无网格法在金属塑性成形数值模拟中的应用研究
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摘要
金属塑性成形技术在金属零件的制造过程中起着十分重要的作用。为了预测各种过程参数对金属流动的影响,必须采用数值分析技术对成形过程进行模拟。由于金属成形过程是一个复杂的物理过程,涉及到几何非线性、物理非线性和接触非线性等。目前有限元数值模拟技术在塑性成形的分析研究中得到了非常广泛的应用,但由于有限元方法是基于网格的数值方法,当网格变形达到一定程度时,计算精度将严重受损,甚至导致计算无法进行下去。此时必须对畸变网格进行网格重划分。而网格重划分不仅耗时、计算精度受损,特别对于三维网格重划分技术至今仍是个世界性难题。
鉴于有限元法对网格的依赖性,无网格法成为近年来学术界的研究热点。无网格法的近似函数没有网格依赖性,减少了因网格畸变而引起的困难,非常适用于处理高速碰撞、动态断裂、塑性流动、流固耦合等涉及大变形的各类应用问题。
本文首先详细论述了配点型无网格法的基本原理及其在金属体积成形二维轴对称问题中的实现过程,包括重构核近似函数的形函数的构造及其一阶、二阶导数,摩擦接触条件的处理等关键性问题的求解。推导了弹塑性、刚塑性无网格法配点格式。并分别通过圆环镦粗和气门镦挤两个算例对算法的可行性进行了验证。
本文详细论述了无网格法的动力显式计算格式,推导了塑性成形过程传热问题的无网格列式,结合有限元方法中常用的金属塑性变形与热传导耦合方法对圆环镦粗问题进行了无网格法热力耦合分析。并通过与前人实验结果的对比,验证了方法的可行性。
推导了三维重构核近似函数的形函数及其形函数的一阶、二阶导数,给出了基于弹塑性材料的无网格法三维数值实现过程,并对时间步长的控制,摩擦边界条件的处理,节点影响域半径的控制等关键性问题进行了详细的阐述。实现了配点型无网格法在三维金属塑性成形过程中的数值模拟。对C型槽型材的挤压过程进行了数值模拟,并与有限元法计算结果进行了对比。最后以彩色塑泥做为模拟材料,采用分层制坯法,对挤压过程进行了物理模拟,结果表明,与数值模拟计算结果比较吻合。
针对无网格法计算结果只包含节点信息,节点之间并没有拓扑关系,从而导致后处理可视化困难的问题,提出了结合模具干涉法和网格质量控制法来生成Delaunay四面体对无网格法计算结果进行可视化后处理的办法,给出了实现该方法的具体程序流程图,并通过实际三维无网格法计算结果验证了该方法的有效性和可行性。
提出了一种新型形函数,详细论述了该形函数的构造方法,论证了该形函数满足的一些特性,推导了该形函数的基于Galerkin离散方案的等效积分弱形式并给出了详细的实施步骤和如何消除该形函数奇异性的方法。该方法中形函数的计算不涉及复杂的矩阵求逆过程,由于具备插值特性,可以直接处理边界条件。通过数值算例,分析了节点影响域半径对求解精度的影响,并与移动最小二乘近似函数比较,验证了该形函数的计算效率和计算精度。这是构造新的无网格法形函数的一个有益的尝试。
The metal plastic forming technique is very important to the manufacturing process of metal parts. In order to predict the influence of various processing parameters to metal flow, the numerical simulation technique is necessary. But the metal forming is a very complex physical process, including non-linear geometry, physical and contact, etc. In present, finite element analysis technique is widely applied in the research of plastic forming. But the finite element method is a numerical method based on mesh. When the mesh distorted seriously, the computation accuracy will lost, even the computation process can not be continued. Remesh process for the distorted mesh is necessary in order to continue the simulation. The remesh procedure is a very time consuming process especially to three dimensions remesh technique.
According to finite element method depends on the mesh, more and more researchers begin to focus on the meshfree method. The shape function of meshfree method is without employment of mesh, which is very suitable for solving the large deformation problems such as high speed impact, dynamic crack expand, plastic forming, solid-liquid coupled, etc.
