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工程力学  2015 

对有限覆盖无网格法中悬挂节点的研究

DOI: 10.6052/j.issn.1000-4750.2014.01.0046, PP. 80-86

Keywords: 无网格伽辽金法,节点布置,悬挂节点,前处理,背景积分,精度

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Abstract:

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。

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