A semi-analytical method with a system of decoupled ordinary differential equations for three-dimensional elastostatic problems

In this paper, a new semi-analytical method is presented for modeling of three-dimensional (3D) elastostatic problems. For this purpose, the domain boundary of the problem is discretized by specific subparametric elements, in which higher-order Chebyshev mapping functions as well as special shape functions are used. For the shape functions, the property of Kronecker Delta is satisfied for displacement function and its derivatives, simultaneously. Furthermore, the first derivatives of shape functions are assigned to zero at any given node. Employing the weighted residual method and implementing Clenshaw–Curtis quadrature, coefficient matrices of equations’ system are converted into diagonal ones, which results in a set of decoupled ordinary differential equations for solving the whole system. In other words, the governing differential equation for each degree of freedom (DOF) becomes independent from other DOFs of the domain. To evaluate the efficiency and accuracy of the proposed method, which is called Decoupled Scaled Boundary Finite Element Method (DSBFEM), four benchmark problems of 3D elastostatics are examined using a few numbers of DOFs. The numerical results of the DSBFEM present very good agreement with the results of available analytical solutions.     

A macro-element to simulate 3D soil–structure interaction considering plasticity and uplift

In structural engineering, soil–structure interaction (SSI) is an important phenomenon that has to be taken into account. This paper presents a 3D non-linear interface element able to compute SSI based on the “macro-element” concept. The particularity of the macro-element lies in the fact that the movement of the foundation is entirely described by a system of generalised variables (forces and displacements) defined at the foundation centre. The non-linear behaviour of the soil and the uplift mechanism of the foundation are reproduced using the plasticity theory. The failure surface is defined using an adequate overturning mechanism. Coupling of the different mechanisms is straight forward following the theory of multi-mechanisms. The macro-element is able to simulate the 3D behaviour of a rigid shallow foundation of circular, rectangular or strip shape, submitted to cyclic loadings. It is implemented into FEDEASLab, a finite element MATLAB toolbox. Comparisons with experimental results under cyclic loadings show the performance of the approach.     

Follow-up of a panel restoration procedure through image correlation and finite element modeling

Residual stress estimation is an important question for structural integrity. Since residual stresses are self-balanced stress fields, a classical way to obtain information on them is to remove a part of the structure, and observe the structure displacement field arising from the stress redistribution. The hole-drilling method is such an approach. In some cases, as for the present one concerning a painted panel of cultural heritage, the hole-drilling method is not suited (a structure with a complex geometry, few tests allowed) but one can take advantage of structural modifications if they are monitored (here, a restoration act). We therefore describe in this article a model updating approach, focusing on the residual stress estimation and not on the material parameter identification.This study couples an optical non-invasive shape measurement (digital image correlation, using a projected speckle pattern on the painted panel, with luminance compensation) and a numerical approach (3D finite elements) for the model updating. The 3D stereo-correlation is used to measure a partial displacement field between three different states of the structure (at three different times of the restoration act). The numerical part concerns stress evaluation, once the model and the experiments are compared using a geometric mapping and a spatial projection of discrete fields. Using modeling and identification, the simulation is used to obtain the residual stresses in the panel, before and after the restoration.     

Full-Field Surface 3D Shape and Displacement Measurements Using an Unfocused Plenoptic Camera

