A high-order control volume finite element method for 3-D transient heat conduction analysis of multilayer functionally graded materials

Abstract

A new three-dimensional (3-D) control volume finite element method (CV-FEM) has been developed for transient heat conduction in multilayer functionally graded materials (FGMs). A 10-node tetrahedral grid is chosen for spatial discretization and a backward difference scheme is adapted for time discretization. By using quadratic tetrahedral grids, the present CV-FEM offers greater potential for enhanced geometric flexibility and for improved numerical accuracy over the linear CV-FEM. The temperature and material properties are defined at the node. Three different types of material variation (exponential, quadratic and trigonometric) are considered in the analysis. Several test cases are provided to verify the numerical implementation. The results of the test cases are in good agreement with analytical solutions and other numerical simulation results.     

3-D elastic-plastic finite element analysis of interface cracks under mixed mode load

A three-dimensional finite element computation was performed for a throughedge cracked bimaterial steel specimen under mixed mode loadings in which the crack was lying on an interface between an elastic-plastic material and a perfectly rigid substratum. In order to take account of the average effect of microvoid nucleation and growth in the deformation, the modified Gurson's constitutive equation suggested by Tvergaard and Needleman was used. It was found that due to the interaction between the singularity along the crack front and that along the interface on the specimen surface, the distributions of stresses, plastic deformations, J-integral and void volume fraction in a bimaterial specimen were significantly different from those in a homogeneous specimen. Based on the numerical results on the distributions of void volume fraction and J-integral, the locations of fracture initiation in bimaterial and homogeneous specimens under mixed mode loadings are discussed.     

Thermoelastic vibration analysis of functionally graded skew plate using nonlinear finite element method

Numerical investigation of nonlinear free vibration of functionally graded skew (FGS) plate in the thermal environment is presented. The mathematical model is proposed for the first time based on higher order shear deformation theory in conjunction with Green–Lagrange-type geometric nonlinearity for the FGS plate subjected to a thermal load. The material properties are considered to be temperature dependent and are graded along the thickness direction as per simple power law of distribution in terms of volume fraction of the constituent phase. The governing algebraic equations are derived using Hamilton’s principle, and the solutions are obtained using the direct iterative method. The proposed finite element model has discretized into an eight-noded quadratic serendipity elements. To validate the model, the obtained results are compared with the available literature. The influence of volume fraction index, skew angle, temperature change, aspect ratio, side–thickness ratio, and boundary conditions on the linear and nonlinear frequency of skew functionally graded material plate is examined and discussed in detail.     

Compressible heat transfer computations by an adaptive finite element method

This paper presents adaptive finite element computations of laminar jet impingement heat transfer. Variable fluid properties and compressibility effects are considered. A unified formulation of the equations is used to treat the simultaneous presence of three flow regimes: incompressible (ρ=constant), compressible (ρ=ρ(p,T)), and anelastic (ρ=ρ(T)). The error estimator uses a local least squares projection method and accounts for errors in velocity, pressure and temperature. The performance of the methodology is verified by solving a problem possessing a closed form solution. Several applications are then considered. We study two different gases (air and CO₂), different conditions (heated, cooled or constant properties), compressibility and inlet velocity profile effects. Heat transfer is a key element of the study. Results indicate that the methodology can produce grid independent solutions even for derived quantities and in thin boundary layers.     

