OPTIMIZATION OF AUTOBODY PANEL STAMPING PROCESS BASED ON DYNAMIC EXPLICIT FINITE ELEMENT METHOD

Taking CPU time cost and analysis accuracy into account, dynamic explicit finite ele- ment method is adopted to optimize the forming process of autobody panels that often have large sizes and complex geometry. In this paper, for the sake of illustrating in detail how dynamic explicit finite element method is applied to the numerical simulation of the autobody panel forming process,an example of optimization of stamping process pain meters of an inner door panel is presented. Using dynamic explicit finite element code Ls-DYNA3D, the inner door panel has been optimized by adapting pa- rameters such as the initial blank geometry and position, blank-holder forces and the location of drawbeads, and satisfied results are obtained.

An explicit finite element－finite difference method for analyzing the effect of visco－elastic local topography on the earthquake motion

An explicit finite element-finite difference method for analyzing the effects of two-dimensional visco-elastic localtopography on earthquake ground motion is prOPosed in this paper. In the method, at first, the finite elementdiscrete model is formed by using the artificial boundary and finite element method, and the dynamic equationsof local nodes in the discrete model are obtained according to the theory of the special finite element method similar to the finite difference method, and then the explicit step-by-step integration formulas are presented by usingthe explicit difference method for solving the visco-elastic dynamic equation and Generalized Multi-transmittingBoundary. The method has the advantages of saving computing time and computer memory space, and it is suitable for any case of topography and has high computing accuracy and good computing stability.

An explicit finite volume element method for solving characteristic level set equation on triangular grids

Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow phenomena.This paper presents a characteristic level set equation which is derived from the two-dimensional level set equation by using the characteristic-based scheme.An explicit finite volume element method is developed to discretize the equation on triangular grids.Several examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time.The proposed level set method is also coupled with the Navier-Stokes equations for two-phase immiscible incompressible flow analysis with surface tension.The Rayleigh-Taylor instability problem is used to test and evaluate the effectiveness of the proposed scheme.

An explicit finite element method for dynamic analysis in three-medium coupling system and its application

In this paper, an explicit finite element method to analyze the dynamic responses of three-medium coupled systems with any terrain is developed on the basis of the numerical simulation of the continuous conditions on the bounda-ries among fluid saturated porous medium, elastic single-phase medium and ideal fluid medium. This method is a very effective one with the characteristic of high calculating speed and small memory needed because the formulae for this explicit finite element method have the characteristic of decoupling, and which does not need to solve sys-tem of linear equations. The method is applied to analyze the dynamic response of a reservoir with considering the dynamic interactions among water, dam, sediment and basement rock. The vertical displacement at the top point of the dam is calculated and some conclusions are given.

An explicit method for numerical simulation of wave equations

In this paper, a method to develop a hierarchy of explicit recursion formulas for numerical simulation in an irregular grid for scalar wave equations is presented and its accuracy is illustrated via 2-D and 1-D models. Approaches to develop the stable formulas which are of 2M-order accuracy in both time and space with Mbeing a positive integer for regular grids are discussed and illustrated by constructing the second order （M= 1） and the fourth order （M = 2） recursion formulas.

An explicit method for numerical simulation of wave equations: 3D wave motion

In this paper, an explicit method is generalized from 1D and 2D models to a 3D model for numerical simulation of wave motion, and the corresponding recursion formulas are developed for 3D irregular grids. For uniform cubic grids, the approach used to establish stable formulas with 2M-order accuracy is discussed in detail, with M being a positive integer, and is illustrated by establishing second order （M=1） recursion formulas. The theoretical results presented in this paper are demonstrated through numerical testing.

Verification of an Explicitly Coupled Thermal-Phase Field-Mechanical Electromagnetic (TPME) Framework by the Method of Manufactured Solutions

An explicitly coupled two-dimensional (2D) multiphysics finite element method (FEM) framework comprised of thermal, phase field, mechanical and electromagnetic (TPME) equations was developed to simulate the conversion of solid kerogen in oil shale to liquid oil through in-situ pyrolysis by radio frequency heating. Radio frequency heating as a method of in-situ pyrolysis represents a tenable enhanced oil recovery method, whereby an applied electrical potential difference across a target oil shale formation is converted to thermal energy, heating the oil shale and causing it to liquify to become liquid oil. A number of in-situ pyrolysis methods are reviewed but the focus of this work is on the verification of the TPME numerical framework to model radio frequency heating as a potential dielectric heating process for enhanced oil recovery. Very few studies exist which describe production from oil shale;furthermore, there are none that specifically address the verification of numerical models describing radio frequency heating. As a result, the Method of Manufactured Solutions (MMS) was used as an analytical verification method of the developed numerical code. Results show that the multiphysics finite element framework was adequately modeled enabling the simulation of kerogen conversion to oil as a part of the analysis of a TPME numerical model.

