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高欣,段庆林,李书卉,陈飙松.裂纹问题的一致性高阶无网格法
Consistent high order meshfree method for crack problems[J].计算力学学报,2018,35(3):275~282
裂纹问题的一致性高阶无网格法
Consistent high order meshfree method for crack problems
Consistent high order meshfree method for crack problems
投稿时间:2017-04-12  修订日期:2017-07-12
DOI:10.7511/jslx20170412002
中文关键词:  裂纹  无网格  断裂  扩展有限元法  高阶近似
英文关键词:crack  meshfree  fracture  extended finite element method  high order approximation
基金项目:科学挑战专题(JCKY2016212A502);国家重点研发计划重点专项(2016YFC1402705,2016YFC1402706);国家自然科学基金(11232003,11372066);中央高校基本科研业务费专项资金(DUT15LK07);水资源与水电工程科学国家重点实验室开放基金(2015SGG03);地质灾害防治与地质环境保护国家重点实验室开放基金(SKLGP2016K007)资助项目.
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 
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中文摘要:
      一致性高阶无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,基于无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;相较于标准的高阶无网格法和低阶一致性无网格法,本文的一致性高阶无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。
英文摘要:
      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.
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