Fixed Domain and Deforming FEM Techniques as Applied to Some Inverse Solidification Problems

本研究解决了与相变铸造工艺相关的反问题的数学模型的发展和验证。该方法基于顺序法和正则化法，结合隐式有限元法（FEM）公式和变形有限元法技术。包括可变材料性能在内的反相变问题的一般分析将得到发展。将考虑涉及糊状区域和复杂几何形状的铸造加工。这种分析性研究与进行相关实验的工业附属机构密切相关。凝固过程具有重要的工程意义。对于逆相变问题的计算分析，目前还没有现成的方法。本研究考虑了相变问题的逆向技术的发展，凝固过程的控制和相关的微观组织是可能的。这可能会对我们的工业机构产生重大的基础和实际贡献。

This research addresses the development and verification of mathematical models for the solution of inverse problems associated with phase change casting processes. The methodology is based on sequential and regularization methods in conjunction with an implicit Finite Element Method (FEM) formulation and deforming FEM techniques. A general analysis of inverse phase change problems including variable material properties will be developed. Casting processing involving mushy regions and complex geometries will be considered. This analytical research is closely tied to an industrial affiliate who is performing the associated experiments. Solidification processes are of vital engineering significance. There is no existing methodology for the computational analysis of inverse phase change problems. This research considers the development of inverse techniques for phase change problems, the control of solidification processes and the associated microstructure is possible. This could lead to significant fundamental and practical contributions of importance to our industrial institutions.