考虑一阶和二阶位移梯度的数字图像相关方法在剪切带测量中的比较

当剪切带中存在二阶位移梯度或应变梯度时,研究了两种数字图像相关(DIC)方法在测量位移、应变及应变梯度中的表现。以基于梯度塑性理论的剪切带的位移解作为基础,通过Matlab仿射变换制作了具有不同平均剪切应变和应变梯度的虚拟剪切带。通过对其计算和分析得到了下列结果:当剪切带的平均剪切应变和应变梯度较高时,与只考虑一阶位移梯度的DIC方法相比,考虑二阶位移梯度的DIC方法优势明显,获得的位移、应变及应变梯度结果与理论解比较吻合,由于DIC方法测量的是平均应变,因此,剪切带中心的峰值应变将被低估;当剪切带的平均剪切应变和应变梯度较低时,剪切带中心的峰值应变可能被高估,受标准偏差的影响,考虑二阶位移梯度的DIC方法没有优势。基于上述研究结果,在单向压缩应力控制加载条件下,对砂样从开始加载至宏观裂纹出现之前变形过程中的3种应变场的4种结果进行了分析。由于应变不超过0.25,因而考虑二阶位移梯度的DIC方法的结果并无优势。     

基于一阶及二阶DIC方法的常应变剪切带的测量误差分析

制作了水平和倾斜的常应变剪切带,使用数字图像相关方法(DIC)对剪切带内、外的位移场和应变场进行了测量,分析了形函数、子区尺寸及测点间距对测量结果的影响。结果表明:在剪切带边界附近,一阶或二阶DIC方法的位移误差限均较大,这是因为这些区域的子区覆盖了一部分剪切带;子区尺寸越大,或测点距离剪切带边界越近,位移误差限越大;一般对于剪切带边界附近测点,二阶DIC方法比一阶DIC方法的位移误差限小;随着测点间距的增加,一阶或二阶DIC方法的剪切带的法向剪应变坐标曲线由陡峭变得平缓,剪切带宽度逐渐增加。     

数字图像相关法测量聚碳酸酯板应力强度因子

本文以数字图像相关方法测量了聚碳酸酯板的张开型应力强度因子（SIF）。实验过程中以聚碳酸酯标准紧凑拉伸式样为样本,由数字图像相关（DIC）方法提取不同载荷下裂纹附近的全场位移。在已计算得到全场位移的情况下,由线弹性断裂理论可知,弹性区域内每一点位移可表示为SIF的函数。在计算SIF时考虑了实验中不可避免存在的刚体平移与转动的影响,应力强度因子、刚体平移与转动可由最小二乘法计算得到;还讨论了位移场的选择及位移展开项项数对SIF的影响。实验结果与理论值进行了比较,结果显示DIC方法准确地测量了聚碳酸酯板的应力强度因子,因此DIC为测量SIF提供了一种有效的试验方法。     

考虑应变梯度及刚度劣化的剪切带局部变形分析

基于梯度塑性理论,研究了应变软化阶段的刚度劣化对剪切带内部的局部应变及相对剪切位移的影响。剪切带被看作一维剪切问题,本构关系为线弹性及线性应变软化。考虑刚度劣化后,剪切带的弹性应变由弹性剪切模量、损伤变量及残余剪切模量确定。剪切带的非局部总应变由双线性的本构关系确定。将非局部总应变减去弹性应变,可得剪切带的非局部塑性应变。剪切带非局部塑性应变与流动应力及损伤变量等参数有关,此关系即为在经典弹塑性理论框架之内的考虑刚度劣化的屈服函数。将二阶应变梯度项引入该函数,可得剪切带内部的局部塑性剪切应变及局部总剪切应变的分布规律。对局部塑性剪切应变积分,得到了局部塑性剪切位移。结果表明:考虑了刚度劣化后,剪切带内部的弹性剪切应变及位移增加,而局部塑性剪切应变及位移降低。若不考虑刚度劣化,理论结果可蜕化为以前的结果。理论结果与岩石局部变形的观测结果在定性是一致的。     

