Nonlinear analysis of functionally graded laminates considering piezoelectric effect

In this paper, static bending analysis of functionally graded plates with piezoelectric layers has been carried out considering geometrical nonlinearity in different sets of mechanical and electrical loadings. Only the geometrical nonlinearity has been taken into account. The governing equations are obtained using potential energy and Hamilton??s principle. The finite element model is derived based on constitutive equation of piezoelectric material accounting for coupling between elasticity and electric effect by using higher order elements. The present finite element used displacement and electric potential as nodal degrees of freedom. Results are presented for two constituent FGM plate under different mechanical boundary conditions. Numerical results for FGM plate are given in dimensionless graphical forms. Effects of material composition and boundary conditions on nonlinear response of the plate are also studied.     

喷丸残余应力场有限元模拟研究进展

喷丸强化处理工艺可以显著提高金属材料的抗疲劳和抗应力腐蚀等性能,这与喷丸后在金属表面层形成的残余应力场紧密相关,因此对喷丸残余应力的大小及分布进行预测具有重要意义.对近年国内外喷丸残余应力场的有限元模拟进行评述,总结出6种典型的残余应力分析模型,分别是二维轴对称模型、四对称面模型、三对称面模型、双对称面模型、单对称面模...     

Coupled finite element analysis of MIG welding assembly on auto-body high-strength steel panel and door hinge

Automotive doors are assembled to auto-body side-frame through hinges by metal inertial gas arc-welding process. Because of thermal effect, the after-welding geometrical deformation of hinges seriously affects assembly accuracy of door position, causing functional problems such as poor sealing, abnormal sound during closing and opening, as well as large residual stress. In order to solve the complexity involved in auto-body arc-welding assembly process due to dynamic coupling between temperature field and structural field, a multi-field coupling finite element method employing the subroutine of commercial code ANSYS-APDL is proposed, and numerical analysis model is established in quantitative detail. Focusing on the arc-welding assembly process for the auto-body plate (which uses high-strength hot-dip galvanized steel), the promising lightweight material, and door hinge (which uses conventional low-carbon steel), moving heating source and birth–death element method are both adopted in this thermal–structural coupling analysis in order to obtain the complicated transient temperature distribution and mechanical stress behavior during the sequential formulation of arc-welding seam. Experiment is carried out to confirm the validity of this newly developed method, including temperature measurement by thermocouple and residual stress test by X-ray diffraction. The agreement between the experimental and numerical results is satisfactory, indicating the reasonability and feasibility of this method in lightweight auto-body assembly research. It can be concluded that the moving heating source multi-field coupling arc-welding model can strongly support the process parameters optimization for obtaining minimum weld deformation and residual stress.     

Semi-analytical solution of magneto-thermo-elastic stresses for functionally graded variable thickness rotating disks

In this paper, a semi-analytical solution for magneto-thermo-elastic problem in functionally graded (FG) hollow rotating disks with variable thickness placed in uniform magnetic and thermal fields is presented. Stresses and perturbation of magnetic field vector in FG rotating disks are determined using infinitesimal theory of magneto-thermo-elasticity under plane stress conditions. The material properties except Poisson’s ratio are modeled as power-law distribution of volume fraction. The profile of disk thickness is assumed to be a parabolic function of radius. The non-dimensional distribution of temperature, displacement, stresses and perturbation of magnetic field vector throughout radius are shown. Effects of material grading index, geometry of the disk and magnetic field on the stress and displacement fields are investigated. The results of stresses and radial displacements for two different boundary conditions with and without the effect of magnetic field are compared for a FG rotating disk with concave thickness profile. It has been found that imposing a magnetic field significantly decreases tensile circumferential stresses. Therefore the fatigue life of the disk will be significantly improved by applying the magnetic field. Results of this investigation could be applied for optimum design of FG hollow rotating disks with variable thickness.     