Based on the detailed explain of basic theory and numerical procedure of meshfree method, the application of metal plastic forming numerical simulation procedure using collocation meshfree method based on reproducing kernel particle functions is researched deeply. Corresponding simulation code is developed, two dimensional symmetric and three dimensional problems are solved. Satisfied results show the feasibility of the method mentioned in this paper.
The basic theory of collocation meshfree method and realization procedure in two dimensional symmetric problem of metal bulk forming are explained, including the construction of shape function and its first-order and second-order derivation, the treatment of friction and contact, etc. The collocation equations of elastic-plastic material and rigid-plastic material are deduced. The feasibility of the method is proved from two numerical examples.
The explicit dynamic and heat transfer equations of metal plastic forming process using meshfree method are explained. Thermal-mechanical coupled meshfree analysis of ring compress process is realized combined with the commonly used metal deformation and heat transfer coupling algorithm in finite element method. The feasibility is proved compared with the experimental results of Male.
The three dimensional equations of reproducing kernel particle function and its first-order and second-order derivation is deduced. The numerical implement procedure of three dimensional collocation meshfree method based on elastic-plastic material is given. Some key problems such as the control of time step, the treatment of friction-contact, the control of nodal influence radio, etc are explained in detail. A C-shape profile metal extrusion process using collocation meshfree method is analyzed and compared with the simulation results by finite element method. Using color plasticine, physical simulation model is carried out for the extrusion process. A method of layer-built billet has been proposed and effectively used. A good agreement of numerical simulation results and physical simulation results show the validity of the meshfree method.
According to the absence of mesh and lack of connection information between the sprinkled nodes, on the other hand, make post-processing of meshfree results such as displacement, stress and strain in the whole domain an issue needs additional effort. A mold interpenetration and mesh quality control method based on incremental algorithm to build Delaunay tetrahedrons are proposed. The detailed flowchart of realizing the method is given. The numerical result shows the topological relationship produced by this method can describe the real shape of the discrete nodes very well.
A new shape function is proposed. The construction procedure of this shape function is discussed. The characteristic of this shape function is proved. The equivalent integral weak form of discrete scheme based on Galerkin is derivated. Detailed implementary steps and the elimination of singularity are given. Without solving the complex anti-matrix, the procedure is simplified. Because of the interpolation property of this function, the essential boundary conditions can be imposed directly. According to a numerical example, the effects of the influence radio of domain to the accuracy are analyzed. Compared with the moving least square function, the effective and accuracy are proved of this shape function. A new way of researching shape function of meshfree method is proposed.
鉴于有限元法对网格的依赖性,无网格法成为近年来学术界的研究热点。无网格法的近似函数没有网格依赖性,减少了因网格畸变而引起的困难,非常适用于处理高速碰撞、动态断裂、塑性流动、流固耦合等涉及大变形的各类应用问题。
本文首先详细论述了配点型无网格法的基本原理及其在金属体积成形二维轴对称问题中的实现过程,包括重构核近似函数的形函数的构造及其一阶、二阶导数,摩擦接触条件的处理等关键性问题的求解。推导了弹塑性、刚塑性无网格法配点格式。并分别通过圆环镦粗和气门镦挤两个算例对算法的可行性进行了验证。
本文详细论述了无网格法的动力显式计算格式,推导了塑性成形过程传热问题的无网格列式,结合有限元方法中常用的金属塑性变形与热传导耦合方法对圆环镦粗问题进行了无网格法热力耦合分析。并通过与前人实验结果的对比,验证了方法的可行性。
推导了三维重构核近似函数的形函数及其形函数的一阶、二阶导数,给出了基于弹塑性材料的无网格法三维数值实现过程,并对时间步长的控制,摩擦边界条件的处理,节点影响域半径的控制等关键性问题进行了详细的阐述。实现了配点型无网格法在三维金属塑性成形过程中的数值模拟。对C型槽型材的挤压过程进行了数值模拟,并与有限元法计算结果进行了对比。最后以彩色塑泥做为模拟材料,采用分层制坯法,对挤压过程进行了物理模拟,结果表明,与数值模拟计算结果比较吻合。
针对无网格法计算结果只包含节点信息,节点之间并没有拓扑关系,从而导致后处理可视化困难的问题,提出了结合模具干涉法和网格质量控制法来生成Delaunay四面体对无网格法计算结果进行可视化后处理的办法,给出了实现该方法的具体程序流程图,并通过实际三维无网格法计算结果验证了该方法的有效性和可行性。
提出了一种新型形函数,详细论述了该形函数的构造方法,论证了该形函数满足的一些特性,推导了该形函数的基于Galerkin离散方案的等效积分弱形式并给出了详细的实施步骤和如何消除该形函数奇异性的方法。该方法中形函数的计算不涉及复杂的矩阵求逆过程,由于具备插值特性,可以直接处理边界条件。通过数值算例,分析了节点影响域半径对求解精度的影响,并与移动最小二乘近似函数比较,验证了该形函数的计算效率和计算精度。这是构造新的无网格法形函数的一个有益的尝试。
