匀化问题．这两个问题的解确定了包含等效位移和一阶近似位移的位移场，由此获得应力场．利用该方法给出了圆柱形孔隙材料和单向纤维复合材料在单向拉伸时的应力场以及空隙材料简支梁的局部应力场，说明了该方法的有效性     

基于拓扑优化的结构弹性成像方法

弹性模量是工程材料重要的性能参数, 可以衡量物体抵抗弹性变形的能力. 弹性成像是一种通过弹性模量表征生物体组织物理特性的医学成像方法. 为了将弹性成像应用于机械装备结构的缺陷识别, 提高弹性成像的局部表征和全局识别能力, 提出一种基于拓扑优化的结构弹性成像方法. 受拓扑优化理论启发, 采用结构离散单元的相对密度(弹性模量系数)作为弹性成像参数来表征损伤程度, 建立成像参数与弹性模量的插值模型, 基于有限元模型构建损伤表征、结构模型与物理响应的映射关系. 以损伤结构和无损结构位移响应的最小二乘为目标函数, 以成像参数上下限为约束, 建立结构弹性成像的优化模型. 以伴随法推导弹性成像问题的灵敏度, 并详细给出了弹性成像反演的数值实施方式. 二维悬臂梁和米歇尔梁算例表明, 本文提出的基于拓扑优化的弹性成像方法无需先验损伤信息, 可有效实现均质/非均质、单/多缺陷结构的弹性成像, 且弹性成像结果不依赖于特定的边界条件, 进一步将弹性成像方法扩展至三维悬臂梁问题验证了其通用性.      

基于矿物构成的非均质岩石材料数值方法研究

基于岩石材料的矿物构成利用矿物细胞元随机性参数赋值方法对岩石材料数值模型进行参数赋值,描述岩石材料的非均质特性.利用该赋值方法所具有的随机性特征和结构性特征,在二维情况下计算整体模型中代表各类别矿物的单元的总面积期望值,讨论了该赋值方法对整体模型中的所有单元网格具有相同尺寸的依赖性,并利用该赋值方法建立非均质巴西圆盘模型,对其纵向受力轴线上的应力进行了数值计算.研究结果表明,矿物细胞元随机性参数赋值方法通过考虑岩石矿物构成,可使数值模型内各矿物含量与岩石材料真实含量相等,且不要求整体模型的所有单元网格具有相同的尺寸;通过均质情形下和非均质情形下巴西圆盘试验的数值模拟结果比较,岩石材料的非均质特性对圆盘的应力分布有着显著影响.     

基于金相图片识别功能梯度材料参数的梯度分布函数

功能梯度材料具有复杂的细观结构.其内部构造远比匀质材料复杂.以目前的实验条件,测量功能梯度材料参数分布函数一般是十分困难的.该文提出一种细观元方法,直接利用功能梯度材料金相图片信息,来进行功能梯度构件宏观响应的跨尺度力学分析.另在功能梯度材料结构静、动力正演分析基础上,根据正演所求得的挠度或固有频率值,采用混和罚函数法来反演识别功能梯度材料参数的宏观梯度分布函数.     

一维随机排列非均质颗粒材料结构刚度系数解析式

针对一维情况下随机排列非均质颗粒材料组成的结构,推导了该结构的刚度系数的解析表达式。颗粒材料由随机算法根据颗粒尺寸分布和结构尺寸生成。通过引入相对破碎参数,将颗粒破碎现象定量体现在颗粒尺寸分布函数的变化上,从而使本文提出的解析表达式能够计及颗粒破碎。数值结果说明本文提出表达式的有效性,并体现了颗粒破碎对颗粒结构刚度系数的影响。     

云纹干涉测量法进展

引言用云纹(Moire)法测量位移是极为引人注目的。云纹法通过观察等位移线的等值线图的分布场,确定变形体的位移场。严格地讲云纹属于几何效应,对弹性体,非弹性体,各向同性体及各向异性体的位移同样地反映良好。已经研究成功测定结构及结构部件面内及离面位移的多种云纹技术,但是几乎所有以前的研究工作使用的都是40线/毫米即1000线/英寸的较粗的光栅,或者更粗一些。这只能测定较大的位移,例如高延性材料的面内弹性位移及结构材料的非弹性位移。      

基于位移响应协方差参数的数值仿真和实测损伤识别研究

本文使用结构位移响应协方差参数进行结构损伤识别，首先推导和建立位移响应协方差参数的解析公式，它是结构频率、振型和阻尼等模态参数的函数，结构物理参数的改变会导致该协方差参数的改变；对一个七层框架结构进行数值模拟分析来演示该方法的有效性，通过比较结构不同状态下各单元位移响应协方差参数CoD的分布曲线，研究各单元CoD与损伤程度的关系曲线，发现损伤位置处的CoD改变最大，其次是对称和附近单元，通过单损伤和多损伤工况研究分析，表明基于结构损伤前后CoD的改变，能成功判定损伤发生和识别出损伤位置，最后把该方法应用于一个实验室简支钢梁的损伤识别，通过对锤击振动下的加速度响应进行二次积分得到位移响应，并比较钢梁损伤前后的CoD，得到损伤概率向量，成功识别出损伤位置。该方法具有较好的噪声鲁棒性，无需结构分析模型，计算简便，具有较好的工程应用性。     