换热边界下变物性梯度功能材料板瞬态热应力

用有限元和有限差分法,分析了由ZrO2 和Ti-6Al-4V组成的变物性梯度功能材料板的瞬态热应力问题,检验了方法的正确性,给出了对流换热边界下变物性梯度功能材料板的瞬态热应力场分布,并与不考虑变物性时的结果进行了比较。结果表明：在计算瞬态热应力场分布时,变物性是影响梯度功能材料板瞬态热应力场的最重要因素之一。此外,材料组分的分布形状系数 M、环境介质温度和对流换热系数的变化对变物性梯度功能材料板的瞬态热应力场分布均有明显的影响。此结果为梯度功能材料的设计和应用提供了理论计算依据。     

Modeling and simulation of polymer melts flow in the extrusion process of plastic profile with metal insert

The extrusion technology of plastic profile with metal insert is recently an advanced plastic processing method whose products keeps rising today for their excellent performance. However, the related fundamental research on polymer forming mechanism in the extrusion process of plastic profile with metal insert is lagging behind. With the development of computational fluid dynamics (CFD) theory, numerical method becomes an effective way to investigate such complex material forming problems as in the polymer extrusion process. In the present study, the mathematical model for three-dimensional non-isothermal viscous flow of the polymer melts obeying a Carreau model is developed based on the CFD theory. The Williams–Landel–Ferry equation is employed to involve the temperature dependence of material parameters. A decoupled numerical algorithm based on the penalty finite element method is conducted to predict the rheological behaviors of polymer melts within the complex flow channel. The streamline upwind/Petrov–Galerkin scheme is employed to improve the computational stability for the calculation of temperature field. Based on the theoretical model, the essential flow characteristics of polymer melts in the extrusion process of plastic profile with metal insert is investigated. The distributions of principal field variables like flow velocity, melt temperature, flow stress and pressure drop are predicted. The effects of die structure parameters including the intake angle and the distribution section length upon the melts flow patterns are further discussed. The variations of melt rheological properties versus different processing conditions like the volume flow rate and the metal insert moving velocity are also investigated. Some advice on practical processing operations of the extrusion process of plastic profile with metal insert is accordingly put forward based on the numerical results.     

燃气涡轮转子盘-片系统三维非线性循环应力-应变分析

燃气涡轮转子盘—片系统的几何形状和结构形式比较复杂，在高温、高转速的恶劣条件下工作，准确的应力分析是进行强度计算和疲劳寿命预测的重要前提。使用ANSYS有限元结构分析软件，建立了燃气涡轮盘—片接触系统三维循环对称有限元模型，考虑了叶片材料的各向异性、涡轮盘与叶片榫头之间的接触非线性、材料的弹塑性变形和温度不均匀引起的热应力等情况，数值模拟涡轮盘—叶片组件的受力状态及边界条件，进行三维非线性循环应力—应变分析。     

A semi-analytical approach for the geometrically nonlinear analysis of trapezoidal plates

This paper presents a semi-analytical approach for the geometrically nonlinear analysis of skew and trapezoidal plates subjected to out-of-plane loads. The thin elastic plate theory with nonlinear von Kármán strains is used for the nonlinear large deflection analysis of the plate. The solution of the governing nonlinear partial differential equations with variable coefficients is reduced to an iterative solution of nonlinear ordinary differential equations using the multi-term extended Kantorovich method. The geometry of the trapezoidal plate is mapped into a rectangular computational domain. Parallelogram (skew) plates are considered as a particular case of the general trapezoidal ones. The capabilities and convergence of the method are numerically examined through comparison with other semi-analytical and numerical methods and with finite element analyses. The applicability of the approach to the nonlinear large deflection analysis of skew and trapezoidal plates is demonstrated through various numerical examples. The numerical study focuses on combinations of geometry, loading and boundary conditions that are beyond the applicability of other semi-analytical methods.     

Numerical and experimental studies on temperature and distortion patterns in butt-welded plates

A computationally efficient solution is adopted for 3D transient analyses of both thermal and structural responses of steel plates to single-pass gas tungsten arc welding. Considering the temperature-varying thermal and mechanical properties of the steel material, the temperature distribution in the plate calculated by the numerical approach turned out to have a good agreement with the experimental results of butt welding tests. The structural response of welded plates including the residual stress and deformation has also been studied. The numerical results generally agree well with the experimental measurements. The effect of the Element Birth–Death technique has been discussed in detail, considering the double ellipsoidal moving heat source. The magnitude of peak temperature in the plates is found 8.76 % higher when taking into account the Element Birth-Death effect. The effects of finite element mesh size and convection coefficient on the simulation result have been discussed. The convection coefficient has a very low effect on the maximum temperature but is critical to the temperature gradient in the cooling stage.     

