基于非结构网格和节点积分算法的电磁成形数值模拟关键技术研究

Electromagnetic forming (EMF) is a complex dynamic procedure which involves the coupled interaction of electromagnetic, stress and thermal fields. The adoption of finite element method (FEM) and structured mesh in EMF numerical simulation is computationally expensive and is also hard to deal with mesh distortion, so the application in complex engineering problems is fairly beyond the reach of FEM with structured mesh. Unstructured mesh is convenient in pro-processing and can be used to approximate complicated geometries, and nodal integration method has fairly attractive features. So based on unstructured mesh and nodal integration method, this project is going to study on high efficient algorithms concerning the features and difficulties of EMF numerical simulation. In electromagnetic field analysis, a stable nodal integration method is going to be proposed based on gradient compensate technique to ensure computation accuracy, and the multigrid method is going to be adopted in equation solving to improve the efficiency. In stress field analysis, the nodal integration method, which is high efficient and insensitive to mesh distortion, is going to be used for explicit dynamic computation, and the adaptive method is going to be adopted to handle local geometric features to avoid model distortion during simulation. And then, corresponding analysis system is going to be integrated based on proposed algorithms. Research results of this project will allow full play to the advantage of unstructured mesh and nodal integration method, and achieve the application of traditional unstructured mesh on complex multi-field coupling analysis. And finally, this project can provide technical support for the CAD/CAE integration high efficient calculation of EMF procedure.

电磁成形是涉及电磁、结构、温度多个物理场耦合的复杂动态过程，采用有限元法和结构网格完成其数值模拟存在计算成本高且难以应对网格畸变的缺陷，在复杂的工程实际问题中难以胜任。本项目拟基于前处理简便、可逼近复杂几何特征的非结构网格，以具备优良特性的节点积分算法为基础，针对电磁成形的特点和难点进行高效计算方法研究。电磁场计算中，拟根据梯度补偿技术构造稳定节点积分算法以保证分析精度，并拟采用多重网格法完成方程求解以提高计算效率。结构场分析时，拟利用高效率、抗网格畸变的节点积分算法完成显示动态模拟，并拟采用自适应策略对模型小特征进行处理以避免模拟过程中模型失真。并拟对相关算法进行集成，形成相应的软件分析系统。该项目的研究成果将能够充分发挥非结构网格和节点积分算法的优势，解决传统非结构网格数值模型无法用于复杂多物理场耦合分析的难题，同时也为电磁成形过程的CAD/CAE一体化高效数值计算提供技术支撑。

本项目针对电磁成形过程的高效、自动化数值模拟展开研究，旨在对其中的关键技术进行深入分析并提出合理有效的解决方案，进一步将所提算法集成形成相应的软件分析系统，并将模拟结果用于指导成形方案的设计。通过对电磁场进行理论分析，在计算中引入了基于梯度补偿技术的稳定项，进而构建了电磁分析的稳定节点积分方法，该方法较传统有限元法和原始节点积分方法在计算精度上具有明显的优势。在热-力耦合分析中，采用高效率的节点积分算法完成计算。在此基础上，本项目提出了电磁成形分析的电磁-热-力耦合方案，实现了网格更新和高效的数据传递，该方案合理的反映了电磁成形过程中各物理场之间的相互影响。进一步，将所提算法集成形成相应的自动化软件分析系统以用于二维或三维电磁成形过程的数值模拟，并在数值算例中验证了分析系统的实际效果。因全程采用非结构网格完成计算，使得所搭建的分析系统在前处理、计算效率、复杂问题的适应性、自动化方面具有优势。针对复杂电磁成形问题的数值模拟，研究了接触界面的力学特性及有效模拟方案，提出了基于网格重划的网格更新方案，确定了网格重划的控制策略及后续处理方法，扩展了所搭建的分析系统的适用范围和进一步开发潜力。

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