剪切压电陶瓷块微位移测量及非线性修正

通过搭建的剪切压电陶瓷块微位移测量系统,进行了5个不同目标电压的剪切压电陶瓷微位移测量实验,对实验数据分别进行二阶、三阶、四阶最小二乘拟合后进行非线性修正实验,其中采用三阶最小二乘拟合进行修正时效果最好,其位移1 050 nm行程时最大非线性误差为3 nm。对所得三阶最小二乘拟合多项式的系数进行样条插值拟合,从而实现对不同目标位移的非线性修正,其中位移900 nm行程时最大非线性误差为4 nm,仅为原始非线性误差的11%。     

结构应变模态参数辨识的最小二乘复频域方法

由于应变模态对结构状态的敏感性,其在结构在线健康监测和损伤识别方面比位移模态更具优势。利用应变和位移的关系,将最小二乘复频域方法应用到结构应力应变分析中,建立基于应变测量数据的结构动力学参数频域辨识方法。由于应变模态和位移模态是同一种物理状态的不同表达形式,两者在数学表达上有相似性。首先建立以应变为变量的参数化公分母模型,在此基础上将非线性最小二乘问题进行线性化,得到加权线性最小二乘的方程误差。然后采用基于缩减正则方程的算法进行求解,减少计算量,并通过对模型参数施加约束来避免参数冗余。然后,设计并搭建一个自由梁的实验结构系统,利用光纤布拉格光栅应变传感器测量结构动应变数据,根据最小二乘复频域方法,基于应变测量数据辨识得到频率和阻尼比,与传统的基于加速度测量数据的辨识结果相吻合。另外,辨识所得应变模态振型与仿真结果也具有一致性。因此,数值仿真和实验验证表明,文中提出的基于最小二乘复频域方法能够准确辨识结构应变模态。     

采用数字图像相关方法的莫来石纤维增强气凝胶复合材料力学试验

基于V型缺口试样双轨剪切法设计了面内剪切试验方案,开展了莫来石纤维增强气凝胶复合材料的室温面内剪切和弯曲性能试验,采用数字图像相关方法对试样表面的位移场和应变场进行测量,并分析了力学行为和破坏模式。结果表明:设计的试验方案可以在测试区域获得均匀的剪切应变场,适用于莫来石纤维增强气凝胶复合材料的面内剪切性能测试。试验获得的面内剪切模量和强度分别为248 MPa和0.95 MPa,弯曲模量和强度分别为294 MPa和2.08 MPa。面内剪切载荷下,试样的裂纹萌生于缺口尖端附近,并沿两缺口连线方向扩展。根据弯曲正应变场的分布特点,发现试样中性层与几何对称面不重合,验证了该材料拉压模量不同的性质。采用数字图像相关方法获得的中性层位置和理论计算值比较接近,相对误差在10%左右。     

基于DIC实验的空间域信号去噪方法研究

通过二维傅里叶连续延拓联合波数域低通滤波的方法,对数字图像相关测量所得位移场进行去噪重构,通过对薄板结构的工况模态分析,验证空间域信号去噪方法的有效性。数字图像相关方法测量结果为结构表面的全场位移响应,因相机本底噪声等因素的影响,由此在位移场测量结果中引入的空间域噪声不可忽略。通过对去噪重构后的时序位移场进行互相关函数计算,使用ERA算法辨识得到薄板的前5阶模态参数,与有限元计算模态结果吻合良好。     

非接触数字图像相关应变测量的仿真与实验研究

数字图像相关法测量全场位移和应变是一种新的实验力学方法.该测量算法中相关函数和子区大小的选择是影响最终应变测量精度的重要因素.本文采用已知应变变形的仿真散斑图,研究了测量算法中主要相关函数和子区大小在正常光照与高斯不均匀光照条件下,对应变测量精度的影响.得出了不同测量要求下,可选择的相关函数和最佳计算窗口.通过实验验证与分析了此算法的测量精度.研究结果表明,数字图像处理技术测量应变的测试精度满足基本要求.     

基于三维点云螺纹中轴线的拟合方法研究

螺纹中轴线的精确测定是决定螺纹三维测量结果是否准确的重要因素之一。中轴线的倾斜、偏移会对工件坐标系的建立、螺纹的三维重构、参数检验等测量操作引入误差。基于三维点云的最小二乘拟合算法,开展了螺纹中轴线的拟合方法研究。根据螺纹表面点云数据,利用螺纹表面与中轴线的特征关系建立最小二乘数学模型,通过计算点云数据的三维凸包滤除螺纹自身三维结构带来的拟合误差,使螺纹中轴线的测定更精准。通过仿真实验,基于三维点云的最小二乘拟合算法拟合的直线与三维点云的距离方差为0.34,在旋合长度范围内与投影法确定的直线两端最大距离为0.15μm,符合三维测量高精度标准,基于三维点云的最小二乘拟合算法可以快速、准确地拟合螺纹中轴线。     

