Three dimensional displacement measurement using Moiré interferometry

Moiré interferometry is used to simultaneously measure the in plane and out of plane displacement components. The high sensitivity of displacement measurement is maintained and high contrast fringes are obtained without recourse to additional filtering.     

Application of electronic speckle-pattern interferometry to measure in-plane thermal displacement in flip-chip packages

Electronic speckle-pattern interferometry (ESPI) was applied for noncontact, real-time evaluation of thermal deformation in a flip-chip package. The spatial resolution of ESPI was increased to submicron scale by magnifying the areas studied in order to measure the deformation of such small-scale components as the solder in the flip-chip package. Thermal deformation in the horizontal and vertical directions around the solder joints was measured as two-dimensional mappings during heating from 25 to 125 °C. ESPI was successful in obtaining information on the complicated deformation field around the solder joints. Furthermore, the shear strain could also be calculated using the measured thermal deformation around each solder joint. The applicability of ESPI to flip-chip packages was verified by comparing the ESPI results with those of finite-element analysis (FEA).     

Measurement of in-plane and out-of-plane ultrasonic displacements by optical heterodyne interferometry

An heterodyne optical probe, which permits one to measure out-of-plane and in-plane displacements at the surface of a specimen excited by ultrasound is presented. The principles at the basis of the two modes of operation are explained and the sensitivities for in-plane and out-of-plane detection are analyzed. The optical layout of the probe and the schematic of its demodulation circuitry are presented. Its accuracy is tested with Rayleigh surface waves. Examples of application to laser-generated Rayleigh and Lamb waves are also presented.     

直角切口柔性平行四杆机构的输出位移分析

柔性铰链是目前被广泛用于微动机器人的主要部件之一.为了深入分析精密传动用柔性平行四杆机构的位移性能,利用材料力学弯曲变形理论的挠曲线近似微分方程,建立了计算直角切口柔性平行四杆机构输出位移的数学模型.设计了一个简单的柔性平行四杆机构模型,采用MATLAB 7.0软件对其进行理论计算,并利用商用软件ANSYS 10.0进行有限元分析.采用线切割的方法加工了一个样件,并进行了相关实验.最终结果表明：数学模型的理论值与有限元仿真值很接近,但与实际样件的实验值有一定的误差.通过误差分析,证实了存在这种误差的合理性,从而验证了所建数学模型具有较高的参考价值,可以作为柔性铰链平行四杆机构行程优化设计的指导理论.     

子孔径拼接检验法中倾斜的影响及消除方法

在子孔径拼接检测大口径光学平面时,子孔径检测的数据往往存在倾斜,它将会导致拼接的数据沿着一个方向的倾斜累加,最后引入很大的倾斜误差。由于这种倾斜误差难以手动修正,通过实验,先用最小二乘法编制软件对所测子孔径数据进行消除倾斜处理,然后把去倾斜的子孔径数据进行拼接处理,对比消除倾斜的子孔径拼接结果与全口径直接检测结果,证明了去倾斜处理在子孔径拼接检测处理中的有效性。     

刚体面内位移激光散斑测量研究

运用散斑统计理论,结合数字图像处理技术,设计了一套激光散斑测量刚体面内微小位移的实验系统,再利用刚体位移前后的散斑图像的互相关性,实现了刚体面内的位移测量.测量结果表明,针对刚体面内小于300μm的微小位移,x轴和y轴的绝对位移误差为±14μm,相对误差为±6.25%左右.     

