Three-Dimensional Rigid-Plastic FEM Simulation of Bulk Forming Processes with New Contact and Remeshing Techniques

Some techniques such as die surface description, contact judgement algorithm and remeshing are proposed to improve the robustness of the numerical solution. Based on these techniques, a three-dimensional rigid-plastic FEM code has been developed. Isothermal forging process of a cylindrical housing has been simulated. The simulation results show that the given techniques and the FEM code are reasonable and feasible for three-dimensional bulk forming processes.

RIGID-PLASTIC/RIGID-VISCOPLASTIC FEM BASED ON LINEAR PROGRAMMING-THEORETICAL MODELING AND APPLICATION FOR PLANE-STRAIN PROBLEMS

A new rigid-plastic/rigid-viscoplastic (RP/RVP) FEM based on linearprogramming (LP) for plane-strain metal forming simulation is proposed. Compared with thetraditional RP/RVP FEM based on iteration solution, it has some remarkable advantages, such a it'sfree of convergence problem and its convenience in contact, incompressibility constraint and rigidzone treatment. Two solution examples are provided to validate its accuracy and efficiency.

Dynamic limit equilibrium analysis of sliding block for rock slope based on nonlinear FEM

Traditional rigid body limit equilibrium method （RBLEM） was adopted for the stability evaluation and analysis of rock slope under earthquake scenario. It is not able to provide the real stress distribution of the structure, while the strength reduction method relies on the arbitrary decision on the failure criteria. The dynamic limit equilibrium solution was proposed for the stability analysis of sliding block based on 3-D multi-grid method, by incorporating implicit stepping integration FEM. There are two independent meshes created in the analysis： One original 3-D FEM mesh is for the simulation of target structure and provides the stress time-history, while the other surface grid is for the simulation of sliding surface and could be selected and designed freely. As long as the stress time-history of the geotechnical structure under earthquake scenario is obtained based on 3-D nonlinear dynamic FEM analysis, the time-history of the force on sliding surface could be derived by projecting the stress time-history from 3-D FEM mesh to surface grid. After that, the safety factor time-history of the sliding block will be determined through applying limit equilibrium method. With those information in place, the structure＇s aseismatic stability ean be further studied. The above theory and method were also applied to the aseismatic stability analysis of Dagangshan arch dam＇s right bank high slope and compared with the the result generated by Quasi-static method. The comparative analysis reveals that the method not only raises the FEM＇s capability in accurate simulation of complicated geologic structure, but also increases the flexibility and comprehensiveness of limit equilibrium method. This method is reliable and recommended for further application in other real geotechnical engineering.

Analysis of a Gyroscope′s Rotor Nonlinear Supported Magnetic Field Based on the B-Spline Wavelet-FEM

A supported framework of a gyroscope＇s rotor is designed and the B-Spline wavelet finite element model of nonlinear supported magnetic field is worked out. A new finite element space is studied in which the scaling function of the B-spline wavelet is considered as the shape function of a tetrahedton. The magnetic field is spited by an artificial absorbing body which used the condition of field radiating, so the solution is unique. The resolution is improved via the varying gradient of the B-spline function under the condition of unchanging gridding. So there are some advantages in dealing with the focus flux and a high varying gradient result from a nonlinear magnetic field. The result is more practical. Plots of flux and in the space is studied via simulating the supported system model. The results of the study are useful in the research of the supported magnetic system for the gyroscope rotor.

ALE FINITE ELEMENT ANALYSIS OF NONLINEAR SLOSHING PROBLEMS BASED ON F LUID VELOCITY POTENTIAL

Base d on fluid velocity potential, an ALE finite element formulation for the analysi s of nonlinear sloshing problems has been developed. The ALE kinemat ical description is introduced to move the computational mesh independently of f luid motion, and the container fixed noninertial coordinate system is employed to establish the governing equations so that the mesh is needed to be updated in this coordinate system only. This leads to a very simple mesh moving algorithm which makes it easy to trace the motion of the moving boundaries and the free su rface without producing undesirable distortion of the computational mesh. The fi nite element method and finite difference method are used spacewise and timewise , respectively. A numerical example involving either forced horizontal oscillati on or forced pitching oscillation of the fluid filled container is presented to illustrate the effectiveness and the robustness of the method. In additi on, this work can be extended for the fluid structure interaction problems.

