金属成形过程自适应耦合无网格—有限元法数值模拟技术研究
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摘要
金属塑性成形技术具有生产效率高、材料利用率高、产品质量稳定等优点,而且还能有效改善工件的力学性能,在金属零件制造过程中占据了重要的地位。随着数值计算方法与计算机技术的不断发展,有限元模拟技术已被广泛地应用于塑性成形过程的分析和预测。然而有限元方法依赖于网格,当工件变形到一定程度的时候,对应的有限元网格将会产生畸变,严重影响计算精度,甚至导致计算中止,需要进行网格重划分。但是网格重划分存在相当的难度,而且会导致计算精度下降,并耗费一定的计算时间,给数值模拟过程带来困难。
无网格法仅基于离散节点的近似,不依赖于网格,能够避免有限元法中因网格畸变带来的困扰,特别适于金属体积成形这类大变形问题的模拟分析。由于摆脱了几何拓扑关系的束缚,无网格法在节点的布置方面也存在很大的灵活性,具有较强的自适应分析能力。尽管具有上述优势,无网格法计算效率却远低于有限元法,从而限制了其进一步的发展和应用。
本论文尝试将无网格法与有限元法相结合,应用于二维局部体积成形过程的数值模拟。在现有耦合方法的基础上,根据工件变形情况实现有限元与无网格计算区域的动态转换与耦合,提出基于刚(粘)塑性流动理论的自适应耦合无网格-有限元方法,发展了数值模拟中的关键技术与算法。
将刚(粘)塑性流动理论与耦合无网格-有限元(EFG-FE)法相结合,根据塑性力学与变分原理,推导离散化的刚度矩阵与数值求解方程,建立二维金属塑性成形问题的刚(粘)塑性耦合无网格-有限元方法。采用修正的罚函数法施加体积不可压缩条件,边界奇异核方法处理本质边界条件。
研究、论述了数值模拟中的若干关键处理技术。提出一种无网格节点影响域的动态确定方法,有效反映节点分布的稀疏程度和局部特性,同时适用于圆形和矩形影响域;根据无网格节点的空间位置分布,动态生成规则背景积分网格;根据节点分布密度,自适应地确定对应的高斯积分阶次;实现动态边界的自动识别与接触处理。
提出自适应的耦合无网格-有限元法,分别利用无网格法计算大变形问题的能力以及有限元法较高的计算效率,发挥这两种数值方法各自的优势。根据塑性变形程度,将发生大变形的有限元计算区域自动转换为无网格计算区域;根据等效应变速率分布情况,将变形不显著的无网格计算区域转换为有限元计算区域。详尽阐述了实现这两种自适应转换的完整方案,包括判断准则、区域划分、转换算法等。对径向挤压、正挤压、反挤压、复合挤压、锻造等一系列典型的局部体积成形过程进行模拟计算,给出了数值算例,与有限元软件模拟和物理实验测量的结果进行比较,充分证明该方法的优点和可靠性。
推导了塑性成形过程传热问题的求解公式,给出金属成形过程热力耦合分析的流程与步骤。对轴对称挤压问题进行热力耦合分析,拓展了自适应耦合方法的应用范围。
本论文的研究结果表明,自适应耦合无网格-有限元法既能够发挥无网格法处理大变形问题的能力,又能够利用有限元法计算效率高的优势,有效地应用于金属局部体积成形过程的数值模拟。
Metal forming technology plays an important role in the manufacturing industry. It has merits on high productivity, stable quality and effective utilization of raw material. The mechanical performance of the metal is also improved in the forming processes. With the development of numerical methods and IT technology, simulation technology based on the finite element method (FEM) has been widely used in the analysis and prediction of metal forming processes. However, the finite element analysis is based on topological meshes which tend to be distorted in the forming processes. Distorted meshes lead to the deterioration of computational accuracy and even the halt of simulations. As a result, burdensome remeshing procedures have to be implemented. Nevertheless, remeshing remains as a challenging task, particularly for 3D problems. In addition, extra loss of accuracy and efficiency is inevitable.
