本文主要研究内容
作者胡清元（2019）在《等几何分析中的闭锁问题与Nitsche方法研究》一文中研究指出：有限元法是20世纪力学领域最重大的成就之一。在五十多年的发展历程中,有限元法形成了深厚的数学力学基础,众多研究者构造了大批的各类单元,发展了成熟的静力学和动力学分析方法和软件,在各个领域得到了广泛的应用。在有限元方法中发展起来的各种单元列式中,拟协调元的基本思想对很多单元的构造具有启发性,该方法以“积分弱化”的方式放松了单元间协调性要求。拟协调单元构造方式简单,单元刚度阵显式表达,研究和构造拟协调单元有助于简便且快速地分析实际问题。针对有限元网格剖分引起的CAE和CAD系统融合的困难,作为新兴的有限元分析框架,等几何分析采用非均匀有理B样条(Non-Uniform Rational B-Spline,NURBS)作为基函数,致力于将设计和分析纳入统一表达,将计算机辅助设计(CAD)和计算机辅助工程(CAE)无缝融合,成为一个发展非常迅速的方向。因此,针对等几何分析的相关研究具有重要的理论意义和工程应用价值。拟协调元在构造高阶次单元时,计算单元域内积分通常使用的等参变换对单元形状敏感、且无法达到理论上的最大代数精度,所构造的单元性能受限。与传统有限元类似,等几何Timoshenko梁、Reissner-Mindlin板壳单元同样存在数值闭锁现象,针对闭锁问题的研究使得单元可以薄厚通用,在稀疏网格下就能得到高精度结果,节省计算资源。等几何分析中边界条件施加问题是热点问题,例如,结构位移边界条件难以直接施加,Kirchhoff-Love薄板单元中的转动边界条件不方便控制,关于多片复杂结构耦合边界条件的施加问题,这些列式及其影响都有待研究。NURBS可以精确描述结构边界,对求解接触问题具有独特的优势,因此,对接触边界条件施加的列式研究以及对结构接触问题的模拟,也是等几何分析中的重要课题。本文针对拟协调元和等几何分析中的上述问题,开展了如下研究工作:(1)拟协调高精度抗畸变单元开发。在开发拟协调高阶次单元时,拟协调单元构造通常使用的等参变换限制了单元整体精度和性能,需要寻求一种新的单元域内积分方法。针对这一问题,基于拟协调有限元列式、采用B网方法,开发了拟协调平面四边形八节点单元,该单元具有高精度、抗畸变的良好性质。单元构造时使用B网方法进行单元域内积分,节省计算量的同时保证了单元的二次精度。由于B网积分的良好性质,单元在网格畸变时仍可得到较为稳定的结果,在凹四边网格下同样能够计算。(2)基于等几何分析的梁板壳单元列式与闭锁问题研究。等几何框架下梁、板壳单元仍存在闭锁问题,当网格畸变与闭锁同时发生时单元计算精度进一步下降。对于平面Timoshenko曲梁单元和Reissner-Mindlin板壳单元,提出形函数降阶法将产生闭锁的应变进行降阶投影,解决了应变离散式中插值阶次不一致的问题。此外还讨论了降阶策略,通过在单元上使用不同阶次的降阶基函数有效地减少了计算量、提高了结果精度。对于空间曲梁单元和实体壳单元进行列式和闭锁方面的研究,采用减缩积分策略减轻了闭锁现象。(3)等几何分析中的位移、转动和耦合边界条件施加列式研究。施加位移和转动边界条件、计算多片复杂结构是结构分析中的常见问题。但等几何分析中直接施加边界条件困难,通常采用Nitsche方法将要施加的边界条件“积分弱化”后代入原问题弱形式。对不同的边界条件Nitsche方法列式各不相同。我们通过整合列式提出了统一的Nitsche列式框架,对Nitsche方法进行了有益补充。提出的斜对称Nitsche列式避免了稳定系数的求解,研究中同样将斜对称Nitsche列式纳入统一框架,并应用到各个问题当中。通过算例展现了 Nitsche列式的数值表现,表明了列式的有效性,此外还研究了 Nitsche耦合过程对结构力学响应的影响。(4)基于等几何分析的接触条件施加列式与接触问题模拟。针对小变形无摩擦接触,将接触条件等效转化为投影算子后,采用Nitsche方法施加接触边界条件。列式推导从弹性体与刚体的接触出发,后扩展至两个弹性体之间的主从接触和适用于自接触的无偏接触Nitsche列式。进一步将摩擦条件引入,基于实体壳大变形列式,采用Nitsche方法模拟大变形摩擦接触。此外还推导了接触列式的线性化过程,介绍了高效稳定的接触搜索方法。通过算例进行了对Nitsche接触列式的相关研究,结果表明Nitsche方法能够有效地施加接触条件、模拟接触问题。
Abstract
you xian yuan fa shi 20shi ji li xue ling yu zui chong da de cheng jiu zhi yi 。zai wu shi duo nian de fa zhan li cheng zhong ,you xian yuan fa xing cheng le shen hou de shu xue li xue ji chu ,zhong duo yan jiu zhe gou zao le da pi de ge lei chan yuan ,fa zhan le cheng shou de jing li xue he dong li xue fen xi fang fa he ruan jian ,zai ge ge ling yu de dao le an fan de ying yong 。zai you xian yuan fang fa zhong fa zhan qi lai de ge chong chan yuan lie shi zhong ,ni xie diao yuan de ji ben sai xiang dui hen duo chan yuan de gou zao ju you qi fa xing ,gai fang fa yi “ji fen ruo hua ”de fang shi fang song le chan yuan jian xie diao xing yao qiu 。ni xie diao chan yuan gou zao fang shi jian chan ,chan yuan gang du zhen xian shi biao da ,yan jiu he gou zao ni xie diao chan yuan you zhu yu jian bian ju kuai su de fen xi shi ji wen ti 。