Full-field surface 3D shape and displacement measurements using a single commercial unfocused plenoptic camera (Lytro Illum) are reported in this work. Before measurements, the unfocused plenoptic camera is calibrated with two consecutive steps, including lateral calibration and depth calibration. Each raw image of a checkerboard pattern recorded by Lytro Illum is first extracted to an array of sub-aperture images (SAIs), and the center sub-aperture images (CSAIs) at diverse poses are used for lateral calibration to determine intrinsic and extrinsic parameters. The parallax maps between the CSAI and the remaining SAIs at each pose are then determined for depth parameters estimation using depth calibration. Furthermore, a newly developed physical-based depth distortion model is established to correct the serious distortion of the depth field. To realize shape and deformation measurements, the raw images of a test sample with speckle patterns premade on its surface are captured by Lytro Illum and extracted to arrays of SAIs. The parallax maps between the CSAI and the target SAIs are obtained using subset-based digital image correlation. Based on the pre-computed intrinsic and depth parameters and the disparity map, the full-field surface 3D shape and displacement of a test object are finally determined. The effectiveness and accuracy of the proposed approach are evaluated by a set of experiments involving the shape reconstruction of a cylinder, in-plane and out-of-plane displacement measurements of a flat plate and 3D full-field displacement measurements of a cantilever beam. The preliminary results indicate that the proposed method is expected to become a novel approach for full-field surface 3D shape and displacement measurements.     

Measuring Multiple Residual-Stress Components using the Contour Method and Multiple Cuts

The conventional contour method determines one component of residual stress over the cross section of a part. The part is cut into two, the contour (topographic shape) of the exposed surface is measured, and Bueckner’s superposition principle is analytically applied to calculate stresses. In this paper, the contour method is extended to the measurement of multiple residual-stress components by making multiple cuts with subsequent applications of superposition. The theory and limitations are described. The theory is experimentally tested on a 316L stainless steel disk with residual stresses induced by plastically indenting the central portion of the disk. The multiple-cut contour method results agree very well with independent measurements using neutron diffraction and with a computational, finite-element model of the indentation process.     

大型汽轮发电机组短路时轴系扭振动力响应计算与分析

大型汽轮发电机组在短路时的轴系扭振动力响应，对于机组的安全可靠运行甚为关键。本文以国产某２００ＭＷ机组为例，建立了轴系的连续质量计算模型，利用传递矩阵法求得其扭振固有频率及主振型，用振型查加法计算轴系在两相短路情况下的动力响应，计算中考虑了叶片叶轮系统与轴系扭振的耦合作用。本文对计算结果进行了分析，讨论了该机组的轴系扭振安全性，为机组的安全运行提供了理论依据。     

A three-dimensional model of the thermomechanical behavior of shape memory alloys

A new macro-scale model of shape memory alloys is developed within the framework of generalized standard materials with internal constraints [Moumni, Z., 1995. Sur la modélisation du changement de phase à l’état solide. Ph.D. Thesis, École Nationale Supérieure des Ponts et Chaussées]. It is shown that the introduction of two state variables: the martensite volume fraction and the martensite orientation strain tensor, is sufficient to account for several effects exhibited by SMAs subject to thermomechanical loading, namely: self-accommodation, orientation and reorientation or martensite, as well as superelasticity and one-way shape memory. These phenomena are simulated using the same set of constitutive equations and evolution laws. A simple procedure for identifying the parameters of the model is described in detail and a validation against experimental data is conducted. The model is then used to analyze a 3D SMA structure representing a superelastic stent. Cyclic loading and other pertaining phenomena like training and two-way shape memory are considered in the second part of this paper.     

Evaluation of finite element based analysis of 3D multicrystalline aggregates plasticity: Application to crystal plasticity model identification and the study of stress and strain fields near grain boundaries

Plastic heterogeneities of hexagonal close-packed (HCP) materials are numerically investigated at the grain level. Intensive use of parallel Finite Elements computations enables us to study micro-plasticity of realistic 3D multicrystalline aggregates, including, macroscopic mechanical responses but also average responses in each grain and particularly local stress and strain fields. This paper focuses on three applications of this simulation method. The first part of this paper is devoted to a fine analysis of micro-plasticity of HCP materials. Intergranular but also intragranular stress and strain heterogeneities are described and micro-plasticity patterns are displayed throughout the 3D microstructures. A special attention is paid to the sensitivity of simulations with respect to the mesh discretization, the element interpolation and the geometrical representation of grain boundaries, in terms of macroscopic and local responses. Later, a simplified homogenization method is evaluated, regarding results of the first part. Afterwards, this method is applied with a zirconium alloy to identify a set of coefficients for a single crystal plasticity model. Finally, in order to provide critical information for intergranular damage phenomena (reported in literature for zirconium alloys), the third part provides a statistical analysis of over-stresses at grain boundaries.     

