薄板坯连铸凝固应力分析的有限元算法的研究

研究了薄板坯凝固过程坯壳中的二维热弹塑性蠕变应力模型有限元求解实现的方法。讨论了采用三角形单元的模型有限元求解理论，铸坯凝固前和凝固后使总刚度矩阵非零元素的半带宽最小的节点与单元自动剖分和编号的原则、顺序及方法，探讨了采用变带宽压缩存储技术实现半带宽内元素存储的方法，以及应用直接三角分解法求解平衡线性方程组的方法；给出了用初荷载法将铸坯热应力和高温蠕变应力问题转换为单元节点等效荷载的结果。该模型已成功应用于薄板坯、方坯等连续凝固过程的应力分析中。

The Study on the Finite Element Calculation Method of the Stress State of Thin Slab during Continuous Casting in Solidifying Process

In this paper the finite element calculation theory and method are studied for the two-demenion thermal elasto-plastic and creep stress model of the solidified shell in the solidifying process of thin slab. The finite element calculation method is discussed when the triangular units are adopted. And the automatic dividing and numbering principle, order and method of the mesh points and its units are studied for making the half bandwith of non-zero elements in the stiffness matrix of whole body smallest both before and after the whole solidification. The method realizing the elements storage in the half bandwith is developed while adopting the technology of changing half bandwith compressing storage. And the method solving the equilibrium linear equations is researched using the corresponding direct triangular disassembling method. The results of the mesh-point equivalent loads changed from the thermal stress and the thermo-creep stress are presented using the original load method. The studying results in this paper have been successfully applied to the stress state analysis of the solidifying process of thin slab and billet in continuous casting.