基于无网格伽辽金法的板坯传热及力学行为

 与基于网格离散的数值计算方法相比,无网格方法利用离散节点代替网格单元,回避了拓扑结构复杂、单元编号和信息传递等问题,在模拟分析相变界面移动、大变形、裂纹动态扩展等方面展现出极大的适用性。依据移动最小二乘法构造了场量近似函数,针对连铸板坯在结晶器初始凝固过程中的传热特征,构造和推导了基于无网格伽辽金法的板坯传热和凝固行为控制方程,结合采用伽辽金积分弱形式和变分原理,建立了铸坯热弹塑性二维横截面数值计算模型,以连铸生产现场实测铜板温度反算的结晶器热流为边界条件,模拟和分析了结晶器内初生坯壳的非均匀传热、应力和应变。研究结果表明,板坯在结晶器内宽度方向的传热和力学行为呈现出显著的非均匀特征,在距离弯月面200 mm范围内是应力应变快速增长阶段,之后应力应变增长速度放缓,距弯月面550 mm处,铸坯等效应力和应变出现极大值,分别为15.97 MPa和0.76%;在宽度方向上,角部受二维散热的影响,温度下降较快,出现应力集中现象,相邻的偏角部存在应力应变低谷,与角部在温度、应力、应变方面存在较大差异。上述结果验证了无网格方法计算铸坯非均匀传热、力学行为的可行性和适用性,为无网格方法应用至铸坯裂纹萌生与扩展的研究提供基础和参考。

Investigation on thermo-mechanical behavior of continuous casting slab based on element-free Galerkin method

Compared with the numerical computation method based on grid discretization,the meshless method avoids the problems of complex topology structure,element numbering and information transfer by replacing the grid with discrete nodes,and shows great flexibility in simulation and analysis of movement interface of phase transition,large deformation and dynamic crack propagation. A field variable approximation function is constructed based on the moving least squares method. According to the heat transfer characteristics of continuous casting slab during the initial solidification in mold,the control equation of thermo behavior of continuous casting slab based on element-free Galerkin method are constructed and derived. Then combined with the weak form of Galerkin integral and the variation principle,the thermal elastoplastic model for two-dimensional cross-section slab is established. Taking the heat flux calculated inversely from the measured temperatures of copper plate as boundary conditions,the non-uniform heat transfer,stress and strain of initial solidified shell inside mold are simulated and analyzed. The results show that in the width direction of mold,thermo-mechanical behavior shows significant non-uniform characteristics. The stress-strain increases rapidly within 200 mm from the meniscus,and then the growth rate of stress-strain slows down. At 550 mm from the meniscus,the equivalent stress-strain appear maximum values,which are 15.97 MPa and 0.76%. In the width direction,due to the influence of two-dimensional cooling,the temperature of the corner decreases rapidly and the phenomenon of stress concentration appears. However,there is a low valley of stress-strain in the adjacent deflection corner,which is different from the corner in temperature,stress and strain. The results verify the feasibility and applicability of the meshless method to calculate the non-uniform heat transfer and mechanical behavior for continuous casting process,and provide a basis and reference for the application of the meshless method to the research of formation and propagation of slab cracks.