扣件刚度非线性对波磨区轮轨瞬态滚动接触行为的影响

WJ-8型扣件橡胶垫板刚度在长期服役过程中表现出非线性特征,静刚度随荷载增加而降低,为提高三维瞬态滚动接触有限元模型计算精确性,本文以LMA踏面车轮及CHN60型钢轨为基础,基于显式积分算法,将以往研究中线弹性扣件转化为非线性扣件,建立考虑扣件刚度非线性特征的三维轮轨瞬态滚动接触有限元模型,研究刚度非线性对车轮与钢轨波磨间高频动态响应及瞬态接触行为的影响,并重点分析了波磨工况下时频域内轮轨接触力、轴箱加速度的变化信息.结果表明:扣件非线性对轮轨接触力变化影响明显,主要表现为车轮行驶至扣件前端时强振动导致橡胶垫板表现为柔软特性使轮轨接触力减小,车轮行驶至扣件上方时在轴重作用下振动减弱表现为刚硬特性使轮轨接触力增大,轮轨力变化差异最大达到13.1%.

Time-domain Finite Element Method for Transient Electric Field and Transient Charge Density on Dielectric Interface

This paper is devoted to solving the transient electric field and transient charge density on the dielectric interface under the electroquasistatic(EQS)field conditions with high accuracy.The proposed method is suitable for both 2-D and 3-D applications.Firstly,the governing equations represented by scalar electric potential are discretized by the nodal finite element method(FEM)in space and the finite difference method in time.Secondly,the transient constrained electric field equation on the boundary(TCEFEB)is derived to calculate the normal component of the transient electric field intensities on the Dirichlet boundary and dielectric interface as well as the transient charge density on the dielectric interface.Finally,a 2-D numerical example is employed to demonstrate the validity of the proposed method.Furthermore,the comparisons of the numerical accuracy of the proposed method in this paper with the existing FEMs for electric field intensity and charge density on the dielectric interface are conducted.The results show that the numerical accuracy of the proposed method for calculating the normal component of transient electric field intensities on the Dirichlet boundary and dielectric interface as well as the transient charge density on the dielectric interface is close to that of nodal electric potential and an order of magnitude higher than those of existing FEMs.

Time-domain Spectral Finite Element Method for Wave Propagation Analysis in Structures with Breathing Cracks

Guided waves are generally considered as a powerful approach for crack detection in structures,which are commonly investigated using the finite element method(FEM).However,the traditional FEM has many disadvantages in solving wave propagation due to the strict requirement of mesh density.To tackle this issue,this paper proposes an efficient time-domain spectral finite element method(SFEM)to analyze wave propagation in cracked structures,in which the breathing crack is modeled by definiiig the spectral gap element.Moreover,novel orthogonal polynomials and Gauss-Lobatto-Legendre quadrature rules are adopted to construct the spectral element.Meanwhile,a separable hard contact is utilized to simulate the breathing behavior.Finally,a comparison of the numerical results between the FEM and the SFEM is conducted to demonstrate the high efficiency and accuracy of the proposed method.Based on the developed SFEM,the nonlinear features of waves and influence of the incident mode are also studied in detail,which provides a helpful guide for a physical understanding of the wave propagation behavior in structures with breathing cracks.

齿轨铁路齿条啮合与轮轨滚动接触间耦合作用机理分析

针对适于山地轨道交通的齿轨铁路,建立基于显式时间积分的三维齿轨轮对-轨道瞬态接触有限元模型,模型可分析齿轮齿条啮合和轮轨滚动接触间中、高频耦合动力作用。轮对和轨道真实几何,齿轮与车轮轮径差导致“车轮悖论”现象及结构振动等均有考虑,齿轮齿条啮合和轮轨接触采用集成库仑摩擦的“面-面”接触算法求解。对比零和非零轮轨摩擦系数工况,解构“车轮悖论”现象对动态接触的影响。以初步设计的Strub型齿轨铁路为例,分析速度为10 km/h和0‰、240‰、480‰坡度下动态接触现象。结果表明,受齿轮啮合影响,齿条、轮轨接触力均呈现周期性波动,但垂向接触总力和总牵引扭矩分别在重力载荷与牵引扭矩附近波动。“车轮悖论”使齿条垂向力和法向接触应力减小,而轮轨垂向力和法向接触应力增加,齿面切向接触应力与接触斑内滑移区面积相应增加,在坡度240‰下,轮轨摩擦系数由0增至0.2,齿条、轮轨最大法向接触应力由248.69、752.66 MPa增至195.17、757.44 MPa,最大切向接触应力相应由24.48、152.84 MPa变成21.31、2.14 MPa。轮轨接触斑因发生显著蠕滑呈现全滑移。相同速度及摩擦条件下,坡度增加使齿条垂向力和牵引力增加,轮轨垂向力和牵引力减小,接触应力呈同相变化。