基于环绕测点子区分割的数字图像相关方法剪切带宽度测量研究

提出了一种致力于改善狭窄、高应变梯度剪切带宽度测量精度的数字图像相关方法.通过对测点的原始子区的有限分割,使后代子区环绕在测点周围,以使一些后代子区位于简单变形区域,进而以最佳后代子区的结果作为测点结果.通过对比提出方法和粗-细方法的虚拟剪切带宽度测量结果,验证了提出方法的有效性,并从理论上分析了剪切带宽度测量误差.研...     

Microstress estimate of stochastically heterogeneous structures by the functional perturbation method: A one dimensional example

A new functional perturbation method (FPM) for calculating the probabilistic response of stochastically heterogeneous, linear elastic structures is developed. The method is based on treating the governing differential operator as well as the unknown displacement function as a functional of material modulus field. By executing a functional perturbation around the homogeneous case, a set of successive differential equations is obtained and solved, from which the average and variance of any local parameter (displacements, stresses, strains) can be found. For a linear problem, the equations to be solved in each approximation order differ from the one for the homogeneous case by a pseudo external loading (right hand side) part only. Thus, only the Green function for the homogeneous case is needed for an analytical solution of the corresponding heterogeneous problem. A one dimensional stochastically heterogeneous rod embedded in a uniform shear resistant elastic medium is solved as an example. The statistical variance of displacements and stresses are found analytically, including the edge regions. Morphological (grain size) and material (modulus) effects on the stochastic response are demonstrated. The above results are essential for estimating the stochastic features of local stress concentrations, which are the source for many strength-related macro properties of materials. Extensive usage of generalized functions (Dirac operator and its derivatives) is needed for the analysis.     

Transverse vibrations of prismatic rods by accounting for shears

Derivations of a differential equation of eight order and boundary conditions of flexural vibrations of a straight rod by accounting for shear strains caused by a transverse load are presented. Unlike existing approaches, use of coefficients of shear and angles of displacements is excluded in all relationships. The article gives the solution of the boundary-value problem on determining the function of plane displacement of sections with transverse shear for a round profile without the traditional introduction and additional determination of the shear function. An exact analytical solution of the boundary-value problem on free flexural vibrations of a cantilever rod by accounting for shears is presented. A numerical example of calculating flexural vibration parameters of a rod with round cross-sectional profile is examined along with evaluation of the effect of shear strain factor on frequency of the principal tone.Translated from Problemy Prochnosti, No. 2, pp. 82–86, February, 1991.     

Basic principle of digital image correlation for in-plane displacement and strain measurement

The basic principle and the algorithm of a digital image correlation method, and the procedure for obtaining displacements and strains are described. In order to describe the basic principle precisely, only in-plane displacement and strain measurement of a planar object are explained. Gray levels between integer pixels of a digital image after deformation are interpolated to obtain displacements with subpixel resolution. Displacements are then determined by solving nonlinear simultaneous equations taking the deformation of a subset into consideration. Strains are obtainable by differentiating the measured displacements. In addition to the basic principle of digital image correlation, the example of the measurement and its results are shown.     

Enhanced mixed interpolation XFEM formulations for discontinuous Timoshenko beam and Mindlin‐Reissner plate

Shear locking is a major issue emerging in the computational formulation of beam and plate finite elements of minimal number of degrees of freedom as it leads to artificial overstiffening. In this paper, discontinuous Timoshenko beam and Mindlin‐Reissner plate elements are developed by adopting the Hellinger‐Reissner functional with the displacements and through‐thickness shear strains as degrees of freedom. Heterogeneous beams and plates with weak discontinuity are considered, and the mixed formulation has been combined with the extended finite element method (FEM); thus, mixed enrichment functions are used. Both the displacement and the shear strain fields are enriched as opposed to the traditional extended FEM where only the displacement functions are enriched. The enrichment type is restricted to extrinsic mesh‐based topological local enrichment. The results from the proposed formulation correlate well with analytical solution in the case of the beam and in the case of the Mindlin‐Reissner plate with those of a finite element package (ABAQUS) and classical FEM and show higher rates of convergence. In all cases, the proposed method captures strain discontinuity accurately. Thus, the proposed method provides an accurate and a computationally more efficient way for the formulation of beam and plate finite elements of minimal number of degrees of freedom.     