基于非线性有限元理论的风力发电机组法兰-螺栓连接分析方法研究

以风力发电机组叶片根部法兰-螺栓连接为例,研究了法兰-螺栓连接分析方法。根据风力发电机组法兰-螺栓连接结构的特点,采用非线性有限元分析方法建立多种法兰-螺栓连接分析模型,对模型的单元类型选择、各部件连接关系的处理及接触对的建立方式进行了研究;分析了单元类型、接触关系等因素对有限元计算结果的影响;提出了针对不同分析需求的风力发电机组法兰-螺栓连接有限元分析方案;为风力发电机组法兰-螺栓连接结构的设计和强度分析提供理论基础。     

具有温度场的冷却叶片振动特性计算方法研究

根据稳态热传导的相关理论,建立了透平冷却叶片温度场和热应力场的四面体三维有限元分析模型和方法,并在此基础上建立了透平冷却叶片振动特性三维有限元分析方法,开发了相关计算软件。对某航空发动机透平高压第1级冷却叶片在不同工作条件下的振动特性进行了计算分析,同时研究了热应力、温度场、转速等对叶片振动特性的影响,表明本文中所建立模型和方法是科学、合理和精确的,为开展透平冷却叶片的设计和振动安全性评价奠定了基础。     

基于有限元法的三维机织复合材料叶片振动特性分析

文章耦合了ANSYS Workbench中的ACP,CFX和Modal模块,通过自定义User Material对1.9 m长的三维正交机织复合材料风机叶片进行了有限元分析。通过叶片正反面的压力云图和风压曲线分析了叶片表面的载荷特性,说明直叶片的最大风压差值并不出现在叶尖处。应用无量纲法对不同工况下叶片振动频率进行的分析可知,离心载荷对叶片的振动频率变化起到了决定性的作用。     

16V280ZJ型柴油机喷油器支座板的三维有限元计算分析

使用ANSYS软件对16V280ZJ型柴油机喷油器的支座板进行三维有限元计算,讨论了对其载荷和边界条件的处理,并通过分析计算结果找出应力最大的部位。结果表明支座板的设计满足强度要求。     

Temperature field analysis of tangential clearance leakage flow for scroll compressor based on fuzzy ridgelet finite element method

To improve the computing precision and efficiency of temperature field analysis in tangential clearance of scroll compressor, the ridgelet finite element method is combined with fuzzy finite element method to construct the fuzzy ridgelet finite element method of analyzing temperature field in tangential clearance. First, the related research progresses on heat transfer of scroll compressor, wavelet finite element method, and fuzzy finite element method are summarized. Second, the leakage flow model of tangential clearance in scroll compressor is studied in depth. Third, the heat transfer model of leakage flow in tangential clearance of scroll compressor is established, and then the fuzzy ridgelet finite element model is constructed, the fuzzy finite element model is transformed to the random model based on information entropy, the corresponding calculating procedure is designed. Finally, the simulation analysis is performed based on fuzzy finite element method, fuzzy Daubechies wavelet finite element method, and the fuzzy ridgelet finite element model, respectively, comparing analysis between simulation and test results shows that the fuzzy ridgelet finite element method has best computing effectiveness on temperature field analysis of tangential clearance of scroll compressor. In addition, the tangential clearance temperature of scroll compressor with and without water cooling has been analyzed based on the fuzzy ridgelet finite element method, and the results show that the water cooling system can reduce the temperature in tangential clearance greatly.     

Performance analysis of a shaded-pole linear induction motor usingsymmetrical components, field analysis, and finite element method

The performance analysis of a shaded-pole linear induction motor using symmetrical components, field analysis and finite element methods is presented. Calculated results and measurements are compared and discussed     

An elasto-plastic finite element for steel pipelines

An efficient finite element for the modeling of inelastic behaviour of three-dimensional pipe systems is presented. The formulation is based on a two-node pipe element with 12 degrees of freedom. The element consists of an elastic portion and two potentially plastic 3D hinges of zero-length lumped at both nodes. The behaviour of the plastic hinges is characterized using recently derived and experimentally validated plastic interaction relations for pipe sections. The normality condition of plasticity is applied to the analytically derived yield hyper-surface at the stress resultant level in order to approximately simulate material elasto-plastic behaviour. The element models shear deformation effects both in the elastic and plastic ranges. Thus, it is suitable for predicting pipe behaviour subjected to high shearing forces. The model captures the essential features of pipe behaviour using a remarkably small number of degrees of freedom and is particularly suited for the analysis of long pipeline systems. Solutions for simple problems are provided and compared to several other well-established elements in the ABAQUS library in order to assess the validity of the results and demonstrate their scope of applicability.     

