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Consistent high order meshfree method for crack problems[J].计算力学学报,2018,35(3):275~282

Consistent high order meshfree method for crack problems
Consistent high order meshfree method for crack problems

DOI：10.7511/jslx20170412002

 作者 单位 高欣 大连理工大学 工业装备结构分析国家重点实验室, 工程力学系, 大连 116024 段庆林 大连理工大学 工业装备结构分析国家重点实验室, 工程力学系, 大连 116024 李书卉 大连理工大学 工业装备结构分析国家重点实验室, 工程力学系, 大连 116024 陈飙松 大连理工大学 工业装备结构分析国家重点实验室, 工程力学系, 大连 116024

一致性高阶网格法能高效精确地求解连续体问题，尤其是能得到高精度的应力场。本文将该方法拓展到应力解析精度至关重要的裂纹问题（即非连续体问题）的数值分析。采用背景积分网格描述裂纹几何，基于需增加节点额外自由度的虚拟节点法描述裂纹处位移场的间断，提出了虚拟节点的引入算法和断裂单元的数值积分方法。为进一步模拟裂纹扩展，采用相互作用积分方法计算应力强度因子，裂纹的扩展方向由最大周向应力准则确定。数值结果表明，本文发展方法能够精确地通过间断分片试验；相较于标准的高阶网格法和低阶一致性网格法，本文的一致性高阶网格法显著改善了应力强度因子的计算精度，能够准确预测裂纹扩展路径。

The consistent high order meshfree method developed in recent years is able to accurately and efficiently solve continuum problems.Especially, it can obtain very accurate stress fields.This work extends this method to crack problems (i.e.discontinuous problems) in which the accuracy of stress solutions is crucial.Background integration mesh is used to describe cracks geometrically.The description of the discontinuity in displacement at cracks is based on the phantom node method which does not need additional nodal degrees of freedom.The algorithm to introduce the phantom nodes and the method to evaluate the domain integral in cracked element are proposed.To further simulate crack propagation, the interaction integral method is used to compute stress intensity factors and the direction of crack propagation is given by the maximum circumferential stress criterion.Numerical results show that the developed method is able to exactly pass the discontinuous patch test.Compared with the standard high order meshfree method and the low order consistent meshfree method, the proposed consistent high order meshfree method remarkably improves the computational accuracy of stress intensity factors.Its ability to accurately predict crack paths is also demonstrated by numerical results.