自然单元法计算裂纹与材料边界问题

提出一种新的非凸边界上自然单元法形函数计算方法,通过边界结点限制点对间的邻点关系,对包括裂纹和材料边界在内的各种类型的非凸边界具有统一的处理原则,所得到的近似函数在边界结点间具有线性插值性.

Treatment for Crack and Material Discontinuity with Natural Element Method

The natural element method(NEM) is based on a Galerkin implementation constructed over the natural neighbour interpolation scheme. The trial functions have the property of linear interpolation along the boundaries of convex domain, For NEM require only nodal data without explicit connectivity between nodes and nodes on one side of crack boundary can influence points on opposite side. On boundaries of materials, it is necessary to include derivative discontinuities. A new technique is proposed to realize the linear variation along boundaries of non-convex domain for the shape functions. Selecting the boundary nodes to restrain neighbour relationship between nodes and points, the new technique can deal with problems contain crack or material boundaries easily, and the trial functions have the property of linear interpolation along the boundaries.