【作者】 张雷；

【导师】 黄天佑；

【作者基本信息】 清华大学 ， 材料科学与工程， 2005， 博士

【摘要】 无网格方法是一种新的数值计算方法,本文对该方法在连铸结晶器内坯壳凝固与热应力分析中的应用进行了研究。论文研究了径向基函数法和有限点法两种配点型的无网格法在分析实际传热与凝固问题时的实现方法。根据经典的高斯迭代法和松弛迭代法,通过对径向基函数法的求解平衡方程进行变换,提出了迭代求解算法。研究表明:(1)迭代法可以节省内存,适合于求解大规模工程问题。(2)有限点方法的实用性较好;(3)有限点方法在求解二维问题时表现良好的权函数影响域放大系数ac,在求解其它类似问题时也能获得较好的结果。以上结果为无网格方法在连铸结晶器内坯壳凝固与热应力分析中的应用提供了依据。基于无网格有限点方法实现了求解凝固导热问题的算法,并用Onate 的稳定性方法处理了Neumann 边界条件,给出了凝固潜热的求解方程式和实施方案,并且考虑了材料非线性。研究表明:对于Neumann 边界条件的处理,能提高计算精度。用经典的凝固问题验证了算法的正确性。在求解弹性静力学方程的无网格局部迦辽金法的基础上,给出了其求解热弹塑性问题的位移求解平衡方程式;采用增量切线刚度法处理了热弹塑性材料非线性,给出了相应的方程式及实现步骤;通过对分片试验、定向拉伸以及等温膨胀等问题的数值分析,验证了该算法的可靠性。作者开发了连铸结晶器内铸坯热-力耦合无网格分析程序,并对小方坯连铸结晶器内铸坯凝固与热应力进行了分析,结果表明:(1)铸坯内不同部位冷却不均匀造成偏角处塑性应变集中,容易发生变形;(2)气隙的产生降低了坯壳角部热流,使得坯壳厚度薄;(3)气隙产生以及随后的扩张,加剧了坯壳内冷却不均匀,使得偏角处产生较大的应力和塑性应变。另外大方坯实例分析显示结晶器内凝固坯壳厚度的无网格计算结果符合测量结果。论文研究表明,无网格方法适合于连铸结晶器铸坯热-力耦合分析,计算结果符合连铸方坯偏角区域缺陷的形成规律和角部内层应力应变分布特征,同实际相符;分析结果同有限元方法一致。更多还原

【Abstract】 Meshless method is a new technique for the numerical analysis. The objective of this thesis is to investigate its usability for calculating the solidification and thermal stress of solid shell in continuous casting mold. Two types of collocation meshless methods, i.e. the Radial Base Functions Method (RBFM) and the Finite Point Method (FPM), are preliminarily studied for the application in the analysis of heat transfer and solidification problem. Based on Gauss-Seidel iteration and relaxation iteration, two iterative schemes are constructed and examined for the meshless computation after analyzing the solution equilibrium equations of RBFM. Both iteration schemes are free of assembling the interpolation matrix and are advantageous for solving large-scale engineering problems with a reasonable storage space. Numerical analysis shows that the FPM is flexible in the practical application. For FPM, the amplification coefficient of support domain radius of weight function, ac, with a high accuracy in solving 2-D problems, also performs a good ability in the analysis of similar problems. These observations provide a foundation for the analysis of solidification and thermal stress of solid shell in continuous casting mold by the meshless method. The meshless scheme for the solidification analysis is developed based on FPM, and the nonlinear characteristics of the material properties and solidification enthalpy are treated. The Neumann boundary conditions are constructed based on Onate stabilization method and the solution accuracy is increased. The meshless scheme is verified by solving the classical solidification problems. In sequence, a meshless scheme for solving the elasto-plastic thermal stress is built based on Local Petrov-Galerkin Method (MLPG). According to the incremental tangent-stiffness methods used in the finite element method, a similar meshless scheme is constructed for solving thermal elasto-plastic material problem. The thermal stress analysis scheme is verified with the patch test, simple tension and isothermal expansion problems. Finally, a meshless software package for the simulation of solidification and thermal stress of solid shell in the continuous casting mold is developed. The calculation results for a billet show that non-uniform temperature distribution of solid shell may lead a plastic strain concentration and a deformation at off-corner region in billet. The air gap, which occurs at the billet corner, reduces the surface heat flux, so the shell thickness becomes thin. Furthermore, the expansion of air gap will aggravate the temperature non-uniformly in the billet crosses section, and the large stress and strain may happen at the billet off-corner. Moreover it is applied to analyze the solid shell growth of a continuous casting large square bland in mold, and the results show that the computation solution is coincided with the measurement. The research shows that meshless method can be used to analyze the solidification and thermal stress of solid shell in continuous casting mold, and the calculation results is consistent with the characteristic of stress and strain distribution and the formation mechanism of the off-corner defects in continuous casting billet. It also indicates that the meshless method can obtain a similar calculation precision as FEM. These observations show that meshless method is a potent numerical analysis tool, and it is worth for the analysis of the continuous casting process.更多还原