部分重叠覆盖的数值流形方法初步研究

数值流形方法（简称流形法）采用基于完全重叠覆盖的有限元网格作为数学网格，物理网格与数学网格的不匹配导致结构一些关键部位的计算精度下降。针对此问题，首次提出部分重叠覆盖的流形法，采用以独立覆盖为主的分析方式，独立覆盖之间仅用较小的部分重叠区域保持连续性，从而将现有的基于完全重叠覆盖的流形法扩展到一般意义上的流形研究。对矩形部分重叠覆盖进行初步研究，通过单个矩形数学网格各结点之间的自由度约束方式，很方便地将完全重叠的覆盖形式及流形法公式转化为部分重叠的覆盖形式及公式。算例分析初步验证了这种新型流形法的有效性。

Preliminary Study on Numerical Manifold Method with Partially Overlapping Covers

Finite element meshes based on completely overlapping covers are currently used as mathematical meshes in Numerical Manifold Method (NMM). The decline of calculation accuracy at some key parts is caused by the mismatch between physical meshes and mathematical meshes. In view of this, NMM with partially overlapping covers is presented for the first time. The method  adopts an analysis mode mainly concerning independent covers, and the continuity between the independent covers is kept by a small partially overlapping region. Thus NMM with completely overlapping covers is extended to the method of covers in a general meaning. Rectangular covers are preliminarily researched. The forms and formulas of partially overlapping covers are derived conveniently from completely overlapping covers by using freedom constraint among nodes of a single rectangular mathematical mesh. Finally, the validity and accuracy of the new NMM are demonstrated by an example.