The metal plastic forming technique is very important to the manufacturing process of metal parts. In order to predict the influence of various processing parameters to metal flow, the numerical simulation technique is necessary. But the metal forming is a very complex physical process, including non-linear geometry, physical and contact, etc. In present, finite element analysis technique is widely applied in the research of plastic forming. But the finite element method is a numerical method based on mesh. When the mesh distorted seriously, the computation accuracy will lost, even the computation process can not be continued. Remesh process for the distorted mesh is necessary in order to continue the simulation. The remesh procedure is a very time consuming process especially to three dimensions remesh technique.
According to finite element method depends on the mesh, more and more researchers begin to focus on the meshfree method. The shape function of meshfree method is without employment of mesh, which is very suitable for solving the large deformation problems such as high speed impact, dynamic crack expand, plastic forming, solid-liquid coupled, etc.
Based on the detailed explain of basic theory and numerical procedure of meshfree method, the application of metal plastic forming numerical simulation procedure using collocation meshfree method based on reproducing kernel particle functions is researched deeply. Corresponding simulation code is developed, two dimensional symmetric and three dimensional problems are solved. Satisfied results show the feasibility of the method mentioned in this paper.
The basic theory of collocation meshfree method and realization procedure in two dimensional symmetric problem of metal bulk forming are explained, including the construction of shape function and its first-order and second-order derivation, the treatment of friction and contact, etc. The collocation equations of elastic-plastic material and rigid-plastic material are deduced. The feasibility of the method is proved from two numerical examples.
The explicit dynamic and heat transfer equations of metal plastic forming process using meshfree method are explained. Thermal-mechanical coupled meshfree analysis of ring compress process is realized combined with the commonly used metal deformation and heat transfer coupling algorithm in finite element method. The feasibility is proved compared with the experimental results of Male.
The three dimensional equations of reproducing kernel particle function and its first-order and second-order derivation is deduced. The numerical implement procedure of three dimensional collocation meshfree method based on elastic-plastic material is given. Some key problems such as the control of time step, the treatment of friction-contact, the control of nodal influence radio, etc are explained in detail. A C-shape profile metal extrusion process using collocation meshfree method is analyzed and compared with the simulation results by finite element method. Using color plasticine, physical simulation model is carried out for the extrusion process. A method of layer-built billet has been proposed and effectively used. A good agreement of numerical simulation results and physical simulation results show the validity of the meshfree method.
According to the absence of mesh and lack of connection information between the sprinkled nodes, on the other hand, make post-processing of meshfree results such as displacement, stress and strain in the whole domain an issue needs additional effort. A mold interpenetration and mesh quality control method based on incremental algorithm to build Delaunay tetrahedrons are proposed. The detailed flowchart of realizing the method is given. The numerical result shows the topological relationship produced by this method can describe the real shape of the discrete nodes very well.
A new shape function is proposed. The construction procedure of this shape function is discussed. The characteristic of this shape function is proved. The equivalent integral weak form of discrete scheme based on Galerkin is derivated. Detailed implementary steps and the elimination of singularity are given. Without solving the complex anti-matrix, the procedure is simplified. Because of the interpolation property of this function, the essential boundary conditions can be imposed directly. According to a numerical example, the effects of the influence radio of domain to the accuracy are analyzed. Compared with the moving least square function, the effective and accuracy are proved of this shape function. A new way of researching shape function of meshfree method is proposed.
引文
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