A novel unsymmetric 8‐node plane element immune to mesh distortion under a quadratic displacement field

An 8‐node quadrilateral plane finite element is developed based on a novel unsymmetric formulation which is characterized by the use of two sets of shape functions, viz., the compatibility enforcing shape functions and completeness enforcing shape functions. The former are chosen to satisfy exactly the minimum inter‐ as well as intra‐element displacement continuity requirements, while the latter are chosen to satisfy all the (linear and higher order) completeness requirements so as to reproduce exactly a quadratic displacement field. Numerical results from test problems reveal that the new element is indeed capable of reproducing exactly a complete quadratic displacement field under all types of admissible mesh distortions. In this respect, the proposed 8‐node unsymmetric element emerges to be better than the existing symmetric QUAD8, QUAD8/9, QUAD9, QUAD12 and QUAD16 elements, and matches the performance of the quartic element, QUAD25. For test problems involving a cubic or higher order displacement field, the proposed element yields a solution accuracy that is comparable to or better than that of QUAD8, QUAD8/9 and QUAD9 elements. Furthermore, the element maintains a good accuracy even with the reduced 2× 2 numerical integration. Copyright © 2003 John Wiley & Sons, Ltd.     

Improvement of plane stress solutions using adaptive finite elements

Abstract

A finite element method is combined with an adaptive meshing technique to improve the accuracy of the finite element solution. The effectiveness of the combined method is evaluated by a plane stress problem that has an exact solution. The problem is that of a panel with a circular cutout subjected to an applied load. The result demonstrates that the adaptive meshing technique can reduce the numbers of the finite elements, the analysis computational time, and improve the accuracy of the analysis solution.     

焊接动态位移场的激光电子散斑法测量

为提供一种能够全场测量整个焊接过程动态位移场的工具,建立了激光电子散斑法测量系统.应用于实际TIG焊接过程中,获得了焊接位移场的散斑原始图像.利用自开发软件,对图像进行灰度变换和直方图均衡化处理后,采用频域同态滤波的方法对图像进行降噪滤波处理.经降噪、二值化、细化、平整、拟合、标定等一系列处理后,即可自动生成相对动态位移场.结果表明,激光电子散斑法能够胜任焊接动态位移场的测量,且具有非接触、测量精度高、对环境的防震要求低、可在明光下操作、能进行全场测量的特点.     

A new method of crack-tip opening displacement determined based on maximum crack opening displacement

In this paper a new method is presented to determine the crack-tip opening displacement (CTOD) for the center cracked plate with uniaxial uniform tension load. The maximum crack opening displacement (MCOD) is adopted to estimate CTOD. Based on the series of calculation results by elastic–plastic finite element simulation, an explicit function expression for the CTOD versus MCOD is determined, which enables to consider the influence effects of crack geometries, plate sizes, applied loads, plane state and material properties. Hence, the presented method of CTOD determined by MCOD is suitable to any center crack finite plate of any material under uniaxial tension.     

A displacement scheme with drilling degrees of freedom for plane elements

A scheme of boundary displacements with drilling degrees of freedom for plane elements is presented. The scheme is free from zero displacement modes and allows the development of hybrid finite elements with vertex and mid-side nodes, each node including a drilling degree of freedom besides the translational ones. Four quadrilateral isoparametric hybrid stress elements are implemented, and numerical results for some current test problems are given.     

A posteriori error estimates of mixed methods for miscible displacement problems

The miscible displacement of one incompressible fluid by another in a porous medium is governed by a system of two equations. One is an elliptic equation of the pressure and the other is a parabolic equation of the concentration of one of the fluids. Since the pressure appears in the concentration only through its velocity field, we choose a mixed finite element method to approximate the pressure equation and for the concentration we use the standard Galerkin method. We shall obtain an explicit a posteriori error estimator in L²(L²) for the semi‐discrete scheme applied to the non‐linear coupled system. Copyright © 2007 John Wiley & Sons, Ltd.     

Contact stress and residual stress in the nose rail of a high manganese steel crossing due to wheel contact loading