多柔性体系统动力学的有限元方法(MUFEM)

本文探讨多柔性体系统动力学的一种新的数值仿真方法一多体有限元方法（MultibodyFiniteElementMethod，MUFEM）。MUFEM以有限元方法为基础，综合区域分解法（DDM）和非连续体变形分析方法（DDA）的主要优点。MUFEM的主要特点是：1）构造边界网格描述系统动态变化的拓扑几何关系；2）采用FEM模型和类似子结构的方法分析多柔性体系统的动力学特性；3）各子块之间可能接触边界的非连续性用Lagrange乘子处理；4）摩擦接触问题用非线性数学规划方法求解。算例表明，MUFEM能很好模拟多柔性体系统的运动以及相互之间的作用，有良好的发展前景。

基于FEM的超高压液压顶升装置力学特性分析

液压顶升装置各部件在超高压下的力学特性是影响其性能的主要因素,也是超高压技术的难题。采用有限元方法研究超高压液压顶升装置各部件的材料、内径、厚度等不同时,其液压系统刚度、模态、固有频率、位移、应力的变化规律。有限元计算结果与压力试验结果较为接近,验证了有限元模型及边界条件的有效性。结果表明:液压弹簧刚度随液压缸内径增大而增加、随振幅增加而下降,其影响随内径增加而减少;系统前3阶固有频率随地面强度增大而增加;Bonded工况极限应力值最小,Frictionless工况极限应力最大,极限应力随地面强度增加而减少;C20地面时,最大位移随摩擦因数增加而增加,最大应力随地面强度增加而增加;C30地面时,最大位移随摩擦因数增大先增后减,其位移、应力临界摩擦值分别为0.43、0.59;结构钢地面时,极限位移显著减少。液压缸同长度不同位置极限位移差值随地面强度而增加;液压缸底端应力值随地面强度增加而增加;液压缸外表面一孔侧位移均小于二孔侧,且极限位移更靠近顶端,并交替出现极值。分析了超高压液压装置的应力-应变过程,为其结构设计、密封设计及使用提供了参考。

Self-adaptive one-dimensional nonlinear finite element method based on element energy projection method

The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.

基于FEM-DFN的页岩气储层水力压裂复杂裂缝交错扩展模型

页岩气藏压裂过程中,常遇到因施工压力超限储层压不开、近井地带裂缝形态复杂而引起砂堵的恶性事故,如何有效模拟复杂裂缝的起裂与交错扩展形态是页岩气体积压裂优化设计的关键。为此,基于有限元—离散裂缝网络(FEM-DFN),考虑水力裂缝扩展的非线性损伤破裂力学行为与裂缝面摩擦效应,改进了拉伸—剪切复合破裂模式的本构方程,建立了基于显式时间积分的页岩气储层水力压裂复杂裂缝交错扩展的多场耦合模型,并在实验室和现场微地震监测中进行了验证。研究结果表明:①水力裂缝与天然裂缝交错机制主要为2类,即被天然裂缝诱导并沿天然裂缝扩展、直接穿透天然裂缝,地质与工程因素对交错机制的转变存在阈值,当排量超过26 m^(3)/min时,或压裂液黏度超过40mPa·s时,或应力差超过18MPa时,或裂缝面摩擦系数超过0.8时,水力裂缝将直接穿透天然裂缝;②天然裂缝对水力裂缝的诱导作用随着两者夹角的变化而变化,在夹角较小的情况下,水力裂缝容易在最大水平主应力方向交汇点之前提前被天然裂缝诱导,而当夹角增大时则在交汇点处进入天然裂缝扩展,且表现为一侧拉张裂缝一侧剪切裂缝;③相邻两簇水力裂缝容易在天然裂缝的诱导作用下相互吸引,进而交汇成优势主裂缝。结论认为,天然裂缝的分布状态是决定压裂裂缝复杂度的关键性因素,研究成果可为中深层页岩气压裂裂缝分析和施工参数优化提供理论与技术支撑。

