金属塑性成形过程无网格伽辽金法数值模拟技术研究

将无网格伽辽金法与刚(粘)塑性流动理论相结合,对无网格伽辽金法在金属塑性成形过程数值模拟中的应用技术进行了研究,分别采用混合变换法和罚函数法实现速度边界条件和体积不变条件,提出了基于刚(粘)塑性力学流动理论的无网格伽辽金法,给出了金属塑性成形无网格伽辽金法数值模拟的关键算法,拓展了无网格方法在金属成形领域的应用范围。典型算例的数值计算结果表明了方法的可行性。     

刚(粘)塑性无网格伽辽金方法及其关键技术研究与应用

在国家杰出青年科学基金资助项目《塑性加工工艺及设备》(No.50425517)，以及国家自然科学基金资助项目《金属体积成形过程的刚(粘)塑性无网格伽辽金方法数值模拟理论及其关键技术研究》(No.50575125)支持下，开展刚(粘)塑性无网格伽辽金方法及其关键技术与应用的研究报告，对刚(粘)塑性无网格伽辽金方法的基础理论、数学模型建立方法、关键处理技术在金属塑性成形过程中应用研究的成果。 将无网格伽辽金方法引入塑性成形过程模拟，提出基于刚(粘)塑性理论的无网格伽辽金方法，推导刚度矩阵方程和求解列式。利用变换法施加本质边界条件，采用反正切摩擦模型描述摩擦力边界条件。对于模具边界任意的塑性成形过程，在局部坐标系下施加摩擦力边界条件，给出局部坐标系和整体坐标系的变换矩阵，解决了模具形状任意的二维塑性成形问题摩擦力边界条件的施加问题。采用直接迭代法获得初始速度场，利用Newton Raphson迭代方法求解刚度方程，给出模拟等温塑性成形问题的分析步骤。对于中高温条件下的塑性成形过程，推导出刚(粘)塑性无网格伽辽金方法热力耦合分析模型，给出热力     

二维无网格伽辽金-有限元耦合方法的研究

论述无网格伽辽金方法（element-free Galerkin method,EFG）的基本原理－－移动最小二乘原理（moving leastsquare,MLS）和EFG方法的位移近似函数，给出变分方程及离散方程。对无网格伽辽金－有限元耦合（EFG－FE coupling）方法进行详细阐述。编制相应程序，通过算例表明拉格朗日乘子对强制边界条件的作用及无网格伽辽金方法在权函数参数变化时的收敛特性，论证无网格伽辽金－有限元耦合的有效性。     

刚塑性无网格方法中体积闭锁问题的缓解算法

将无网格伽辽金方法引入金属塑性成形过程分析,在给出基于刚塑性理论的无网格伽辽金方法及其基本理论方程的基础上,重点研究应用无网格方法分析金属塑性成形问题时所面临体积闭锁问题的缓解算法,采用体积应变率映射方法,对能量速率泛函中的体积应变率进行修正处理,通过将速度场计算的体积应变率映射到低维空间,降低独立约束方程数目,从而建立体积闭锁现象的缓解算法。应用所建立的方法对典型锻造过程进行了无网格分析,结果表明,该算法能够有效解决体积闭锁问题。     

大变形成形过程刚塑性无网格伽辽金方法

在非稳态大变形塑性成形过程中，由于节点的大范围移动和流动的非均匀性，导致分析精度下降。针对移动最小二乘近似精度的提高，尤其是边界附近节点分析近似精度的提高，提出了相应的处理方案，以保证分析的精度。通过采用影响域节点控制方法以及边界节点分布密度动态控制方法，实现了塑性成形过程的无网格伽辽金方法的自适应分析。对拉普拉斯方程及典型的大变形成形过程进行了分析，通过与拉普拉斯方程解析解和相应的商品化刚塑性有限元软件Deform的分析结果进行对比，验证了处理方案的正确性。     

无网格伽辽金方法在线弹性断裂力学中的应用研究

通过对移动最小二乘形函数进行局部修正,将混合变换法应用于无网格伽辽金方法,给出分析线弹性断裂力学问题的有效的无网格伽辽金方法。这一方法克服了无网格伽辽金方法中常用的拉格朗日乘子法和罚函数法的缺点,实现了本质边界条件在节点处的精确施加。运用线弹性断裂力学理论,采用基于t-分布的新型权函数和部分扩展基函数,对有限板单边裂纹的应力强度因子和拉剪复合型裂纹的扩展进行分析。由于该方法仅需节点信息,而不需要节点的连接信息,从而避免了有限元方法中的网格重构,大大简化了裂纹扩展的分析过程。数值计算结果表明了方法的有效性。     

