弹性问题的自适应数值解析研究

Study on adaptive numerical resolution for elastic problems

传统思维中,用边界元法求解弹性问题时根据不同的精度要求需反复划分单元网格并分析计算结果。针对以上过程存在的弊端,本文提出一种H-R自适应单元网格划分方法,在程序中自动生成新的自适应数据文件,这就节省了大量的前处理和后处理工作;另外,自适应过程的判别采用了一种新的自适应误差分析方法,即以连续误差分析作为局部误差分析和以迭代误差分析作为整体误差分析相结合的误差分析方法,从而大大提高了边界元解的计算精度。

In traditional thinking, when the elastic problems are solved, we need to repeatedly plot element grids and analyze com- puting results according to diverse precision requirement. Against the malpractice exists in the above process, a new H-R adaptive method to plot element grids is proposed, which is carried out in the program by automatically creating new adaptive data files. Thena great dealof fore-disposaland post-disposal canbesaved. Atthesame time, anew adaptive error analysis method is adopted in the adaptive process, namely continuum error analysis acts as the local error analysis and iterative erroranalysis acts as the whole error analysis, which greatly improves the computing precision of boundary element solution.