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一维六方准晶带裂纹的弹性半平面无摩擦接触问题研究.docx

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一维六方准晶带裂纹的弹性半平面无摩擦接触问题研究 摘要 本文研究了一维六方准晶带裂纹的弹性半平面无摩擦接触问题。通过应力场和位移场的分析，得出了接触区域内的应力和位移分布。研究结果表明，接触区域的应力集中在裂纹顶端附近，并且位移沿接触面法线方向存在微小的非零值。这些结果对于材料科学领域的接触力学研究有一定的参考价值。 关键词：一维六方准晶；带裂纹；弹性半平面；无摩擦接触 Introduction Inrecentyears,thestudyofcontactmechanicshasbecomeanimportantresearchfieldinthematerialscience.Theinvestigationofthestressanddisplacementfieldsinthecontactregionisessentialforunderstandingthecontactbehaviorofmaterials.Thesix-foldquasi-crystalsareatypeofnon-periodiccrystalstructures,whichhaveattractedagreatdealofattentionduetotheiruniqueelectronicandmechanicalproperties.Inthepresentwork,weinvestigatethecontactproblemofaone-dimensionalsix-foldquasi-crystalstripwithacrackonanelastichalf-plane.Thestressanddisplacementfieldsinthecontactregionareanalyzedindetail. Theory Thestressanddisplacementfieldsinthecontactregionareobtainedbyusingtheanalyticalandnumericalmethods.Theanalyticalmethodisbasedonthecomplexvariablefunctiontheory,whichisaneffectivetoolfordealingwiththeboundaryvalueproblemsinelasticity.Thenumericalmethodisbasedonthefiniteelementmethod,whichiswidelyusedinthemechanicsofmaterials.Thetwomethodsarecomplementarytoeachother,andthecombinationofthetwomethodscanprovideamoreaccurateandreliablesolutiontothecontactproblem. ResultsandDiscussion Thestressanddisplacementfieldsinthecontactregionareanalyzedfordifferentcontactpressuresanddifferentcracklengths.Theresultsshowthatthestressisconcentratednearthecracktip,andthemaximumstressoccursatthecracktip.Thecracklengthhasasignificanteffectonthestressdistributioninthecontactregion.Whenthecontactpressureisincreased,thestressconcentrationbecomesmoresevere.Inaddition,thedisplacementalongthenormaldirectionofthecontactsurfacehasasmallnon-zerovalue,whichindicatesthatthereisasmalldeformationinthecontactregion. Conclusion Inthispaper,theelasticcontactproblemofaone-dimensionalsix-foldquasi-crystalstripwithacrackonanelastichalf-planeisstudied.Thestressanddisplacementfieldsinthecontactregionareanalyzedindetail.Theanalyticalandnumericalmethodsare