广义逆特征值方法在动力模型修正中的应用

本文针对土木工程中理论计算的要求和特点,基于逆特征值理论给出了一种适合有限元动力模型修正的广义逆特征值方法,该方法在给出修正解的表达式基础上,要求修正解满足动力模型的力学特征,且仅需要少量试验数据,是一种简单、实用的有限元模型修正方法。     

Modelling Strategies for Property Identification Based on Full‐Field Surface Displacement Data

Abstract: The use of full‐field displacement measurements in mechanical testing provides detailed response information that can be used, in conjunction with modelling and optimisation, for precise material property identification. One limitation of this technique is that the collection of response data and the sectioning of a specimen to reveal the material microstructure are both destructive tests and mutually exclusive, as the displacement measurement occurs only on the exposed surface. Therefore, modelling of an experiment to interpret a full‐field experiment requires assumptions about the structure of the material below the visible surface. This study evaluates the effects of several possible modelling assumptions on the errors in model‐predicted response and on the resulting material property estimates. A 3‐D microstructural model, for which the subsurface grain geometry and orientations are known, provides the basis for comparison of several common modelling assumptions based on the grain geometry and orientations on the visible surface of a specimen.     

Time‐resolved integrated digital image correlation

This paper discusses a method that provides the direct identification of constitutive model parameters by intimately integrating the finite element method (FEM) with digital image correlation (DIC), namely, directly connecting the experimentally obtained images for all time increments to the unknown material parameters. The problem is formulated as a single minimization problem that incorporates all the experimental data. It allows for precise specification of the unknowns, which can be, but are not limited to, the unknown material properties. The tight integration between FEM and DIC enables for identification while providing necessary regularization of the DIC procedure, making the method robust and noise insensitive. Through this approach, the versatility of the FE method is extended to the experimental realm, enhancing the analyses of existing experiments and opening new experimental opportunities. Copyright © 2015 John Wiley & Sons, Ltd.     

静力模型修正的逆特征值方法

本文利用这特征值理论，提出了一种参数型静力模型修正方法．根据特征方程，建立起关于设计参数的非线性方程组，把模型修正问题转化为用Ｎｅｗｔｏｎ法求解非线性方程组的问题．本文给出的数值求解方法具有精度高、收敛性好、计算过程简洁的特点，数值仿真结果表明了该方法有很好的效果．     

A Dissipation Gap Method for full‐field measurement‐based identification of elasto‐plastic material parameters

Using enriched data such as displacement fields obtained from digital image correlation is a pathway to the local identification of material parameters. Up to now, most of the identification techniques for nonlinear models are based on Finite Element Updating Methods. This article explains how an appropriate use of the Dissipation Gap Method can help in this context and be an interesting alternative to these classical techniques. The Dissipation Gap Methods rely on the concept of error in dissipation that has been used mainly for the verification of finite element simulations. We provide here an original application of these founding developments to the identification of material parameters for nonlinear behaviors. The proposed technique and especially the main technical keypoint of building the admissible fields are described in detail. The approach is then illustrated through the identification of heterogeneous isotropic elasto‐plastic properties. The basic numerical features highlighted through these simple examples demonstrate this approach to be a promising tool for nonlinear identification.Copyright © 2012 John Wiley & Sons, Ltd.     

数字图像相关方法辅助的IM7/8552碳纤维/环氧树脂复合材料单向带层合板沿厚度方向非线性本构参数识别

提出了采用数字图像相关(DIC)方法和有限元模型修正(FEMU)技术相结合,通过短梁剪切(SBS)试验获得碳纤维增强环氧树脂(IM7/8552)正交各向异性复合材料单向带层合板沿厚度方向压缩本构关系参数的试验方法.该方法根据假设材料初始本构,采用3D有限元模型(FEM)计算获得主平面压头下方沿厚度方向的应力和应变分布,...     

数字图像技术在航空铝合金形变测量中的应用

利用DIC(Digital image correlation)非接触全场应变测量系统分析2024铝合金板材静态拉伸应变场。对散斑质量参数、图像采集系统参数进行正交试验优化。优化结果表明,影响散斑质量的主次因素及最优结果分别为:散斑半径0.02in,散斑密度50%,散斑分布随机性69%;影响图像采集系统的主次因素及最优结果分别为:子集大小59个像素,步长值12个像素,相机间的角度20~25°,光圈值5.6~8。采用该优化参数测量无孔及不同开孔尺寸铝合金板材静态拉伸应变场。首先,对无孔试样裂纹两侧取点,研究裂纹扩展趋势,判定裂纹源及相应载荷。其次,研究长短轴之比及开孔面积对力学性能的影响,并沿孔径方向取点,分析局部应变情况。研究表明,越靠近开孔位置,应变越集中。减小开孔面积,降低开孔的长短轴之比,可以有效降低试样的应变集中系数,延长使用寿命。最后,对比分析非接触测量方法、引伸计法及Patran建模仿真方法试验结果。     

