基于非重叠Mortar方法的比例边界等几何分析

Scaled boundary isogeometric analysis based on non-overlapping Mortar method

在比例边界等几何分析的建模剖分过程中会出现交界面网格非匹配现象,给计算分析带来困难。为了能够处理此类问题,提出了基于非重叠Mortar方法的比例边界等几何分析。该方法能在将全域分解为若干子域时,针对每个子域分别建模和剖分网格,交界面网格无需逐点匹配;采用交叉点修正的非均匀有理B-样条基函数构造Lagrange乘子空间,子域交界面连续条件可通过Mortar条件满足;并根据交界面连续条件进行自由度凝聚,得到对称正定的系数矩阵,可直接求解。分片试验、U形结构和半无限空间上的柔性基础等数值算例验证了本文方法的有效性,计算精度满足要求。

In the scaled boundary isogeometric analysis,the discretization will lead to non-matching meshes across the interface.The non-matching meshes bring difficulties to the analysis and calculation.In order to handle these problems,the scaled boundary isogeometric analysis based on non-overlapping Mortar method was proposed.The full domain was decomposed into several sub-domains by this method.Sub-domains were discretized independently,so the meshes across the interface were no need to match point by point.The non-uniform rational B-spline functions with a cross point modification were employed to construct the space of Lagrange multipliers.The continuity condition across the interface was satisfied by applying the Mortar condition.The degrees of freedom were condensed according to the continuity condition of the interface led to a symmetric positive definite matrix.Numerical examples of a U-shape structure and flexible circular footing on a half-space and a patch test are presented.The numerical results validate the efficiency and accuracy of the proposed method.