Elastic-plastic analysis of a nozzle corner crack by finite element method

The paper presents the results of an elastic-plastic three-dimensional finite element analysis for a nozzle corner crack in a pressurised reactor test vessel. The calculations were performed by the finite element program ADINA incorporating von Mise's yield condition and isotropic hardening. The crack plane was taken parallel to the axis of the vessel and the crack front straight and perpendicular to the symmetry line of the nozzle corner in order to obtain the worst position for a nozzle corner crack. The calculations were performed up to that pressure level where general yield of the ligament in the nozzle corner section takes place.For the chosen crack length, which is relatively small in comparison to the ligament, the crack opening stress as well as the crack opening displacement have a maximum in the centre of the crack. The differences between the maximum and minimum values along the crack front increase rapidly in the plastic range when the pressure load is raised above half of the general yield pressure. The results of the finite element analysis are compared with figures obtained from analytical procedures of elastic-plastic fracture mechanics.     

Sensitivity analysis in thermoelastic problems using the complex finite element method

This article presents the complex finite element method (ZFEM) for the sensitivity analysis of thermoelastic systems. ZFEM, based on the complex Taylor series approach, performs finite element procedures using complex variables such that the response variables (temperature, stress) and their sensitivities with respect to an input parameter of interest (shape, mechanical and thermal properties, loading) are obtained simultaneously. ZFEM offers significant advantages over alternative sensitivity analyses that require direct derivations of the sensitivity formulae, multiple runs, and/or remeshing. To verify the numerical implementation, a hollow cylinder with convective boundary conditions on the inside and outside surface was considered. First-order derivatives of the stress fields were compared with exact solutions to demonstrate the accuracy of ZFEM sensitivities. The results indicate that the ZFEM-based derivatives are of high accuracy, thereby showing its applicability in the design and analysis of thermoelastic problems.     

3-D finite element simulation of wafer thermal distortion and stress fields in exposure process

A 3-D thermo-elastic finite element model was established in this paper to study the transient behavior of thermal expansion and the distribution of thermal stress in a wafer by the absorption of exposure energy during the exposure process. The analysis procedure of investigating the thermal expansion of the wafer including the transient behavior in a single exposure region, the thermal interactions between neighboring exposure regions to the variation of exposure energy, the interval of exposure locations, and ends with the interval of exposure time under continuous exposure. The results indicate that the thermal deformation gradient of the wafer can be improved by adjusting the location interval and the time interval between the neighboring exposure regions. Widening the interval of exposure locations has a greater impact in improving the thermal deformation of wafer than extending the interval of exposure time between the image fields. The physical phenomenon can serve as a supporting reference tool for engineers in planning exposure paths, and the simulation model can serve as an analysis tool to understand the behavior during the exposure process.     

Numerical simulation of laser-induced transient temperature field in film-substrate system by finite element method

The transient temperature fields generated by a pulsed laser in film-substrate system are obtained by using the finite element method. Time integrations of the semi-discrete finite element equations are achieved by using approximate one order derivative of temperature. The temperature dependences of material properties are taken into account, which has a great influence on the temperature fields indicated by the numerical results. The pulsed laser-induced transient temperature fields in aluminum/methyl-methacrylate system and aluminum/copper system are obtained, which will be useful in the research on thermoelastic excitation of laser ultrasonic waves in film-substrate system.     