zhen dui you xian yuan wang ge pou fen yin qi de CAEhe CADji tong rong ge de kun nan ,zuo wei xin xing de you xian yuan fen xi kuang jia ,deng ji he fen xi cai yong fei jun yun you li Byang tiao (Non-Uniform Rational B-Spline,NURBS)zuo wei ji han shu ,zhi li yu jiang she ji he fen xi na ru tong yi biao da ,jiang ji suan ji fu zhu she ji (CAD)he ji suan ji fu zhu gong cheng (CAE)mo feng rong ge ,cheng wei yi ge fa zhan fei chang xun su de fang xiang 。yin ci ,zhen dui deng ji he fen xi de xiang guan yan jiu ju you chong yao de li lun yi yi he gong cheng ying yong jia zhi 。ni xie diao yuan zai gou zao gao jie ci chan yuan shi ,ji suan chan yuan yu nei ji fen tong chang shi yong de deng can bian huan dui chan yuan xing zhuang min gan 、ju mo fa da dao li lun shang de zui da dai shu jing du ,suo gou zao de chan yuan xing neng shou xian 。yu chuan tong you xian yuan lei shi ,deng ji he Timoshenkoliang 、Reissner-Mindlinban ke chan yuan tong yang cun zai shu zhi bi suo xian xiang ,zhen dui bi suo wen ti de yan jiu shi de chan yuan ke yi bao hou tong yong ,zai xi shu wang ge xia jiu neng de dao gao jing du jie guo ,jie sheng ji suan zi yuan 。deng ji he fen xi zhong bian jie tiao jian shi jia wen ti shi re dian wen ti ,li ru ,jie gou wei yi bian jie tiao jian nan yi zhi jie shi jia ,Kirchhoff-Lovebao ban chan yuan zhong de zhuai dong bian jie tiao jian bu fang bian kong zhi ,guan yu duo pian fu za jie gou ou ge bian jie tiao jian de shi jia wen ti ,zhe xie lie shi ji ji ying xiang dou you dai yan jiu 。NURBSke yi jing que miao shu jie gou bian jie ,dui qiu jie jie chu wen ti ju you du te de you shi ,yin ci ,dui jie chu bian jie tiao jian shi jia de lie shi yan jiu yi ji dui jie gou jie chu wen ti de mo ni ,ye shi deng ji he fen xi zhong de chong yao ke ti 。ben wen zhen dui ni xie diao yuan he deng ji he fen xi zhong de shang shu wen ti ,kai zhan le ru xia yan jiu gong zuo :(1)ni xie diao gao jing du kang ji bian chan yuan kai fa 。zai kai fa ni xie diao gao jie ci chan yuan shi ,ni xie diao chan yuan gou zao tong chang shi yong de deng can bian huan xian zhi le chan yuan zheng ti jing du he xing neng ,xu yao xun qiu yi chong xin de chan yuan yu nei ji fen fang fa 。zhen dui zhe yi wen ti ,ji yu ni xie diao you xian yuan lie shi 、cai yong Bwang fang fa ,kai fa le ni xie diao ping mian si bian xing ba jie dian chan yuan ,gai chan yuan ju you gao jing du 、kang ji bian de liang hao xing zhi 。chan yuan gou zao shi shi yong Bwang fang fa jin hang chan yuan yu nei ji fen ,jie sheng ji suan liang de tong shi bao zheng le chan yuan de er ci jing du 。you yu Bwang ji fen de liang hao xing zhi ,chan yuan zai wang ge ji bian shi reng ke de dao jiao wei wen ding de jie guo ,zai ao si bian wang ge xia tong yang neng gou ji suan 。