基于CFD-FEM的浮式结构水弹性响应数值模拟

开发并验证了一种基于CFD-FEM耦合的弹性浮体水弹性响应计算模拟方法。采用CFD方法建立黏性数值水池模拟非线性波浪,弹性浮板进行有限元离散,并在交界面进行数据交互实现耦合计算;通过与水池试验数据和三维板理论在各种波浪环境下的浮体垂向位移结果对比,证实CFD-FEM耦合方法的有效性。并进一步研究了浮板的厚度、入射波波幅和浮板的三维效应对浮板水弹性响应的影响。结论表明,波幅的增加会加剧弹性浮板的水弹性响应,浮板各点处的垂向位移随波幅的增加而增大;当浮板厚度改变时,不同厚度浮板自由端处的垂向位移差异较小,而在中部等位置处,厚度对浮板的水弹性响应有较大的影响。

A New Pursuit Mode of Nonlinear Wave Surface

The numerical mode of nonlinear wave transformation based on both the Laplace equation for water field and the Bernoulli equation for water surface is a kind of time-domain boundary problem with initial conditions. And the basis for establishing the numerical mode of nonlinear wave in time domain is to trace the position of wave free surface and to calculate the instantaneous surface height and surface potential function. This paper firstly utilizes the ‘0-1' combined BEM to separate the boundary by means of discretization of Green's integral equation based on the Laplace equation, then separates the free surface of wave with FEM and derives the FEM equation of wave surface that satisfies the nonlinear boundary conditions. By jointly solving the above BEM and FEM equations, the wave potential and surface height could be obtained with iteration in time domain. Thus a new kind of nonlinear numerical mode is established for calculating wave transformation. The wave test in the numerical wave tank shows that the numerical simulation with this mode is of high accuracy.

FEM Simulation of Effect of Process Parameters on Static Recrystallization in 60SiMnA Spring Steel

Two-dimensional rigid-plastic finite element method (FEM) was used for simulation of the effect of process parameterson the static recrystallization of 60SiMnA spring steel using MARC/AutoForge 3.1 software. A thermo-mechanicalcoupled analysis was conducted considering the heat transfer between the workpiece, the roll and the environment,and the heat generation due to plastic work. The static recrystallization laws under different processing conditionsand the predicted distribution of the static recrystallization volume fraction on the deformation cross section arepresented.

FEM Analysis of Effect of Die Angle on Tube Inversion Forming Process under Conical Die

Tube inversion including free deformation under conical die is an advanced forming process for manufacturing complicated thin-walled parts with high strength/weight ratio, high efficiency, and good flexibility for size changing.However, the successful reality of forming process, the change of deforming mode and shape and size of part formedare mainly on the die angle. Based on the analysis of the forming process, the model of rigid-plastic FEM (finiteelement method) is established and a numerical simulation system is developed. The effect of die angle on the tubeinversion forming process is investigated with the code developed. The results of the effect of half die angle on shapeof free deformation zone and on deforming load are obtained. There is an optimal die angle (about 75 deg), whichmakes the forming load minimum.

椭圆波导FEM放大器的非线性特性研究

以椭圆波导、平板摇摆器为 FEM放大器的模型 ,导出了自洽的注波互作用三维非线性方程组。在此基础上编制了相应的程序。利用该程序分析了 FEM放大器的饱和功率、效率以及带宽等高频特性。考虑了摇摆器渐变、空间电荷波、电子初始速度零散对高频特性的影响。

基于Java的OOFEM框架模型研究

面向对象的有限元(OOFEM)通用框架的构造对于有限元算法和并行有限元的研究具有重要意义。该文利用Java和面向对象技术,初步实现了这种非线性有限元框架模型,并且对其理论基础、功能构造、类库实现和算法设计等进行了研究。算例表明:数值结果与理论值是吻合的,框架模型是正确的和可靠的。

A new beam element for analyzing geometrical and physical nonlinearity

Based on Timoshenko＇s beam theory and Vlasov＇s thin-walled member theory, a new model of spatial thin-walled beam element is developed for analyzing geometrical and physical nonlinearity, which incorporates an interior node and independent interpolations of bending angles and warp and takes diversified factors into consideration, such as traverse shear deformation, torsional shear deformation and their coupling, coupling of flexure and torsion, and the second shear stress. The geometrical nonlinear strain is formulated in updated Lagarange （UL） and the corresponding stiffness matrix is derived. The perfectly plastic model is used to account for physical nonlinearity, and the yield rule of von Mises and incremental relationship of Prandtle-Reuss are adopted. Elastoplastic stiffness matrix is obtained by numerical integration based on the finite segment method, and a finite element program is compiled. Numerical examples manifest that the proposed model is accurate and feasible in the analysis of thin-walled structures.