On the modeling of equilibrium twin interfaces in a single-crystalline magnetic shape-memory alloy sample—III: Magneto-mechanical behaviors

This is the concluding part III of a series of papers. The aim of the current paper is to simulate and analyze the procedure of variant reorientation in a magnetic shape-memory alloy (MSMA) sample and to predict the response of the sample subject to various loading conditions. The sample to be considered in this paper has a 3D cuboid shape and is subject to typical magneto-mechanical loading conditions. Variant reorientation in the sample is realized through twin interface movements. To investigate the key features of twin interface movements, the properties of configurational forces on the twin interfaces are analyzed. For both the stress-assisted MFIS tests and the field-assisted quasi-elasticity tests, the magneto-mechanical behavior of the MSMA sample during the whole loading procedure is simulated by using the finite element method. The influence of the initial variant distribution in the sample on its global response is discussed. The obtained numerical results are compared with the experimental results. It can be seen that the model predictions can fit the experimental results both at a qualitative as well as at a quantitative level.     

A finite point method for adaptive three‐dimensional compressible flow calculations

The finite point method (FPM) is a meshless technique, which is based on both, a weighted least‐squares numerical approximation on local clouds of points and a collocation technique which allows obtaining the discrete system of equations. The research work we present is part of a broader investigation into the capabilities of the FPM to deal with 3D applications concerning real compressible fluid flow problems. In the first part of this work, the upwind‐biased scheme employed for solving the flow equations is described. Secondly, with the aim of exploiting the meshless capabilities, an h‐adaptive methodology for 2D and 3D compressible flow calculations is developed. This adaptive technique applies a solution‐based indicator in order to identify local clouds where new points should be inserted in or existing points could be safely removed from the computational domain. The flow solver and the adaptive procedure have been evaluated and the results are encouraging. Several numerical examples are provided in order to illustrate the good performance of the numerical methods presented. Copyright © 2008 John Wiley & Sons, Ltd.     

Color Stereo-Digital Image Correlation Method Using a Single 3CCD Color Camera

This paper presents a novel color stereo-digital image correlation (stereo-DIC) method using a single 3CCD color camera for full-field shape, motion, and deformation measurements without any sacrifice of the camera sensor spatial resolution. With the aid of a specially designed color separation device using a beam splitter and two optical bandpass filters, images of blue and red colors are simultaneously recorded by the 3CCD camera from two different optical paths. The blue and red channel sub-images extracted from the recorded color images can be analyzed using the regular stereo-DIC algorithm to obtain the full-field three dimensional (3D) information of a test object surface. The effectiveness and accuracy of the proposed technique are demonstrated by a series of real shape, in-plane and out-of-plane translation, and 3D deformation tests.     

Detection of a slant crack in a rotor bearing system during shut-down

Abstract

The transient response of a slant-cracked rotor system during shut-down has been analyzed while it is decelerating through the critical speed. Vibration response has been simulated by using finite element method (FEM) for flexural vibrations. An unbalance force and a harmonically-varying torque is applied on the rotor system. Subharmonic frequency components at an interval frequency corresponding to torsional frequency were found in the frequency domain (Fast Fourier Transform (FFT) plot). These peaks are centered on the critical speed of the rotor system when a slant crack is present and can be used to detect the crack. The fundamental mode shapes of the rotor bearing systems are wavelet transformed to identify the crack location. A peak is observed at the crack location in the spatial variation of the wavelet-transformed fundamental mode shape. A few suggestions for the detection of slant cracks in the rotor during shut-down are described.     