Combining X-FEM and a multilevel mesh superposition method for the analysis of thick composite structures

The use of simultaneous multiple plate models offers an attractive and alternative solution to full scale three-dimensional finite element method for the global–local analysis of laminated composite structures. In this paper, an approach is proposed where the less accurate plate model, used to carry out the analysis at the global level, is enhanced by more accurate and complex plate models in each laminate subregion where more accurate transverse stress or strain estimation is required (the local level).The total displacement is represented as the superposition of the displacements of a number of plate models. By appropriately defining boundaries to the enhancing model/region, it is demonstrated that the superposition of displacements can be used to locally enrich the solution where accurate through-the-thickness stresses are required. In this manner, a computationally efficient global model can be used to determine gross displacements, and potentially the enriched models can be used to determine stresses at lamina interfaces for the accurate prediction of localized phenomena such as damage initiation and growth. The model is implemented combining an extended FEM (X-FEM) and multilevel mesh superposition approach (MMSA). Extra degrees-of-freedom are added to the model to represent the additional displacement fields, and the meshing process remains independent for each field.The displacements and stresses computed by this approach are compared to literature data and analytical solutions for various plate geometries and loads showing an excellent correlation. Morevoer, the results showed, as expected, that the accuracy of the approximation is improved by the proposed approach compared to using the global plate model alone.     

Global and local coordinates in digital image correlation

Digital image correlation (DIC) is commonly used to measure specimen displacements by correlating an image of a specimen in an undeformed or reference configuration and a second image under load. To establish the correlation between the images, numerical techniques are used to locate an initially square image subset in a reference image. In this process, choosing appropriate coordinates is of fundamental importance to ensure accurate results. Both global and local coordinates can be used in shape functions. However, large rigid body rotations and deformations are accurately obtained by using global rather than local shape functions. In addition, points located after displacement may not be at an integer pixel distance from the original position. Hence subpixel displacement estimation methods such as interpolation or fitting of correlation coefficients are essential. A solution using the least-squares method is employed by choosing proper coordinates, and the feasibility of using local coordinates is demonstrated and validated with a mathematical model. Both simulated and experimental results show that the proper choice of coordinates does ensure the reliability and improve the accuracy of measurements in DIC.     

An analytical solution of the population balance equation for simultaneous Brownian and shear coagulation in the continuum regime

Brownian coagulation of aerosol particles can take place in both laminar and turbulent flows. Thus, the simultaneous Brownian and shear coagulation will always occur in practical applications. This study presents an analytical solution to describe the size evolution of polydisperse particles undergoing simultaneous Brownian and shear coagulation. The analytical solution is derived using the log-normal method of moments (LNMOM) with some approximations. Then, the analytical solution is validated by comparing with previous analytical solutions derived for limiting cases. The results show that the present analytical solution is consistent with previous analytical solutions for these limiting cases. Further, the time trajectories of the total particle number concentration, the geometric standard deviation and the geometric number mean particle volume predicted by the present analytical solution are compared with those of a numerical LNMOM model. The results show that the present analytical solution gives good predictions of the total particle number concentration but less accurate predictions of the geometric standard deviation and the geometric number mean particle volume. A dimensionless analysis shows that the coagulation rate ratio and the initial polydispersity are two important factors for characterizing the size evolution of simultaneous Brownian and shear coagulation.     

A new discrete Kirchhoff quadrilateral element based on the third-order theory for composite plates

A new discrete Kirchhoff quadrilateral element based on the refined third-order theory is developed for the analysis of composite plates. The element has seven degrees of freedom per node, namely, the three displacements, two rotations and two transverse shear strain components at the mid-surface. The inplane displacements and the shear strains are interpolated using bilinear interpolation functions and the mid-surface rotations are interpolated using bi-quadratic functions based on the discrete Kirchhoff technique. The element stiffness matrix and the consistent load vector are developed using the principle of virtual work. The finite element formulation is validated by comparing the results for simply-supported plate with the analytical Navier solution. Comparison of the present results with those using other available elements based on the TOT establishes the superiority of the present element in respect of simplicity, accuracy and computational efficiency. The element is free from shear locking