缩尺车轮-环轨滚动接触与磨耗特性仿真分析

为了研究缩尺车轮-环轨滚动接触与磨耗特性,基于轮轨滚动行为(WRRB)模拟试验台参数,利用ANSYS/LS-DYNA建立瞬态滚动接触有限元模型,集成弹性蠕滑率求解程序和Tγ磨耗模型,通过试验验证模型的正确性.重点分析轮轨力、蠕滑率、接触应力和钢轨磨耗深度,并考虑车轮驱动扭矩和速度的影响规律.结果表明:缩尺车轮-环轨结构的高频弹性振动造成轮轨垂向力波动;在比例载荷作用下,纵向动力学行为和钢轨磨耗深度变化趋势与服役轮轨一致;由于环轨的极小曲线半径,自由滚动工况下的横向蠕滑力/率、自旋蠕滑率、钢轨磨耗深度偏大,切向接触应力峰值出现在接触斑后沿两侧;车轮驱动扭矩和速度的影响规律可拟合为一组经验公式.研究可以为此类试验台的设计与应用工作提供理论依据.

嵌入式轨道三维滚动接触模型冲击特性研究

嵌入式轨道在城市轨道交通领域得到广泛运用,在高速铁路方面,国内外也有少量的相关报道和理论研究。嵌入式轨道对减缓轮轨冲击有显著效果,其中焊接接头是引起轮轨冲击的重要原因之一,对于时速400公里以及更高运行速度的列车,焊接接头冲击激励引起的轮轨力变化十分显著,目前对于高速工况下嵌入式轨道的研究尚不充分。基于显式动力学有限元方法,采用三维高速轮轨瞬态滚动接触模型对轮轨冲击过程进行数值模拟,并探究时速400公里速度下的嵌入式轨道的冲击特性。得出以下结论:嵌入式轨道与扣件式轨道在受到不同波长冲击时均能够减小垂向轮轨力变化幅值,焊接接头波长越长,垂向轮轨冲击力越能快速趋于平缓;车轮在受到焊接接头长波冲击时,嵌入式轨道能明显降低纵向轮轨力。研究结果可为嵌入式轨道在高速铁路的运用提供参考。

SV和SH波垂直入射下二维盆地-子盆地共振对比研究

盆地-子盆地中的子盆地除了底部直达的入射体波外,还存在大盆地产生的横向传播的面波入射,导致子盆地共振特性的变化。基于显式有限元法,对比分析了SH波和SV波垂直入射下,子盆地基底阻抗比、大盆地倾角和半宽对二维梯形盆地-子盆地的二维共振频率及其对应放大系数的影响。研究表明:受大盆地产生的横向传播面波的影响,子盆地的速度峰值PGV和累积能量Ex最大值均有明显放大,且SV波入射下的放大系数大于SH波;子盆地基底阻抗比对盆地-子盆地的PGV最大值、Ex最大值、二维共振频率及其对应放大系数影响较大,大盆地倾角和半宽的影响不大。SV波和SH波入射下子盆地二维共振频率较单一小盆地均有所增加,且同阻抗比下SV波入射的增幅大于SH波。SH波入射下二维共振频率下的放大系数基本大于单一小盆地,而SV波在低阻抗比下低于单一小盆地,高阻抗比下高于单一小盆地和SH波入射下的结果。SV波入射下盆地-子盆地的二维共振频率及其对应放大系数受大盆地的影响较SH波更大。

Time-Domain Analysis of Underground Station-Layered Soil Interaction Based on High-Order Doubly Asymptotic Transmitting Boundary

Based on the modified scale boundary finite element method and continued fraction solution,a high-order doubly asymptotic transmitting boundary(DATB)is derived and extended to the simulation of vector wave propagation in complex layered soils.The high-order DATB converges rapidly to the exact solution throughout the entire frequency range and its formulation is local in the time domain,possessing high accuracy and good efficiency.Combining with finite element method,a coupled model is constructed for time-domain analysis of underground station-layered soil interaction.The coupled model is divided into the near and far field by the truncated boundary,of which the near field is modelled by FEM while the far field is modelled by the high-order DATB.The coupled model is implemented in an open source finite element software,OpenSees,in which the DATB is employed as a super element.Numerical examples demonstrate that results of the coupled model are stable,accurate and efficient compared with those of the extended mesh model and the viscous-spring boundary model.Besides,it has also shown the fitness for long-time seismic response analysis of underground station-layered soil interaction.Therefore,it is believed that the coupled model could provide a new approach for seismic analysis of underground station-layered soil interaction and could be further developed for engineering.