Three-dimensional point cloud registration by matching surface features with relaxation labeling method

Automated approaches for the conversion of multiple overlapped three-dimensional (3D) point clouds into an integrated surface shape measurement in the form of a complete polygon surface are important in the general field of reverse engineering. Traditionally, the conversion process is achieved in a semi-automated manner that requires extensive user interaction. In this work, automated methods for point set registration are developed and experimentally validated using polygon surface reconstruction to represent raw, 3D point clouds obtained from non-contacting measurement systems. Using local differential properties extracted from the polygon surface representation for a measurement data set, a robust sculpture surface feature-matching method is described for automatically obtaining the initial orientation and mismatch estimates for each overlapped data set. Using both simulated and measured experimental data to quantify the performance of the method, it is shown that differential local surface features are appropriate metrics for identifying common features and initializing the relative positions of individual point clouds, thereby providing the basis for automating the registration and integration processes while improving the speed of the surface distance minimization method developed for the initial registration process.     

The effects of corrugation and wing planform on the aerodynamic force production of sweeping model insect wings

The effects of corrugation and wing planform (shape and aspect ratio) on the aerodynamic force production of model insect wings in sweeping (rotating after an initial start) motion at Reynolds number 200 and 3500 at angle of attack 40° are investigated, using the method of computational fluid dynamics. A representative wing corrugation is considered. Wing-shape and aspect ratio (AR) of ten representative insect wings are considered; they are the wings of fruit fly, cranefly, dronefly, hoverfly, ladybird, bumblebee, honeybee, lacewing (forewing), hawkmoth and dragonfly (forewing), respectively (AR of these wings varies greatly, from 2.84 to 5.45). The following facts are shown. (1) The corrugated and flat-plate wings produce approximately the same aerodynamic forces. This is because for a sweeping wing at large angle of attack, the length scale of the corrugation is much smaller than the size of the separated flow region or the size of the leading edge vortex (LEV). (2) The variation in wing shape can have considerable effects on the aerodynamic force; but it has only minor effects on the force coefficients when the velocity at r ₂ (the radius of the second moment of wing area) is used as the reference velocity; i.e. the force coefficients are almost unaffected by the variation in wing shape. (3) The effects of AR are remarkably small: when AR increases from 2.8 to 5.5, the force coefficients vary only slightly; flowfield results show that when AR is relatively large, the part of the LEV on the outer part of the wings sheds during the sweeping motion. As AR is increased, on one hand, the force coefficients will be increased due to the reduction of 3-dimensional flow effects; on the other hand, they will be decreased due to the shedding of part of the LEV; these two effects approximately cancel each other, resulting in only minor change of the force coefficients. The project supported by the National Natural Science Foundation of China (10232010 and 10472008) and Ph. D. Student Foundation of Chinese Ministry of Education (20030006022) The English text was polished by Keren Wang.     

A hybrid analytical–numerical solution for 3D notched plates

This study used a hybrid analytical and numerical method to analyze three-dimensional (3D) elastic bodies with sharp-V notches. The proposed method separates the 3D equilibrium equation into primary and shadow parts, where the solution of the primary part is the analytical solution under the generalized plane-strain theory, and the shadow part is solved numerically using a weak form based on the finite element theory. A least-squares method is then used to find the multiplication factors of these primary and shadow modes using 3D finite element results. Numerical simulations indicate that the proposed method can accurately simulate the singularities near a sharp V-notch. The major advantage of this method is that a 3D whole displacement field with the singular effect based on the theoretical solution near the notch can be obtained for anisotropic materials under arbitrary loads.     

HC轧机辊间接触与辊系变形的Taylor级数多极边界元数学规划解析

分析HC轧机辊间接触分布和辊系弹性变形对于改善辊间压力分布状态,减少轧故褂檬倜案纳瓢逍畏浅Ｖ匾?醯捎诩扑懔亢艽?使用传统数值方法(有限元法或边界元法)分析辊间接触和辊系变形是非常困难的.本文描述了一种基于点-面接触模型的三维弹性接触Taylor级数多极边界元法,给出了数学规划解析方法,适合大规模弹性接触问题的求解....     