A Multigrid PGD‐based Algorithm for Volumetric Displacement Fields Measurements

The use of a finite elements‐based Digital Volume Correlation (FE‐DVC) leads to lower measurement uncertainties in comparison to subset‐based approaches. However, the associated computing time may become prohibitive when dealing with high‐resolution measurements. To overcome this limitation, a Proper Generalised Decomposition solver was recently applied to 2D digital image correlation. In this paper, this method is extended to measure volumetric displacements from 3D digital images. In addition, a multigrid Proper Generalised Decomposition algorithm is developed, which allows to use different discretisations in each term of the decomposition. Associated to a coarse graining of the digital images, this allows to avoid local minima, especially in presence of large displacements. Synthetic and practical cases are analysed with the present approach, and measurement uncertainties are compared with standard FE‐DVC. Results show that such an approach reduces the computational cost (when compared to FE‐DVC) whilst maintaining lower measurement uncertainties than standard subset‐based DVC.     

Application of High Magnification Digital Image Correlation Technique to Micromechanical Strain Analysis

Abstract: This paper describes an experimental apparatus and its application for the full‐field measurement of heterogeneous strains at high magnifications. The apparatus consists of an image acquisition and analysis system, an optical microscope and a stable tensile stage. Magnified images of the specimen surface are acquired and analysed using the digital image correlation (DIC) method. The response of the heterogeneous microstructure of a nodular cast iron is investigated during a tensile test. Strains obtained by using the DIC method and averaged over the observation window correlate with strain measurements simultaneously obtained by using an extensometer. The strain maps of DIC reveal the heterogeneous development of plasticity in the nodular cast iron microstructure. The apparatus has the potential to investigate material behaviour at the microscopic scale.     

用有限元分析和DICM确定纸浆模塑材料弹性常数的逆问题

用有限元法分析纸浆模塑包装结构,需要事先确定纸浆模塑材料的弹性常数.基于纸浆模塑薄壁圆锥筒的压缩试验,讨论了可以利用有限元分析和数字相关测量方法(DICM)来识别纸浆模塑材料弹性常数的逆问题.     

一种动力模型的局部修改方法

本文基于矩阵反问题理论，给出了一种动力学有限元模型的修正方法，这种方法的表达式简洁。考虑到模型误差主要产生于结构的某些特殊部位，因此有限元模型中的误差可以认为是局部性的。为了减少修正时对模型正确部分的影响和减少不必要的计算量，本文只对刚度或质量矩阵的局部加以修正。首先将所要修改的部分重新组成一个矩阵，利用特征方程，建立一个待修正的有限元模型，然后应用本文给出的方法进行修正。本文方法得到数值算例的证     

3D Residual Stress Field in Arteries: Novel Inverse Method Based on Optical Full‐field Measurements

Abstract: Arterial tissue consists of multiple structurally important constituents that have individual material properties and associated stress‐free configurations that evolve over time. This gives rise to residual stresses contributing to the homoeostatic state of stress in vivo as well as adaptations to perturbed loads, disease or injury. The existence of residual stresses in an intact but load‐free excised arterial segment suggests compressive and tensile stresses, respectively, in the inner and outer walls. Accordingly, an artery ring springs open into a sector after a radial cut. The measurement of the opening angle is commonly used to deduce the residual stresses, which are the stresses required to close back the ring. The opening angle method provides an average estimate of circumferential residual stresses but it gives no information on local distributions through the thickness and along the axial direction. To address this lack, a new method is proposed in this article to derive maps of residual stresses using an approach based on the contour method. A piece of freshly excised tissue is carefully cut into the specimen, and the local distribution of residual strains and stresses is determined from whole‐body digital image correlation measurements using an inverse approach based on a finite element model.     

An approach to calculate the J‐integral by digital image correlation displacement field measurement

This paper presents a combined experimental‐numerical technique for the calculation of the J‐integral as an area integral in cracked specimens. The proposed technique is based on full‐field measurement using digital image correlation (DIC) and the finite element method. The J‐integral is probably the most generalised and widely used parameter to quantify the fracture behaviour of both elastic and elastoplastic materials. The proposed technique has the advantage that it does not require crack length measurements nor is it limited to elastic fracture mechanics, provided that only small scale yielding is present. Evaluated are three test geometries; compact tension, three‐point bend and the double torsion beam. Possible errors and their magnitude and the limitations of the method are considered.     