In meshless methods, approximations are constructed in terms of discrete nodes. It is free of the trouble caused by mesh distortion. Meshless methods exhibit their unique advantages in the analysis of bulk metal forming where large deformation takes place frequently. As meshless methods are free of topology, the spatial layout of nodes is flexible. This property endows meshless methods with the capabilities of adaptive analysis. Despite these advantages, the computational efficiency of meshless methods is much lower than that of FEM. This disadvantage restricts their further development and application.
In this dissertation, efforts have been made to combine the EFG method with the FEM in the analysis of 2D local bulk metal forming. Based on the coupling methods which have been published, it is intended to implement the dynamic conversion from FEM modeling regions to EFG ones according to the deformation level. An adaptive EFG-FE coupling method based on the rigid-visco plastic flow theory was proposed. Key techniques and algorithms in the numerical analysis were developed.
The rigid-visco plastic EFG-FE coupling method for 2D metal forming processes was established. Discretized stiffness matrices and equations are derived according to the mechanics of plasticity and variational theory. The modified penalty function method is used to enforce the incompressible constraints. The boundary singular kernel method is used to impose the essential boundary conditions.
Key techniques in the numerical simulation are studied and given in detail. An algorithm is proposed to dynamically determine the sizes of nodal supports, which reflect the node density and local characteristics. The algorithm is effective for both circular supports and rectangular supports. Two schemes are presented to generate background cells and select the order of Gaussian quadrature, respectively, according to the spatial distribution of EFG nodes. Automatic contact treatments are achieved on the dynamic interface between tools and billets.
The adaptive EFG-FE coupling method is proposed. It retains both the capability of handling large deformation by meshless methods and high computational efficiency by FEM. During the numerical simulations, FEM elements are converted to EFG nodes automatically according to the level of distortion. Meanwhile, EFG regions are partially reverted to FEM ones according to the strain rate distribution. The schemes to implement adaptive conversion and coupling are elaborated. Numerical examples of local bulk metal forming processes including lateral extrusion, forward extrusion, backward extrusion, forward-backward extrusion and forging were given. The numerical results were compared with the FEM solutions and experimental data. The accuracy and merits of numerical simulations were demonstrated.
The formulations for the heat transfer in the metal forming processes were derived. The procedures for thermo-mechanical analysis were given. The thermo-mechanical analysis of axis-symmetric extrusion was implemented.
The research in this dissertation shows that the adaptive EFG-FE coupling method makes use of the advantages of both meshless methods and FEM. It is effective for the numerical analysis of local bulk metal forming processes.
无网格法仅基于离散节点的近似,不依赖于网格,能够避免有限元法中因网格畸变带来的困扰,特别适于金属体积成形这类大变形问题的模拟分析。由于摆脱了几何拓扑关系的束缚,无网格法在节点的布置方面也存在很大的灵活性,具有较强的自适应分析能力。尽管具有上述优势,无网格法计算效率却远低于有限元法,从而限制了其进一步的发展和应用。
本论文尝试将无网格法与有限元法相结合,应用于二维局部体积成形过程的数值模拟。在现有耦合方法的基础上,根据工件变形情况实现有限元与无网格计算区域的动态转换与耦合,提出基于刚(粘)塑性流动理论的自适应耦合无网格-有限元方法,发展了数值模拟中的关键技术与算法。
将刚(粘)塑性流动理论与耦合无网格-有限元(EFG-FE)法相结合,根据塑性力学与变分原理,推导离散化的刚度矩阵与数值求解方程,建立二维金属塑性成形问题的刚(粘)塑性耦合无网格-有限元方法。采用修正的罚函数法施加体积不可压缩条件,边界奇异核方法处理本质边界条件。
研究、论述了数值模拟中的若干关键处理技术。提出一种无网格节点影响域的动态确定方法,有效反映节点分布的稀疏程度和局部特性,同时适用于圆形和矩形影响域;根据无网格节点的空间位置分布,动态生成规则背景积分网格;根据节点分布密度,自适应地确定对应的高斯积分阶次;实现动态边界的自动识别与接触处理。
提出自适应的耦合无网格-有限元法,分别利用无网格法计算大变形问题的能力以及有限元法较高的计算效率,发挥这两种数值方法各自的优势。根据塑性变形程度,将发生大变形的有限元计算区域自动转换为无网格计算区域;根据等效应变速率分布情况,将变形不显著的无网格计算区域转换为有限元计算区域。详尽阐述了实现这两种自适应转换的完整方案,包括判断准则、区域划分、转换算法等。对径向挤压、正挤压、反挤压、复合挤压、锻造等一系列典型的局部体积成形过程进行模拟计算,给出了数值算例,与有限元软件模拟和物理实验测量的结果进行比较,充分证明该方法的优点和可靠性。
推导了塑性成形过程传热问题的求解公式,给出金属成形过程热力耦合分析的流程与步骤。对轴对称挤压问题进行热力耦合分析,拓展了自适应耦合方法的应用范围。
本论文的研究结果表明,自适应耦合无网格-有限元法既能够发挥无网格法处理大变形问题的能力,又能够利用有限元法计算效率高的优势,有效地应用于金属局部体积成形过程的数值模拟。