Time domain method for calculating free field motion of a layered half-space subjected to obliquely incident body waves

In numerical simulation of wave scattering under oblique incident body waves using the finite element method, the free field motion at the incident lateral boundary induced by the background layered half-space complicates the computational area. In order to replace the complex frequency domain method, a time-domain method to calculate the free field motion of a layered half-space subjected to oblique incident body waves is developed in this paper. The new method decouples the equations of motion used in the finite element method and offers an interpolation formula of the free field motion. This formula is based on the fact that the apparent horizontal velocity of the free field motion is constant and can be calculated exactly. Both the theoretical analysis and numerical results demonstrate that the proposed method offers a high degree of accuracy.

HOW TO PROVE THE DISCRETE RELIABILITY FOR NONCONFORMING FINITE ELEMENT METHODS

Optimal convergence rates of adaptive finite element methods are well understood in terms of the axioms of adaptivity.One key ingredient is the discrete reliability of a residualbased a posteriori error estimator,which controls the error of two discrete finite element solutions based on two nested triangulations.In the error analysis of nonconforming finite element methods,like the Crouzeix-Raviart or Morley finite element schemes,the difference of the piecewise derivatives of discontinuous approximations to the distributional gradients of global Sobolev functions plays a dominant role and is the object of this paper.The nonconforming interpolation operator,which comes natural with the definition of the aforementioned nonconforming finite element in the sense of Ciarlet,allows for stability and approximation properties that enable direct proofs of the reliability for the residual that monitors the equilibrium condition.The novel approach of this paper is the suggestion of a right-inverse of this interpolation operator in conforming piecewise polynomials to design a nonconforming approximation of a given coarse-grid approximation on a refined triangulation.The results of this paper allow for simple proofs of the discrete reliability in any space dimension and multiply connected domains on general shape-regular triangulations beyond newest-vertex bisection of simplices.Particular attention is on optimal constants in some standard discrete estimates listed in the appendices.

Time-Domain Nonlinear Wave-Current Interaction with A Steep Wave Riser Considering Internal Flow Effect

The nonlinear dynamic response induced by the wave-current interaction on a deepwater steep wave riser(SWR)is numerically investigated based on a three-dimensional(3 D)time-domain finite element method(FEM).The governing equation considering internal flow is established in the global coordinate system.The whole SWR consists of three segments:the decline segment,buoyancy segment and hang-off segment,in which the buoyancy segment is wrapped by several buoyancy modules in the middle section,leading to the arch bend and sag bend.A Newmark-β iterative scheme is adopted for the accurate analysis to solve the governing equation and update the dynamic response at each time step.The proposed method is verified through the published results for the dynamic response of steel catenary riser(SCR)and static configuration of steel lazy wave riser(SLWR).Simulations are executed to study the influence of wave height,current velocity/direction,internal flow density/velocity and top-end pressure on the tension,configuration and bending moment of the SWR.The results indicate that the influence of the current on the configuration and mechanical behavior of the SWR is greater than that of the wave,especially in the middle section.With increasing current velocity,the suspending height of the middle section drops,meanwhile,its bending moment decreases accordingly,but the tension increases significantly.For a fixed external load,the increasing internal flow density induces the amplification of the tension at the hang-off segment and the mitigation at the decline segment,while the opposite trend occurs at the bending moment.

Developing Finite Element Methods for Simulating Transformation Optics Devices with Metamaterials

In this paper,we first develop the mathematical modeling equations for wave propagation in several transformation optics devices,including electromagnetic concentrator,rotator and splitter.Then we propose the corresponding finite element time-domain methods for simulating wave propagation in these transformation optics devices.We implement the proposed algorithms and our numerical results demonstrate the effectiveness of our modeling equations.To our best knowledge,this is the first work on time-domain finite element simulation carried out for the electromagnetic concentrator,rotator and splitter.

基于ABAQUS/Explicit的一种新型空调室外机的跌落仿真分析

利用UG、Hypermesh等软件对空调室外机结构进行建模及网格划分等前处理工作,并利用ABAQUS软件中的动态计算模块对空调室外机多种跌落过程进行了仿真分析,仿真结果表明左支撑与右后板在跌落中容易发生塑性变形,是需要进一步加强的结构,同时比较了不同角度跌落对于室外机结构的破坏程度。