Fatigue failure of a high manganese steel crossing is related to its internal crack initiation and growth, which is affected significantly by the magnitude and distribution pattern of contact stress and residual stress in the crossing. Considering the actual service conditions of a crossing and the accuracy requirement for numerical calculation, a whole model of wheel/crossing/ties and a partial model of wheel/crossing are established using elastic‐plastic finite element method. The distributions of contact stress fields and residual stress fields due to wheel contact loading are studied. The effect of train speed on the residual stress in the nose rail is discussed. The contact stress field shows regular contours in the cross‐section of nose rail and decreases remarkably with increasing distance of the wheel‐crossing contact position. The maximum contact stress is located at the contact surface between wheel and crossing. The maximum residual stress is located at a position of 1.5‐2.0 mm below the surface of the nose rail, rather than at the contact surface of wheel and crossing. In a failed high manganese steel crossing, the dense cracks mainly were observed neither at the position of maximum contact stress (the contact surface between the wheel and the crossing), nor at the position of maximum residual stress (1.5‐2.0 mm below the surface of the nose rail), but around the depth of 0.8‐1.0 mm from the worn surface, which is between the position of maximum contact stress and the position of maximum residual stress. It indicates that the combined effects of the maximum contact stress and the maximum residual stress play important roles in fatigue crack initiation in the nose rail. The size of high residual stress region increases with the increase of the train speed. The maximum residual stress in the nose rail increases remarkably with the increase of the train speed.     

Investigation of Analytical Solutions for Bonded Structures by Photomechanical Methods

Abstract:  In this paper, both photoelasticity and moiré interferometry were successively incorporated with finite element method to investigate the predicted thermal stresses and lateral displacement of bonded structures calculated from different theories. It was found that the distributions of moment and transverse force play significant roles in making different values of thermal stresses in the adherends by authors' and Suhir's 1986 theories. On the other hand, the values of lateral displacement obtained from different theories are almost identical.     

A new approach for displacement functions of a curved Timoshenko beam element in motions normal to its initial plane

In existing literature, either analytical methods or numerical methods, the formulations for free vibration analysis of circularly curved beams normal to its initial plane are somewhat complicated, particularly if the effects of both shear deformation (SD) and rotary inertia (RI) are considered. It is hoped that the simple approach presented in this paper may improve the above‐mentioned drawback of the existing techniques. First, the three functions for axial (or normal to plane) displacement and rotational angles about radial and circumferential (or tangential) axes of a curved beam element were assumed. Since each function consists of six integration constants, one has 18 unknown constants for the three assumed displacement functions. Next, from the last three displacement functions, the three force–displacement differential equations and the three static equilibrium equations for the arc element, one obtained three polynomial expressions. Equating to zero the coefficients of the terms in each of the last three expressions, respectively, one obtained 17 simultaneous equations as functions of the 18 unknown constants. Excluding the five dependent ones among the last 17 equations, one obtained 12 independent simultaneous equations. Solving the last 12 independent equations, one obtained a unique solution in terms of six unknown constants. Finally, imposing the six boundary conditions at the two ends of an arc element, one determined the last six unknown constants and completely defined the three displacement functions. By means of the last displacement functions, one may calculate the shape functions, stiffness matrix, mass matrix and external loading vector for each arc element and then perform the free and forced vibration analyses of the entire curved beam. Good agreement between the results of this paper and those of the existing literature confirms the reliability of the presented theory. Copyright © 2005 John Wiley & Sons, Ltd.     

Adaptive Poly-FEM for the analysis of plane elasticity problems

In this work, we present an adaptive polygonal finite element method (Poly-FEM) for the analysis of two-dimensional plane elasticity problems. The generation of meshes consisting of n ? sided polygonal finite elements is based on the generation of a centroidal Voronoi tessellation (CVT). An unstructured tessellation of a scattered point set, that minimally covers the proximal space around each point in the point set, is generated whereby the method also includes tessellation of nonconvex domains. In this work, we propose a region by region adaptive polygonal element mesh generation. A patch recovery type of stress smoothing technique that utilizes polygonal element patches for obtaining smooth stresses is proposed for obtaining the smoothed finite element stresses. A recovery type a ? posteriori error estimator that estimates the energy norm of the error from the recovered solution is then adopted for the Poly-FEM. The refinement of the polygonal elements is then made on an region by region basis through a refinement index. For the numerical integration of the Galerkin weak form over polygonal finite element domains, we resort to classical Gaussian quadrature applied to triangular subdomains of each polygonal element. Numerical examples of two-dimensional plane elasticity problems are presented to demonstrate the efficiency of the proposed adaptive Poly-FEM.     

