对有限覆盖无网格法中悬挂节点的研究

当前基于Galerkin法的无网格法都只在域内和边界上布置节点。基于无网格方法背景网格独立于节点布置这一性质,该文探讨了无网格域外布置悬挂节点的可行性,提出了一种统一的、均匀的无网格节点布置方案,并设计了相应的背景网格方案,称为有限覆盖无网格法。通过数值算例讨论了悬挂节点对精度的影响,在此基础上讨论了悬挂节点的数目、节点影响域的形状、尺寸以及背景积分方案等对求解精度的影响,并给出了推荐的做法。算例结果表明,悬挂节点能够显著提高求解精度,尤其是边界附近的应力精度。

STUDY ON THE HAINGING NODES IN THE FINITE-COVER-BASED MESHFREE METHOD

For the meshfree methods based on the Galerkin method, all nodes are distributed in the computational domain or on domain boundaries. This study explores the feasibility of using hanging nodes for meshfree methods as the nodal arrangement is independent of background cells. A unified and uniform strategy of the nodal arrangement is proposed, along with a corresponding scheme for the distribution of background cells. Numerical examples are employed to discuss the following influential factors: the necessity of using hanging nodes, the number of hanging nodes, the shape and size of nodal influential domain, and the background integral scheme. Results show that the proposed method can greatly improve the accuracy of meshfree methods, especially in the calculation of stresses near domain boundaries.