岩石弹塑性破裂过程的数值模拟研究

分析了对于非均质、非连续且材料参数分布具有分散性和随机性的岩体介质，采用传统有限元法解决其工程问题的局限性．阐述了用岩石力学性质的分布特性来描述岩石材料不均匀性，并用蒙特卡洛模拟方法，将符合Weibull分布规律的材料参数赋予岩体结构中的各个单元体，进而用计算机进行数值模拟的研究方法．应用了在Windows95环境下利用FORTRAN Power Station4．0平台开发的具有可视性的“岩石弹塑性破裂过程分析”软件——REPFPA软件，对典型的岩石试样和巷道模型的弹塑性破裂过程进行数值模拟研究，得到了有价值的实验结果．证明把材料参数随机赋值方法引入到岩土类材料的弹塑性破裂过程分析中去，并用计算机进行数值模拟是研究岩石弹塑性破裂过程的一种有效方法。     

Static analysis of functionally graded doubly-curved shells and panels of revolution

The Generalized Differential Quadrature (GDQ) Method is applied to study four parameter functionally graded and laminated composite shells and panels of revolution. The mechanical model is based on the so-called First-order Shear Deformation Theory (FSDT), in particular on the Toorani-Lakis Theory. The solution is given in terms of generalized displacement components of points lying on the middle surface of the shell. The generalized strains and stress resultants are evaluated by applying the Differential Quadrature rule to the generalized displacements. The transverse shear and normal stress profiles through the thickness are reconstructed a posteriori by using local three-dimensional elasticity equilibrium equations. In order to verify the accuracy of the present method, GDQ results are compared with the ones obtained with semi-analytical formulations and with 3D finite element method. A parametric study is performed to illustrate the influence of the parameters on the mechanical behavior of functionally graded shell structures made of a mixture of ceramics and metal.     

Identification of elastic property and loading fields from full-field displacement measurements

A method is introduced to identify simultaneously elastic properties and loading fields from a measured displacement field. Since the mechanical behavior of micro-electro-mechanical systems (MEMS) is governed by surface effects, this type of identification tool is thought to be of major interest. However, increasing the number of parameters to retrieve affects the redundancy necessary for an accurate identification. A finite-element formulation of a distance between measured and statically admissible (SA) displacement fields is shown to be equivalent to a standard least-squares distance to kinematically admissible (KA) fields if the used modeling is suitable. Any deviation from this equivalence is then the signature of a modeling error. Balancing the distance to KA and SA displacement fields allows one to retrieve unknown modeling parameters. This method is detailed on heterogeneous Euler–Bernoulli beams submitted to an unknown loading field and applied to experimental displacement fields of micro-cantilevers obtained with an electrostatic set-up. An elastic property field and a parameterized loading field are then identified, and the quality of the identification is assessed.     

基于Kriging代理模型的迭代更新高效反演方法

为提高混凝土坝等大体积结构参数反演效率和精度,减少由于应用有限元进行大量正分析而产生的计算机时,建立了一种结合Kriging代理模型和粒子群优化(PSO)算法的迭代更新反演方法。通过拉丁超立方抽样(LHS)方法确定初始样本点的空间分布,并使用有限元正分析获取对应的响应值,构建粗糙的初始代理模型,结合具有全局寻优能力的PSO算法,反演大体积结构的分区弹性模量,随之再代入有限元模型中,计算获取新的位移响应,并将其作为新样本加入到样本集中,通过迭代更新获得局部更高精度的代理模型。工程实际算例表明,该方法对混凝土坝等大体积结构参数反演精度较高和适用性好,且能大幅减少传统有限元模型反演方法所需消耗的正分析机时,提高反演效率。     

Reconstruction of inhomogeneous characteristics of a transverse inhomogeneous layer in antiplane vibrations

Direct and inverse problems of forced antiplane vibrations of a transverse inhomogeneous elastic layer are considered. The mechanical characteristics of the layer (density and shear modulus) are considered to be functions of the transverse coordinate. A method for solving the direct problem, based on using the integral Fourier transform and solving the boundary problem by the shooting method, is proposed. The inverse problem of determining the distributions of the mechanical parameters based on the known information on the wave field on some part of the upper surface is considered. Iterative sequences of integral equations are constructed. Results of numerical experiments and recommendations on the optimal choice of the vibration frequency and the interval, on which the displacements are determined, are given.     