Metal forming technology plays an important role in the manufacturing industry. It has merits on high productivity, stable quality and effective utilization of raw material. The mechanical performance of the metal is also improved in the forming processes. With the development of numerical methods and IT technology, simulation technology based on the finite element method (FEM) has been widely used in the analysis and prediction of metal forming processes. However, the finite element analysis is based on topological meshes which tend to be distorted in the forming processes. Distorted meshes lead to the deterioration of computational accuracy and even the halt of simulations. As a result, burdensome remeshing procedures have to be implemented. Nevertheless, remeshing remains as a challenging task, particularly for 3D problems. In addition, extra loss of accuracy and efficiency is inevitable.
In meshless methods, approximations are constructed in terms of discrete nodes. It is free of the trouble caused by mesh distortion. Meshless methods exhibit their unique advantages in the analysis of bulk metal forming where large deformation takes place frequently. As meshless methods are free of topology, the spatial layout of nodes is flexible. This property endows meshless methods with the capabilities of adaptive analysis. Despite these advantages, the computational efficiency of meshless methods is much lower than that of FEM. This disadvantage restricts their further development and application.
In this dissertation, efforts have been made to combine the EFG method with the FEM in the analysis of 2D local bulk metal forming. Based on the coupling methods which have been published, it is intended to implement the dynamic conversion from FEM modeling regions to EFG ones according to the deformation level. An adaptive EFG-FE coupling method based on the rigid-visco plastic flow theory was proposed. Key techniques and algorithms in the numerical analysis were developed.
The rigid-visco plastic EFG-FE coupling method for 2D metal forming processes was established. Discretized stiffness matrices and equations are derived according to the mechanics of plasticity and variational theory. The modified penalty function method is used to enforce the incompressible constraints. The boundary singular kernel method is used to impose the essential boundary conditions.
Key techniques in the numerical simulation are studied and given in detail. An algorithm is proposed to dynamically determine the sizes of nodal supports, which reflect the node density and local characteristics. The algorithm is effective for both circular supports and rectangular supports. Two schemes are presented to generate background cells and select the order of Gaussian quadrature, respectively, according to the spatial distribution of EFG nodes. Automatic contact treatments are achieved on the dynamic interface between tools and billets.
The adaptive EFG-FE coupling method is proposed. It retains both the capability of handling large deformation by meshless methods and high computational efficiency by FEM. During the numerical simulations, FEM elements are converted to EFG nodes automatically according to the level of distortion. Meanwhile, EFG regions are partially reverted to FEM ones according to the strain rate distribution. The schemes to implement adaptive conversion and coupling are elaborated. Numerical examples of local bulk metal forming processes including lateral extrusion, forward extrusion, backward extrusion, forward-backward extrusion and forging were given. The numerical results were compared with the FEM solutions and experimental data. The accuracy and merits of numerical simulations were demonstrated.
The formulations for the heat transfer in the metal forming processes were derived. The procedures for thermo-mechanical analysis were given. The thermo-mechanical analysis of axis-symmetric extrusion was implemented.
The research in this dissertation shows that the adaptive EFG-FE coupling method makes use of the advantages of both meshless methods and FEM. It is effective for the numerical analysis of local bulk metal forming processes.
引文
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