工程科学学报.第42卷.第2期：186-193.2020年2月 Chinese Journal of Engineering,Vol.42,No.2:186-193,February 2020 https://doi.org/10.13374/j.issn2095-9389.2019.02.02.001;http://cje.ustb.edu.cn 基于无网格伽辽金法的连铸坯凝固计算方法 王 宁12)，王旭东2)四，蔡来强2)，姚曼2 1)大连理工大学材料科学与工程学院.大连1160242)辽宁省凝固控制与数字化制备技术重点实验室，大连116024 ☒通信作者，E-mail:hler@dlut.edu.cn 摘要为考察无网格方法求解铸坯凝固过程的可行性，本文依据移动最小二乘和变分原理，推导并建立了基于无网格伽辽 金法的结晶器内铸坯凝固过程二维非稳态传热/凝固数学模型.以小方坯凝固过程为对象，分别采用节点均匀布置、加密布 置、随机布置方式，模拟分析了小方坯凝固过程的温度场变化，并将计算结果与参考解、有限元法数值解进行了对比，结果证 实无网格侧辽金法在计算精度、自适应性、网格依赖性等方面均优于有限元法.研究结果为无网格方法应用于连铸过程的传 热、凝固以及应力/应变行为的数值计算提供参考. 关键词无网格伽辽金法：移动最小二乘：传热：凝固：连铸 分类号TG244+.3 Calculation of continuous casting billet solidification based on element-free Galerkin method WANG Ning 2).WANG Xu-dong CAI Lai-giang 2)YAO Man2) 1)School of Materials Science and Engineering,Dalian University of Technology,Dalian 116024,China 2)Key Laboratory of Solidification Control and Digital Preparation Technology (Liaoning Province),Dalian University of Technology,Dalian 116024, China Corresponding author,E-mail:hler@dlut.edu.cn ABSTRACT The mold is the core component of a continuous caster,and the complex metallurgical behavior in the mold is the primary factor determining the quality of continuous casting slabs.The numerical simulation method based on meshing,such as the finite element method,has become an important method to study the complex heat transfer and mechanical behavior in the mold.With in-depth research,the meshing-based numerical simulation method has been found incapable of accurately reconstructing the solidified shell shape of slabs and tracing the liquid-solid phases coexisting region,and addressing some complex problems such as large deformation and crack propagation is difficult.To investigate the feasibility of the meshless method for solving the solidification process of continuous casting billet,according to the moving least square method and variational principle,a two-dimensional unsteady transient heat transfer mathematical model of billet solidification process in mold was established based on element-free Galerkin method.In this work,an arrangement of the uniform,increased density,and randomly distributed nodes was used to calculate the change of temperature field during the billet solidification process.The calculation results of the element-free Galerkin method were compared with the reference solution and the numerical solution of the finite element method.The results show that the element-free Galerkin method outperforms the finite element method in terms of accuracy,adaptability,and mesh-dependence.The study results provide references for applying the meshless method to the numerical calculation of heat transfer,solidification,and stress/strain behaviors in the continuous casting process. 收稿日期：2019-02-02 基金项目：国家自然科学基金资助项目(51474047)基于无网格伽辽金法的连铸坯凝固计算方法 王    宁1,2)，王旭东1,2) 苣，蔡来强1,2)，姚    曼1,2) 1) 大连理工大学材料科学与工程学院，大连 116024    2) 辽宁省凝固控制与数字化制备技术重点实验室，大连 116024 苣通信作者，E-mail：hler@dlut.edu.cn 摘    要    为考察无网格方法求解铸坯凝固过程的可行性，本文依据移动最小二乘和变分原理，推导并建立了基于无网格伽辽 金法的结晶器内铸坯凝固过程二维非稳态传热/凝固数学模型. 以小方坯凝固过程为对象，分别采用节点均匀布置、加密布 置、随机布置方式，模拟分析了小方坯凝固过程的温度场变化，并将计算结果与参考解、有限元法数值解进行了对比，结果证 实无网格伽辽金法在计算精度、自适应性、网格依赖性等方面均优于有限元法. 研究结果为无网格方法应用于连铸过程的传 热、凝固以及应力/应变行为的数值计算提供参考. 关键词    无网格伽辽金法；移动最小二乘；传热；凝固；连铸 分类号    TG244+.3 Calculation  of  continuous  casting  billet  solidification  based  on  element-free  Galerkin method WANG Ning1,2) ，WANG Xu-dong1,2) 苣 ，CAI Lai-qiang1,2) ，YAO Man1,2) 1) School of Materials Science and Engineering, Dalian University of Technology, Dalian 116024, China 2) Key Laboratory of Solidification Control and Digital Preparation Technology (Liaoning Province), Dalian University of Technology, Dalian 116024, China 苣 Corresponding author, E-mail: hler@dlut.edu.cn ABSTRACT    The  mold  is  the  core  component  of  a  continuous  caster,  and  the  complex  metallurgical  behavior  in  the  mold  is  the primary  factor  determining  the  quality  of  continuous  casting  slabs.  The  numerical  simulation  method  based  on  meshing,  such  as  the finite element method, has become an important method to study the complex heat transfer and mechanical behavior in the mold. With in-depth research, the meshing-based numerical simulation method has been found incapable of accurately reconstructing the solidified shell  shape  of  slabs  and  tracing  the  liquid-solid  phases  coexisting  region,  and  addressing  some  complex  problems  such  as  large deformation and crack propagation is difficult. To investigate the feasibility of the meshless method for solving the solidification process of continuous casting billet, according to the moving least square method and variational principle, a two-dimensional unsteady transient heat transfer mathematical model of billet solidification process in mold was established based on element-free Galerkin method. In this work, an arrangement of the uniform, increased density, and randomly distributed nodes was used to calculate the change of temperature field  during  the  billet  solidification  process.  The  calculation  results  of  the  element-free  Galerkin  method  were  compared  with  the reference  solution  and  the  numerical  solution  of  the  finite  element  method.  The  results  show  that  the  element-free  Galerkin  method outperforms the finite element method in terms of accuracy, adaptability, and mesh-dependence. The study results provide references for applying the meshless method to the numerical calculation of heat transfer, solidification, and stress/strain behaviors in the continuous casting process. 收稿日期: 2019−02−02 基金项目: 国家自然科学基金资助项目（51474047） 工程科学学报，第 42 卷，第 2 期：186−193，2020 年 2 月 Chinese Journal of Engineering, Vol. 42, No. 2: 186−193, February 2020 https://doi.org/10.13374/j.issn2095-9389.2019.02.02.001; http://cje.ustb.edu.cn