Dimensionally Scaled Miscible Displacements in Heterogeneous Permeable Media

Understanding and predicting the performance of solvent drives and remediation of contaminated aquifers in heterogeneous reservoirs is of great importance to the petroleum and environmental industries. In this paper, a general method to scale flow through heterogeneous reservoirs is presented for a miscible displacement of oil by a solvent. Results show that scaling miscible displacements in a two-dimensional, heterogeneous, anisotropic vertical cross section requires the matching of 13 dimensionless scaling groups. These groups were derived using a general procedure of inspectional analysis. A detailed numerical sensitivity study was performed to reveal the relationship between the scaling groups and the fractional oil recovery of miscible displacements in heterogeneous reservoirs. This relationship was then mapped using an artificial neural network, which can be used as a quick prediction tool for the fractional oil recovery for any combinations of the scaling groups, thus eliminating the need for the expensive fine-mesh simulations. These results have potential applications in modeling miscible displacements and in the scaling of laboratory displacements to field conditions.     

Shape sensing of 3D frame structures using an inverse Finite Element Method

A robust and efficient computational method for reconstructing the elastodynamic structural response of truss, beam, and frame structures, using measured surface-strain data, is presented. Known as “shape sensing”, this inverse problem has important implications for real-time actuation and control of smart structures, and for monitoring of structural integrity. The present formulation, based on the inverse Finite Element Method (iFEM), uses a least-squares variational principle involving section strains (also known as strain measures) of Timoshenko theory for stretching, torsion, bending, and transverse shear. The present iFEM methodology is based on strain–displacement relations only, without invoking force equilibrium. Consequently, both static and time-varying displacement fields can be reconstructed without the knowledge of material properties, applied loading, or damping characteristics. Two finite elements capable of modeling frame structures are derived using interdependent interpolations, in which interior degrees of freedom are condensed out at the element level. In addition, relationships between the order of kinematic-element interpolations and the number of required strain gauges are established. Several example problems involving cantilevered beams and three-dimensional frame structures undergoing static and dynamic response are discussed. To simulate experimentally measured strains and to establish reference displacements, high-fidelity MSC/NASTRAN finite element analyses are performed. Furthermore, numerically simulated measurement errors, based on Gaussian distribution, are also considered in order to verify the stability and robustness of the methodology. The iFEM solution accuracy is examined with respect to various levels of discretization and the number of strain gauges.     

基于绝对节点坐标法的平面梁有限变形下变形重构

现有的对有限变形条件下柔性结构变形重构的研究往往单纯基于曲率与应变间的几何关系, 同时忽略了被测体的纵向变形及其与弯曲变形的耦合效应. 为得到一种更加精确且能借助现有的力学工具进行应用方向扩展的变形重构方法, 以平面梁为对象, 借鉴变形重构逆有限元法的思想, 将平面梁的变形重构问题视作一类最优化问题. 首先, 通过引入绝对节点坐标法(absolute nodal coordinate formulation, ANCF)对柔性结构大变形下非线性的平面梁应变?位移关系进行精确描述, 构造了一种逆梯度缩减ANCF平面索梁单元. 然后, 对此逆ANCF单元进行改进, 在简化节点自由度的同时通过引入罚函数确保单元节点处的曲率连续性, 既保证了本问题的适定性, 也提升了最终解的精确性. 最后, 基于该单元利用Newton法构造了平面梁有限变形下变形重构问题的两种求解算法, 即逐单元算法和多单元整体算法, 以实现不同需求下的稳定求解. 数值仿真结果表明, 本方法在大变形条件下的变形重构误差小于1%, 而且在测点较少的情况下依然保持较高的精度, 同时验证了本方法的收敛性与计算效率.      

Evaluation of contact stress during rolling process,by three dimensional analytical inverse method

A fully analytical three-dimensional inverse method has been developed in order to evaluate contact stress in the roll bite during rolling process. Stress measurements can be done by inserting fibre optics inside the roll body, (however no real measurements were available and simulations have been used instead). The inverse method takes as inputs three independent measured (or simulated) components of the stress tensor under the surface of the roll, and evaluates surface tractions of the roll especially in the contact in the roll gap. Stress, deformation and displacements can be obtained in the whole roll as well. This approach uses the theory of 3D isotropic elasticity and relies on displacement harmonic and bi-harmonic potentials expanded into a double Fourier series along the circumferential and axial directions. The identification of the solution involves matrices of size (3 × 3) computed off-line. This simple solution involves mainly the on-line computation of Fast Fourier Transform (fft) of three inputs, which takes 0.5 s for each (processor 2.8 GHz, time displayed by Scilab 5.3). Good accuracy is obtained, and the number of sensors along the axial direction is studied. Thus, this work encourages the development of an on-line industrial tool.