试函数扩展的径向基点插值无网格-有限元耦合法在断裂力学的应用

Coupled radial basis point interpolation meshless method of enriched trial function and FEM to the application of fracture mechanics

为了发挥无网格法和有限元法各自的优势,提出径向基点插值无网格法与有限元直接耦合的计算方法(RPM-EFM)。无网格法只需要节点信息,无需单元信息,克服了有限元计算中网格畸变和重新生成带来的困难,故其在分析裂纹扩展和局部大变形等问题方面具有优势。应用试函数扩展的径向基点插值无网格法与有限元法耦合(ERPM-FEM),对含边裂纹的矩形板的裂纹尖端应力场和应力强度因子进行计算分析,结果与精确解高度吻合,且效率更高。

In order to display respective superiority of meshless method and finite element method,a coupled meshless radial point interpolation method of enriched treed the trial function and finite element method（ RPM-FEM） is introduced. Since a meshless method needs only to node information,this overcomes the difficulties resulting from element distortion and mesh regeneration in the FEM when analyzing crack propagation and local large deformation problems. A coupled FEM and ERPM method is more efficient for the calculation of rectangular plate with edge crack tip stress field and stress intensity factor and the results are highly consistent with the exact solutions.