On the modeling of equilibrium twin interfaces in a single-crystalline magnetic shape memory alloy sample. II: numerical algorithm

This is part II of this series of papers. The aim of the current paper was to solve the governing PDE system derived in part I numerically, such that the procedure of variant reorientation in a magnetic shape memory alloy (MSMA) sample can be simulated. The sample to be considered in this paper has a 3D cuboid shape and is subject to typical magnetic and mechanical loading conditions. To investigate the demagnetization effect on the sample’s response, the surrounding space of the sample is taken into account. By considering the different properties of the independent variables, an iterative numerical algorithm is proposed to solve the governing system. The related mathematical formulas and some techniques facilitating the numerical calculations are introduced. Based on the results of numerical simulations, the distributions of some important physical quantities (e.g., magnetization, demagnetization field, and mechanical stress) in the sample can be determined. Furthermore, the properties of configurational force on the twin interfaces are investigated. By virtue of the twin interface movement criteria derived in part I, the whole procedure of magnetic field- or stress-induced variant reorientations in the MSMA sample can be properly simulated.     

A 3D direct coupling method for steady ship hydroelastic analysis

Asides from the influence of incoming waves, ships can experience steady motions, such as rigid-body sinkage and trim motions, and flexible-body vertical bending motions, due to a constant forward speed even under calm water conditions. In this paper, a novel approach to analyze steady-ship hydroelasticity, particularly for the steady-ship motions and surrounding steady-wave disturbances, is proposed using a three-dimensional (3D) direct coupling method, based on a higher-order boundary element method (HOBEM) and a higher-order shell finite element method (FEM). Within the linearized framework, a solution method is proposed based on a two-step procedure, using two types of Neumann–Kelvin (NK) linear flow models for the fluid part and a virtual work equilibrium equation for the structural part. The first step is to compute a mean position wave-resistance problem using the modified NK equation, the second step is to solve a perturbed position wave-resistance problem, by employing a classical NK model and a virtual work equation based on the first step’s solution. Detailed mathematical formulation and numerical procedures are described, and a few numerical results are illustrated. These include both rigid and flexible steady-ship motions, Von-Mises stress distributions, and wave-resistance coefficients for Froude numbers ranging from 0.15 to 0.5. Furthermore, the numerical results obtained using the present direct coupling method and a modal-based one are compared.     

A continuous shape sensitivity equation method for unsteady laminar flows

This paper presents the application of a general shape sensitivity equation method (SEM) to unsteady laminar flows. The formulation accounts for complex parameter dependence and is suitable for a wide range of problems. The flow and sensitivity equations are solved on 3D meshes using a Streamline-Upwind Petrov Galerkin (SUPG) finite element method. In the case of shape parameters, boundary conditions for sensitivities depend on the flow gradient at the boundary. Therefore, an accurate recovery of solution gradients is crucial to the success of shape sensitivity computations. In this work, solution gradients at boundary points are extracted using the Finite Node Displacement (FiND) method on which the finite element discretization is enriched locally via the insertion of nodes close to the boundary points. The normal derivative of the solution is then determined using finite differences. This approach to evaluate shape sensitivity boundary conditions is embedded in the continuous SEM. The methodology is applied to the flow past a cylinder in ground proximity. First, the proposed method is verified on a steady state problem. The computed sensitivity is compared to the actual change in the solution when a small perturbation is imposed to the shape parameter. Then, the study investigates the ability of the SEM to anticipate the unsteady flow response to changes in the ground to cylinder gap. A reduction of the gap causes damping of the vortex shedding while an increase amplifies the unsteadiness.     

打捆机驱动轮系统接触三维有限元分析

应用ANSYS软件对打捆机驱动轮系统进行了三维接触非线性有限元分析，得出了接触应力的分布规律，并将其最大接触应力与应用简化方法进行了比较，两相吻合的结果表明，有限元分析结果可为系统的进一步精确分析提供依据．