用Taylor展开随机无网格法和免疫算法分析结构可靠性

首先用Taylor展开随机无网格伽辽金法(Taylor expansion stochastic element-free Galerkin method,TSEFGM)进行随机结构分析.在无网格伽辽金法中,所求解问题的域由分布的节点表示,并采用移动最小二乘函数近似试函数.以及用罚函数法施加本质边界条件.同时利用Taylor展开法,建立随机结构分析的Taylor展开随机无网格伽辽金法;然后应用人工免疫遗传算法对结构可靠性进行分析.人工免疫遗传算法是一种新的综合人工免疫算法和遗传算法的智能优化算法,它避免了遗传算法易出现早熟、搜索效率低和不能很好地保持个体多样性等问题.数值实例表明,在随机结构与可靠性分析方面,Tlaylor展开随机无网格伽辽金法与人工免疫遗传算法具有明显的优势和广泛的应用前景.     

基于一致径向基函数的金属塑性成形过程无网格方法分析

径向基函数满足δ条件,可以直接施加本质边界条件.通过耦合多项式基函数可以精确重构任意多项式.将无网格伽辽金方法引入到塑性成形过程模拟,结合刚塑性材料的假设,提出基于一致径向基函数的无网格刚塑性伽辽金方法.采用体积应变率映射法处理体积不可压缩条件;采用反正切摩擦模型在局部坐标系下施加摩擦力边界条件,实现任意边界形状的塑性成形过程模拟.对典型塑性成形过程进行无网格方法分析,并与刚塑性有限元方法及试验数据进行比较,验证了建立方法的可行性.     

压电裂纹的插值型无单元伽辽金比例边界法分析

为了获得更为精确高效的压电裂纹分析方法,基于改进的插值型移动最小二乘法,提出压电材料断裂分析的插值型无单元伽辽金比例边界法,这种方法可以直接根据定义求得应力强度因子和电位移强度因子。该方法只需要在求解域的边界上采用无单元伽辽金法进行数值离散,减少了一个空间维数,并且不需要边界元法所需要的基本解。在没有离散的径向采用解析的方法求解,从而具有较高的计算精度。在改进的插值型移动最小二乘法中,不仅形函数满足Kronecker delta函数性质,而且权函数是非奇异的。此外,改进的插值型移动最小二乘法计算形函数时待定系数比传统的移动最小二乘法少一个。给出数值算例,并验证了所提方法的有效性和正确性。     

非均质材料无网格Galerkin法

提出了采用无网格Galerkin方法来分析非均质材料。无网格伽辽金法（EFGM）是近些年发展起来的一种数值算法，它采用移动的最小二乘法构造形函数，从能量泛函的弱变分形式中得到控制方程，该法只需节点信息，不需将节点连成单元。在积分网格中，取高斯点的材料参数来模拟材料特性的变化。算例的结果显示用该法来分析非均质材料得到的结果精度高，表明该方法在非均质材料领域有着广阔的应用前景。     

Numerical simulation of three-dimensional bulk forming processes by the element-free Galerkin method

A new approach for simulating three-dimensional (3D) bulk metal forming processes is proposed by combining element-free Galerkin method (EFGM) with the flow theory of 3D rigid-plastic/viscoplastic mechanics. Different from the conventional rigid-plastic FEM, the velocity field is constructed by the moving least-squares (MLS) approximation. Special emphasis is placed on the treatments of essential boundary conditions, incompressibility constraint and friction boundaries. The stiffness equation for the analysis of 3D bulk metal forming using EFGM is derived and its key algorithms are given. To test the validity of the proposed meshless approach, a typical 3D upsetting forming process is analyzed and the numerical results are compared with those obtained by commercialized rigid-plastic FEM software Deform^3D. As results show, when handling 3D plastic deformations, the proposed approach eliminates the need of expensive meshing and remeshing procedures unavoidable in conventional FEM, and still provides results that are in good agreement with finite element predictions.     