非球面玻璃透镜模压成形有限元分析

针对玻璃与模具的材料属性、随时间变化的黏弹性和结构松弛原理,基于非线性有限元软件MSC.Marc建立了非球面玻璃透镜的超精密模压成形的有限元数值仿真分析模型,对比分析了不同工艺参数（模压温度、模压速度、摩擦因数等）对成形透镜残余应力与轮廓偏移量的影响。研究结果表明：随着模压温度的升高、模压速度和摩擦因数的减小,残余应力相应减小;随着模压温度和退火速度的增大,以及模压速度的减小,轮廓偏移量相应变小。     

基于MATLAB、UG的泛函通用型线涡旋盘有限元建模及分析

利用基于泛函的通用涡旋型线的几何理论,研究涡旋型线方程,改进了传统式生成型线方法的局限性,为涡旋盘的加工和制造提供了理论价值和参考意义。通过MATLAB软件的编程功能,生成数学模型的关键点。在UG环境下生成涡旋型线,使用UG中的拉伸命令,完成涡旋盘的精确三维实体造型,然后将生成的三维实体转换到高级仿真环境下,通过定义材料属性、指派材料、物理属性、划分网格,建立有限元模型,最后建立边界约束条件并加载作用载荷,进行有限元分析。     

平面非定常温度场的有限元素法

用有限元素法求解非定常温度场,如大家所知,在空间量纲方面,应用有限元素离散;而在时间量纲方面,通常仍采用有限差分离散。文中分析和比较了时间量纲方面用克兰克-尼可松（Crank-Nicholson）和伽辽金（Galerkin）离散的两种不同计算格式。着重讨论了初始短时精度,指出两种格式的适用条件,并以实例作了验证。对非线性边界条件下问题的求解,建议采用一种能以较快速度,经少数几次迭代就容易达到一定精度的“等正切”逐次逼近法最后还讨论了计算时步长的选择,如何以最少的机器时间求得精确数值解等问题。     

Shakedown Criterion Employing Actual Residual Stress Field and Its Application in Numerical Shakedown Analysis

Construction of the static admissible residual stress field and searching the optimal field are key tasks in the shakedown analysis methods applying the static theorem. These methods always meet dimension obstacles when dealing with complex problems. In this paper, a novel shakedown criterion is proposed employing actual residual stress field based on the static shakedown theorem. The actual residual stress field used here is produced under a specified load path, which is a sequence of proportional loading and unloading from zero to all the vertices of the given load domain. This ensures that the shakedown behavior in the whole load domain can be determined based on the theorem proposed by K?nig. The shakedown criterion is then implemented in numerical shakedown analysis. The actual residual stress fields are calculated by incremental finite element elastic-plastic analysis technique for finite deformation under the specified load path with different load levels. The shakedown behavior and the shakedown limit load are determined according to the proposed criterion. The validation of the criterion is performed by a benchmark shakedown example, which is a square plate with a central hole under biaxial loading. The results are consistent with existing results in the literatures and are validated by full cyclic elastic-plastic finite element analysis. The numerical shakedown analysis applying the proposed criterion avoids processing dimension obstacles and performing full cyclic elastic-plastic analysis under arbitrary load paths which should be accounted for appearing. The effect of material model and geometric changes on shakedown behavior can be considered conveniently.     

A novel approach for in-plane/out-of-plane frequency analysis of functionally graded circular/annular plates

An exact closed-form frequency equation is presented for free vibration analysis of circular and annular moderately thick FG plates based on the Mindlin's first-order shear deformation plate theory. The edges of plate may be restrained by different combinations of free, soft simply supported, hard simply supported or clamped boundary conditions. The material properties change continuously through the thickness of the plate, which can vary according to a power-law distribution of the volume fraction of the constituents, whereas Poisson's ratio is set to be constant. The equilibrium equations which govern the dynamic stability of plate and its natural boundary conditions are derived by the Hamilton's principle. Several comparison studies with analytical and numerical techniques reported in literature and the finite element analysis are carried out to establish the high accuracy and superiority of the presented method. Also, these comparisons prove the numerical accuracy of solutions to calculate the in-plane and out-of-plane modes. The influences of the material property, graded index, thickness to outer radius ratios and boundary conditions on the in-plane and out-of-plane frequency parameters are also studied for different functionally graded circular and annular plates.     