Fault analysis of a PM brushless DC Motor using finite element method

Three-phase trapezoidal back-EMF permanent magnet (PM) machines are used in many applications where the reliability and fault tolerance are important requirements. Knowledge of the machine transient processes under various fault conditions is the key issue in evaluating the impact of machine fault on the entire electromechanical system. The machine electrical and mechanical quantities whose transient behaviors are of importance under fault conditions include the voltages and currents of the coils and phases, the electromagnetic torque, and the rotor speed. Experimental test based on true machines for such a purpose is impractical for its high cost and difficulty to make. Computer simulation based on the finite element method has shown its effectiveness in fault study in this paper. Before the finite element model was used to perform simulations under fault conditions, it was validated by test data under normal conditions. Three types of fault conditions-single-phase open circuit fault, phase-to-phase terminal short-circuit, and internal turn-to-turn short-circuit have been studied.     

Design of a steam-heated sterilizer based on finite element method stress analysis

A steam-heated sterilizer is a pressure vessel of rectangular cross section externally reinforced by members welded to the flat surfaces of the vessel. These members are pressure vessels too with rectangular cross section. The ASME code provides alternative rules (Division 2) for the design of pressure vessels based on a Design By Analysis route. The stresses on the sterilizer were computed by the finite element method followed by the calculation of the stress fields according to the classification established in the ASME code. Structural members with shell intersections (as in the present case) present difficulties due to problems of linearisation and categorisation. In the present work the shell stress resultants were used instead of smoothed stresses. The operating conditions of the vessel involve cyclic application of loads requiring design based on fatigue analysis.     

A finite element analysis for inverse heat conduction problems

This paper presents an efficient inverse analysis technique based on a sensitivity coefficient algorithm to estimate the unknown boundary conditions of multidimensional steady and transient heat conduction problems. Sensitivity coefficients were used to represent the temperature response of a system under unit loading conditions. The proposed method, coupled with the sensitivity analysis in the finite element formulation, is capable of estimating both the unknown temperature and heat flux on the surface provided that temperature data are given at discrete points in the interior of a solid body. Inverse heat conduction problems are referred to as ill-posed because minor inaccuracy or error in temperature measurements cause a drastic effect on the predicted surface temperature and heat flux. To verify the accuracy and validity of the new method, two-dimensional steady and transient problems are considered. Their surface temperature and heat flux are evaluated. From a comparison with the exact solution, the effects of measurement accuracy, number and location of measuring points, a time step, and regularization terms are discussed. © 1998 Scripta Technica. Heat Trans Jpn Res, 26(6): 345–359, 1997     

Experiences using three-dimensional finite element analysis for leak-before-break assessment

Because of practical limitations, analytical problems in fracture mechanics have often been solved using simplified geometries (e.g. plane stress/strain, shell models). We have applied the Leak-Before-Break approach extensively to the large diameter piping of a new nuclear power plant. Various piping components such as elbows, tee and branch connections with postulated cracks were analyzed. Since no credible geometric simplification was possible, fully three-dimensional (3D) analytical models were found to be essential.

The paper describes our experiences in performing 3D Finite Element (FE) analysis of these components. Included are comparisons of numerical and test results of compact specimens, material modeling considerations, handling of 3D effects, such as the variation of the J-integral along a crack front, and especially, the effects of plasticity.

The overall intent of the paper is not simply to present specific numerical results, but rather to give some perspective on the effort required and results attainable.     

Torque ripple analysis of a PM brushless DC motor using finite element method

Three-phase permanent magnet brushless DC motors are widely used. As a function of the rotor position, the torque produced by these machines has a pulsating component in addition to the DC component. This pulsating torque has a fundamental frequency corresponding to six pulses per electrical revolution of the motor. The shape of the torque waveform and, thus, the frequency content of the waveform can be influenced by several factors in the motor design and construction. This paper addresses the various factors that influence the torque waveshape. It is shown that in addition to the basic induced electromotive force (EMF) waveshape, the magnetic saturation in the stator core, and the accuracy in the skewing are also key factors in determining the torque waveshape. Computer simulation using finite element technique has been conducted to study the torque waveform. Simulation results successfully duplicated the torque waveforms measured in experiments under different excitation currents.