Evaluation of the Impact of Truck Overloading on Flexible Compacted Gravel Lateritic Soil’s Pavements by FEM with Cast3M^©

Within the framework of a FEM of the nonlinear behavior of lateritic pavement of Senegal, the effect of truck overloading is studied to estimate its impact on the deformability of road pavement on compacted gravel lateritic soils. For that purpose, various loading conditions were tested to measure the impact on the critical response parameters of road pavement design. The implementation of the models was realized with Cast3M©. This study allowed us to point out that the observed variations are linear and would help to plan in advance the impact of axle overloads for a better evaluation within the framework of the mechanistic (M. E.) design of pavements.

A Coupling Model of Nonlinear Wave and Sandy Seabed Dynamic Interaction

In the paper, a weak coupling numerical model is developed for the study of the nonlinear dynamic interaction between water waves and permeable sandy seabed. The wave field solveris based on the VOF （Volume of Fluid） method for continuity equation and the two-dimensional Reynolds Averaged Navier Stokes （RANS） equations with a k-ε closure. The free surface of cnoidal wave is traced through the PLIC-VOF （P/ecewise Linear/nterface Construction）. Blot＇s equations have been applied to solve the sandy seabed, and the u-p fmite dement formulations are derived by the application of the Galerkin weighted-residual procedure. The continuity of the pressure on the interface between fluid and porous medium domains is considered. Laboratory tests were performed to verify the proposed numerical model, and it is shown that the pore-water pressures and the wave heights computed by the VOF-FEM models are in good agreement with the experimental results. It is found that the proposed model is effective in predicting the seabed-nonlinear wave interaction and is able to handle the wave-breakwater-seabed interaction problem.

An Improved Numerical Simulation Mode of Nonlinear Wave with Consideration of High Order Terms

SUN Da-peng BAO Wei-bin, WU Hao and LI Yu-cheng （ In this paper the 0-1 combined BEM is adopted to subdivide the computational domain boundary, and to discretize the Green＇s integral expression based on Laplace equation. The FEM is used to subdivide the wave surface and deduce the surface equation which satisfies the nonlinear boundary conditions on the surface. The equations with potential function and wave surface height as an unknown quantity by application of Taylor expansion approach can be solved by iteration within the time step. In m-time iteration within the computational process of time step （n-1）At to nat, the results of the previous iteration are taken as the initial value of the two-order unknown terms in the present iteration. Thus, an improved tracking mode of nonlinear wave surface is estabIished, and numerical results of wave tank test indicate that this mode is improved obviously and is more precise than the previous numerical model which ignored the two-order unknown terms of wave surface location and velocity potential function in comparison with the theoretical values.

Nonlinear buckling finite element analysis of stiffened B-Al plates

Nonlinear buckling behavior of stiffened composite B-Al plates was analyzed by means of finite element analysis(FEA) method. In the method, the composite material was taken as B matrix into which Al fibers were embedded in different configurations. The laminated B-Al material in the form of rectangular plates was subjected to lateral compressive loading. It is observed that stiffeners have significant effect on the buckling behavior of plates under compressive loading and for various geometrical configurations. The stiffeners used in the modeling are one-sided and have rectangular cross-sections. It is found that there are physically important loading intervals and the critical buckling modes make transitions back and forth between stable and unstable states. Bifurcation buckling regions resulting from various configurations of fiber orientations and different plate aspect ratios are determined. The whole analysis is performed by using ANSYS finite element computations. Only the buckling patterns of stiffened plate configurations under simply supported boundary conditions are studied. Distributions of compressive stresses(σx) vs in-plane contractions(u) and compressive stresses(σx) vs out-of plane deflections(δ) are obtained. Nonlinear analysis of the C2 fiber configuration yields the safest critical buckling stress amongst C1, C2, C3 and C4 configurations. It is concluded that FEA method for the nonlinear buckling analysis generates accurate results.