Global 2D digital image correlation for motion estimation in a finite element framework: a variational formulation and a regularized,pyramidal, multi‐grid implementation

In this study, the inverse problem of reconstructing the in‐plane (2D) displacements of a monitored surface through a sequence of two‐dimensional digital images, severely ill‐posed in Hadamard's sense, is deeply investigated. A novel variational formulation is presented for the continuum 2D digital image correlation problem, and critical issues such as semi‐coercivity and solution multiplicity are discussed by functional analysis tools. In the framework of a Galerkin, finite element discretization of the displacement field, a robust implementation for 2D digital image correlation is outlined, aiming to attenuate the spurious oscillations which corrupt the deformation scenario, especially when very fine meshes are adopted. Recourse is made to a hierarchical family of grids linked by suitable restriction and prolongation operators and defined over an image pyramid. Multi‐grid cycles are performed ascending and descending along the pyramid, with only one Newton iteration per level irrespective of the tolerance satisfaction, as if the problem were linear. At each level, the conventional least‐square matching functional is herein enriched by a Tychonoff regularization provision, preserving the solution against an unstable response. The algorithm is assessed on the basis of both synthetic and truly experimental image pairs. Copyright © 2013 John Wiley & Sons, Ltd.     

A finite element formulation to identify damage fields: the equilibrium gap method

It is proposed to determine damage parameters in two dimensions (surface of a material) or three dimensions (in the bulk of a solid) by using full‐field displacement measurements. A finite‐element approach is developed to evaluate piece‐wise constant elastic parameters modeled by an isotropic damage variable. Two sets of examples are discussed. The first series deals with mechanical fields obtained by finite element simulations to assess the performance of the approach. The second series is concerned with displacement measurements performed during a biaxial test on a composite material. Copyright © 2004 John Wiley & Sons, Ltd.     

Investigation of the Uncertainty of DIC Under Heterogeneous Strain States with Numerical Tests

Abstract: In this research, numerical 2D digital image correlation (DIC) tests are carried out to assess the uncertainty of DIC under heterogeneous strain states. DIC is implemented to measure the deformation of the numerically deformed images with respect to the undeformed counterparts, which are taken from the real tensile specimens. The tensile specimens are made of three materials, that is, steel DC06, steel DX54D+Z and aluminium alloy Al6016 and cut into three different geometries, namely one standard design and two complex designs. The specimens are all painted manually with random speckle patterns. The original images are deformed by imposed displacement fields, which are obtained by simulating uni‐axial tensile tests of the specimens with finite element analysis (FEA). In this way, the errors sourcing from the hardware of the image system are excluded. According to the geometries of the specimens, homogeneous and heterogeneous strain states are achieved by FEA. The optimum mesh sizes of the models are identified to minimise theirs influence on the imposed fields. The impacts of subset sizes, step sizes and strain window sizes are studied for an optimum correlation. Finally, the influence of the strain state is investigated. It is found that the DIC accuracy and precision decrease under highly heterogeneous strain states.     

Model updating of a rotating machine using the self-adaptive differential evolution algorithm

Despite the good accuracy of finite element (FE) models to represent the dynamic behaviour of mechanical systems, practical applications show significant discrepancies between analytical predictions and experimental results, which are mostly due to uncertainties on the geometry configuration, imprecise material parameters and vague boundary conditions. Thereby, different approaches have been proposed to solve the inverse problems associated with the updating of FE models. Among them, the techniques based on minimization processes have shown to be some of the most promising ones. In this paper, a self-adaptive heuristic optimization method, namely the self-adaptive differential evolution (SADE), is evaluated. Differently from the canonical differential evolution (DE) algorithm, the SADE strategy is able to update dynamically the required parameters such as population size, crossover parameter and perturbation rate. This is done by considering a defined convergence rate on the evolution process of the algorithm in order to reduce the number of evaluations of the objective function. For illustration purposes, the SADE strategy is applied to the solution of typical mathematical functions. Additionally, the strategy is equally used to update the FE model of a rotating machine composed by a horizontal flexible shaft, two rigid discs and two unsymmetrical bearings. For comparison purposes, the canonical DE is also used. The results indicate that the SADE algorithm is a recommended technique for dealing with this kind of inverse problem.