<?xml version="1.1" encoding="utf-8"?>
<article xsi:noNamespaceSchemaLocation="http://jats.nlm.nih.gov/publishing/1.1/xsd/JATS-journalpublishing1-mathml3.xsd" dtd-version="1.1" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><front><journal-meta><journal-id journal-id-type="publisher-id">ECE</journal-id><journal-title-group><journal-title>Educational Continuity and Enhancement</journal-title></journal-title-group><issn>3066-845X</issn><eissn>3066-8476</eissn><publisher><publisher-name>Art and Technology</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.61369/ECE.2025020022</article-id><article-categories><subj-group subj-group-type="heading"><subject>Article</subject></subj-group></article-categories><title>立方准晶梁反平面问题力学特性研究</title><url>https://artdesignp.com/journal/ECE/1/2/10.61369/ECE.2025020022</url><author>毛圣植,周德骏,王朔昕,徐靖雨,夏金鹏,赵宝生</author><pub-date pub-type="publication-year"><year>2025</year></pub-date><volume>1</volume><issue>2</issue><history><date date-type="pub"><published-time>2025-03-28</published-time></date></history><abstract>为了研究立方准晶梁反平面问题，对立方准晶梁的应力和变形进行分析。首先从立方准晶材料的基本方程出发，获得声子场和相位子场的第三方向位移满足的方程。然后利用Lur&amp;rsquo;e方法，引入单变量待定函数，将位移用算子函数表示出来，再利用几何方程和本构方程，得到用算子函数表示的应力场，并将应力场带入边界条件当中，确定待定函数，从而获得特定问题的位移场和应力场。最后将各物理量无量纲化，并根据声子场和相位子场的位移、声子场中的应力分布情况，得到相应的结论。</abstract><keywords>弹性理论,立方准晶材料,反平面,应力场,位移场</keywords></article-meta></front><body/><back><ref-list><ref id="B1" content-type="article"><label>1</label><element-citation publication-type="journal"><p>[1]SHECHTMAN D,BLECH I,GRATIAS D,et al.Metallic phase with long-range orientational order and no translational symmetry[J]. Physical Review Letters,1984,53(20):1951-1953.&amp;nbsp;[2]YE H Q,WANG D,KUO K H.Five-fold symmetry in real and reciprocal spaces[J].&amp;nbsp;Ultramicrosscopy,1985,16(2):273-277.&amp;nbsp;[3]ZHANG Z,YE H Q,KUO K H.A new icosahedral phase with m35 symmetry[J].&amp;nbsp;Philosophical Magazine A,1985,52(6):L49-L52.&amp;nbsp;[4]FENG Y C,LU G,WITHERS R L.An incommensurate structure with cubic point group symmetry in rapidly solidified V-Vi-Si alloy[J].Journal of Physics Condensed Matter,1989,1(23): 3695-3700.&amp;nbsp;[5]王仁卉,胡承正,桂嘉年.准晶物理学[M].北京:科学出版社,2004: 1-7.&amp;nbsp;[6]HU C Z,WANG R H, DING D H,et al.Point groups and elasic properties of two-dimensional quasicrystals[J].Acta Crystallog,1996,A 52(2):251-256&amp;nbsp;[7]YANG W G,WANG R H,DING D H,et al.Linear elasticity theory of cubic quasicrystals[J].Physical Review B,1993,48(10):6999-7002.&amp;nbsp;[8]范天佑.固体与软物质准晶数学弹性与相关理论及应用[M].北京:北京理工大学出版社,2014: 200-203.&amp;nbsp;[9]Gao Y.Governing equations and general solutions of plane elasticity of cubic quasicrystals[J].Physics Letters A,2009,373:885&amp;ndash;889.&amp;nbsp;[10]姜腾霄,李公庆,赵宝生.立方准晶材料平面轴对称问题研究[J].辽宁科技大学学报,2023,46(2):140-146.&amp;nbsp;[11]刘兴伟,李星,汪文帅.一维六方压电准晶中正n边形孔边裂纹的反平面问题[J].应用数学和力学,2020,41(07):713-724.&amp;nbsp;[12]郭怀民,赵国忠,刘官厅,等.含唇口次生两不对称裂纹的一维六方压电准晶体的反平面剪切问题[J].固体力学学报,2024, 45(01): 123-134.&amp;nbsp;[13]崔晓微,李联和.含螺型位错有限大一维六方压电准晶楔形体的反平面问题[J].应用力学学报,2019,36(05):1058-1062+1257.&amp;nbsp;[14]LUR&amp;rsquo;E A I.Three-dimensional Problems in the Theory of Elasticity[M].New York:Interscience Press,1964:60-62.&amp;nbsp;[15]曹婷,付笑宇,张亮亮,等．三维立方准晶椭球夹杂的Eshelby张量[J]．固体力学学报，2022,43(6):750-762.</p><pub-id pub-id-type="doi"/></element-citation></ref></ref-list></back></article>