Four‐node incompatible plane and axisymmetric elements with quadratic completeness in the physical space

In this paper, four‐node incompatible elements with quadratic completeness in the physical space are developed for plane and axisymmetric problems. Various revision techniques of the incompatible strain matrix or shape function are proposed to guarantee the incompatible elements to pass the constant stress patch test. In contrast with other elements in the same level, the present one gives reasonable stress solutions without any stress recovery such as the bilinear extrapolation and least square approximation. Numerical examples are given to investigate the accuracy, sensitivity to mesh distortion and locking in the incompressible calculation of the present method when irregular coarse meshes are used. Copyright © 2004 John Wiley & Sons, Ltd.     

Three‐dimensional analyses of in‐plane and out‐of‐plane crack‐tip constraint characterization for fracture specimens

Three‐dimensional elastic–plastic finite element analyses have been conducted for 21 experimental specimens with different in‐plane and out‐of‐plane constraints in the literature. The distributions of five constraint parameters (namely T‐stress, Q, h, T_z and A_p) along crack fronts (specimen thickness) for the specimens were calculated. The capability and applicability of the parameters for characterizing in‐plane and out‐of‐plane crack‐tip constraints and establishing unified correlation with fracture toughness of a steel were investigated. The results show that the four constraint parameters (T‐stress, Q, h and T_z) based on crack‐tip stress fields are only sensitive to in‐plane or out‐of‐plane constraints. Therefore, the monotonic unified correlation curves with fracture toughness (toughness loci) cannot obtained by using them. The parameter A_p based on crack‐tip equivalent plastic strain is sensitive to both in‐plane and out‐of‐plane constraints, and may effectively characterize both of them. The monotonic unified correlation curves with fracture toughness can be obtained by using A_p. In structural integrity assessments, the correlation curves may be used in the failure assessment diagram (FAD) methodology for incorporating both in‐plane and out‐of‐plane constraint effects in structures for improving accuracy.     

Three‐dimensional analyses of unified characterization parameter of in‐plane and out‐of‐plane creep constraint

Based on extensive three‐dimensional finite element analyses, the unified characterization parameter A_c of in‐plane and out‐of‐plane creep constraint based on crack‐tip equivalent creep strain for three specimen geometries (C(T), SEN(T) and M(T)) were quantified for 316H steel at 550 °C and steady‐state creep. The distributions of the parameter A_c along crack fronts (specimen thickness) were calculated, and its capability and applicability for characterizing a wide range of in‐plane and out‐of‐plane creep constraints in different specimen geometries have been comparatively analysed with the constraint parameters based on crack‐tip stress fields (namely R*, h and T_Z). The results show that the parameter A_c in the centre region of all specimens appears uniform distribution and lower value (higher constraint), and in the region near free surface it shows protuberant distribution and higher value (lower constraint). The parameter A_c can simultaneously and effectively characterize a wide range of in‐plane and out‐of‐plane creep constraints, while the parameters R*, h and T_Z based on crack‐tip stress fields cannot achieve this. The different capabilities of these parameters for characterizing in‐plane and out‐of‐plane creep constraints originate from their underlying theories. The parameter A_c may be useful for accurately characterizing the overall constraint level composed of in‐plane and out‐of‐plane constraints in actual high‐temperature components, and it may be used in creep life assessments for improving accuracy.     

Discrete chirp Fourier transform based analysis of reconstructed interference fields in digital holographic interferometry

In digital holographic interferometry, the information on the measurand is encoded in the phase of the reconstructed interference fields. This letter introduces a new method for the analysis of the reconstructed interference fields using discrete chirp Fourier transform (DCFT). In the proposed method, the interference phase to be estimated is modelled as a piecewise polynomial signal. Each row of the reconstructed interference field is subsequently divided into several segments, and a parametric estimation of the phase using DCFT is performed in each segment. We show that the phase estimated in this manner is accurate and continuous, thereby enabling us to bypass the commonly followed practices of filtering and 2-D phase unwrapping. Simulation and experimental results substantiate the effectiveness of the proposed method.