刚塑性成形模拟中有限元和无网格迦辽金法的自动耦合算法

利用有限元法分析金属的刚塑性问题时,在变形的高梯度区域单元容易严重畸变,这极大地降低了分析精度.在刚塑性有限元方法的框架中,文中根据计算增量步的网格质量,提出金属刚塑性有限元和无网格迦辽金法的自动耦合算法,在单元严重畸变的区域转换为无网格迦辽金法进行计算.数值实例表明:算法在很大程度上既保持了有限元法的计算效率,又能够...     

ADAPTIVE RIGID-PLASTIC MESHLESS GALERKIN METHOD AND ITS APPLICATION IN ANALYSIS OF EXTRUSION PROCESSES

Under the hypothesis of the rigid-plastic material,specific efforts are placed on the deve-lopments of the key simulation techniques of the meshless Galerkin method because of the complexity of the deformation process as well as the generality and atomization of the simulation procedures for non-steady state large deformation plastic processes,therefore,an adaptive rigid meshless Galerkin method is developed. The influence domain control method is used in the least square approximation by dynamic evaluation of the magnitude of the influence domain and the effective control of the amount and the positions of the points in the least square approximation in order to improve approxi-mation precision. The amount of the Gauss integration points in the discrete domain is maintained in a considerable magnitude in order to ensure the integration precision in the discrete domain. The length of the frictional boundary of the plastic deformation process may be getting longer when its deforma-tion is getting severe. Thus,the densities of the boundary points of some places get lower. The adap-tive boundary points setting method is employed to improve the approximation precision of the boundary points and enhance the constraint of the boundary condition by adaptive control of boun-dary point density. Some typical extrusion processes are analyzed,detail simulation results such as the deformation field,velocity field,effective strain field,effective strain rate field,the volume loss curve and load-stroke curve are obtained. The effectiveness of the method developed is demonstrated and the precision of the meshless simulation is proved by overall comparison with the results obtained by using the commercial software deform.     

直角平面内圆形刚性动夹杂对边界出平面点源载荷的动态响应

采用复变函数法和多极坐标移动技术研究二维直角平面区域内可动圆形刚性夹杂在边界出平面点源载荷作用下的动态响应问题.首先构造出直角平面区域内不含有夹杂时满足直角边界应力条件的格林(Green)函数解;其次求解波动方程边值问题,建立直角平面区域内含有夹杂时满足直边界应力自由条件的散射波解,利用叠加原理写出问题的总波场.借助于夹杂边界处的位移条件和夹杂运动的动力学条件,确定夹杂运动的位移幅度和散射波解中的未知系数.给出的算例结果表明本文方法的有效实用性.     

Research on rigid/visco-plastic element-free Galerkin method and key simulation techniques for three-dimensional bulk metal forming processes

The element-free Galerkin method is introduced into the analysis of three-dimensional bulk metal forming processes according to flow formulation for rigid/visco-plastic material. The transformation method is used to impose the essential boundary condition directly. The stiffness matrix equation is derived according to incomplete generalized variational principle. And the corresponding key simulation techniques are developed. The case that matrix A(x) appears irreversible is discussed, and the approaches for treating with this problem are given. Volumetric strain rate method is proposed for releasing the volume locking problem. The method for describing shapes of dies is presented. In order to impose arbitrarily shaped boundary conditions in three-dimensional problems, the local coordinate system is established and the transformation matrix between the local coordinate system and the global coordinate system is calculated. Methods for exerting velocity and frictional contact conditions are introduced. Dynamic adjustment techniques for the boundary of the workpiece including the contact/detachment judgment criterion and the method for modifying the contact nodes?? positions are given. Finally, the effectiveness of the method and key techniques is demonstrated by simulating a two-stage three-dimensional forging process.     

基于积分弱形式的无网格-有限元法耦合方法研究

无网格伽辽金法是基于移动最小二乘法的一种求解偏微分方程非常有效的方法,但是对于一些规模较大的问题,其计算费用较高,将无网格法与有限元耦合可以极大提高求解效率.文中根据D. Hegen提出的基于积分弱形式耦合方法,进一步明确处理耦合区域部分的数学、物理意义, 有效地引入一个综合控制因子反映权函数的紧支性, 并经算例验证方法的正确性及控制因子的有效性.