纳米结构WC/12Co涂层精密平面磨削表面残余应力有限元模拟与试验

对金刚石砂轮精密平面磨削纳米结构WC/12Co涂层的磨削表面残余应力进行有限元模拟,忽略相变影响,基于ANSYS平台,利用ANSYS参数设计语言完成建立模型、给定材料属性、划分单元、加载和求解整个过程。对纳米结构WC/12Co涂层表面磨削残余应力进行试验研究,通过改变磨削条件得到不同磨削条件下残余应力的变化规律。将试验结果与相同磨削条件下的有限元模拟结果进行对比,发现试验结果与有限元模拟结果是一致的,证明了有限元模型的正确性。     

Experimental verification of rate-dependent elastoplastic analogy friction model and its application to FE analysis

When two solid bodies in contact slide slowly past each other without lubrication, an intermittent vibration phenomenon might be observed. Such rate-dependent frictional behaviors are referred to as stick–slip motions, and such motions can impair the stability of machines and structures. The aim of this study is to propose a numerical approach for analyzing stick–slip motion; the approach is based on the finite element method implemented using a rate-dependent friction model. First, we demonstrate the capability of the rate-dependent friction model by comparing its results with experimental results obtained under various material and dynamic conditions. Then, a simple finite element analysis of rate-dependent frictional sliding behavior, including stick–slip motion, is carried out to examine the effect of the material and geometric properties and boundary conditions on the numerical results. The present numerical approach can consider not only the properties of friction and materials but also variations in boundary conditions.     

机车制动盘三维瞬态温度场与应力场仿真

基于三维循环对称有限元模型,提出了机车制动盘制动过程中温度场和应力场的计算方法。讨论了边界条件和各种相关参数的确定方法,尤其是机车整个制动过程中制动盘换热系数的计算方法。同时运用有限元软件ANSYS7进行了制动盘及相关部件三维瞬态温度场和应力场的仿真与分析。仿真结果表明:在制动开始阶段,制动盘迅速升温,高温区集中在制动盘摩擦面表层,最高温度达220℃;制动过程结束后,整个制动盘有一段较长时间的降温过程;制动盘系统各部分的最大热应力-时间曲线变化规律不一致,但均满足材料强度要求。仿真结果与实验数据相符,证明了该三维有限元模型及其温度场计算方法的正确性。     

Numerical simulation of ultrasonic minimum reflection for residual stress evaluation in 2D case

A number of interesting phenomena at fluid-solid interfaces can be observed when the incident angle approaches the Rayleigh angle, including Schoch displacement and leaky Rayleigh waves. Besides the experimental and theoretical research on these problems, numerical tools have been more and more widely used for these complex problems. Based on previous experimental and numerical researches, a 2D finite element model has been built to reproduce the Schoch effects. With the same model, the minimum reflection profile is investigated for the feasibility of material characterization, especially for residual stress evaluation. Residual stress is one of the important properties for structures, and its measurement is a popular research topic in nondestructive evaluation. However, it is not possible to put the residual stress into the numerical model directly. According to the relation of residual stress with mechanical properties, the material damping and wave speed have been alternatively adopted in this work. The influence of minimum reflection profile by residual stress has been shown by the change of wave speed and damping factor. Simulation results show that the minimum reflection profile is a potential method for residual stress evaluation.     

铝合金平板钨极氩弧焊数值模拟与残余应力预测

利用ABAQUS有限元软件对铝合金平板钨极氩弧焊(TIG)焊接过程进行了数值模拟.首先应用移动的椭圆高斯分布表面热源作为输入热源,对TIG焊过程中的焊件温度场及应力场进行了模拟计算.高度不均匀的焊接温度场,导致构件中产生较大的残余应力与变形.最后,对冷却后的平板残余应力进行了预测,并将有限元计算结果与残余应力的实测结果进行了对比,两者吻合很好.     

微电子机械系统中典型构件的力电耦合分析及其应用研究

力电耦合是大多数微电子机械系统（尤其是以静电驱动的微机械）的重要特征。文中采用有限元（FEM）结合边界元（BEM）的方法来混合求解MEMS中的力电耦合问题,利用自行研制的程序给出了几种典型构件（平行板、悬臂梁和固支梁）的分析结果,并同其他商业软件（ANSYS和Intelisuite）的计算结果进行了比较。同时,还将这种分析方法应用到微继电器的设计和MEMS构件残余应力的检测中。