(2)ji yu deng ji he fen xi de liang ban ke chan yuan lie shi yu bi suo wen ti yan jiu 。deng ji he kuang jia xia liang 、ban ke chan yuan reng cun zai bi suo wen ti ,dang wang ge ji bian yu bi suo tong shi fa sheng shi chan yuan ji suan jing du jin yi bu xia jiang 。dui yu ping mian Timoshenkoqu liang chan yuan he Reissner-Mindlinban ke chan yuan ,di chu xing han shu jiang jie fa jiang chan sheng bi suo de ying bian jin hang jiang jie tou ying ,jie jue le ying bian li san shi zhong cha zhi jie ci bu yi zhi de wen ti 。ci wai hai tao lun le jiang jie ce lve ,tong guo zai chan yuan shang shi yong bu tong jie ci de jiang jie ji han shu you xiao de jian shao le ji suan liang 、di gao le jie guo jing du 。dui yu kong jian qu liang chan yuan he shi ti ke chan yuan jin hang lie shi he bi suo fang mian de yan jiu ,cai yong jian su ji fen ce lve jian qing le bi suo xian xiang 。(3)deng ji he fen xi zhong de wei yi 、zhuai dong he ou ge bian jie tiao jian shi jia lie shi yan jiu 。shi jia wei yi he zhuai dong bian jie tiao jian 、ji suan duo pian fu za jie gou shi jie gou fen xi zhong de chang jian wen ti 。dan deng ji he fen xi zhong zhi jie shi jia bian jie tiao jian kun nan ,tong chang cai yong Nitschefang fa jiang yao shi jia de bian jie tiao jian “ji fen ruo hua ”hou dai ru yuan wen ti ruo xing shi 。dui bu tong de bian jie tiao jian Nitschefang fa lie shi ge bu xiang tong 。wo men tong guo zheng ge lie shi di chu le tong yi de Nitschelie shi kuang jia ,dui Nitschefang fa jin hang le you yi bu chong 。di chu de xie dui chen Nitschelie shi bi mian le wen ding ji shu de qiu jie ,yan jiu zhong tong yang jiang xie dui chen Nitschelie shi na ru tong yi kuang jia ,bing ying yong dao ge ge wen ti dang zhong 。tong guo suan li zhan xian le Nitschelie shi de shu zhi biao xian ,biao ming le lie shi de you xiao xing ,ci wai hai yan jiu le Nitscheou ge guo cheng dui jie gou li xue xiang ying de ying xiang 。(4)ji yu deng ji he fen xi de jie chu tiao jian shi jia lie shi yu jie chu wen ti mo ni 。zhen dui xiao bian xing mo ma ca jie chu ,jiang jie chu tiao jian deng xiao zhuai hua wei tou ying suan zi hou ,cai yong Nitschefang fa shi jia jie chu bian jie tiao jian 。lie shi tui dao cong dan xing ti yu gang ti de jie chu chu fa ,hou kuo zhan zhi liang ge dan xing ti zhi jian de zhu cong jie chu he kuo yong yu zi jie chu de mo pian jie chu Nitschelie shi 。jin yi bu jiang ma ca tiao jian yin ru ,ji yu shi ti ke da bian xing lie shi ,cai yong Nitschefang fa mo ni da bian xing ma ca jie chu 。ci wai hai tui dao le jie chu lie shi de xian xing hua guo cheng ,jie shao le gao xiao wen ding de jie chu sou suo fang fa 。tong guo suan li jin hang le dui Nitschejie chu lie shi de xiang guan yan jiu ,jie guo biao ming Nitschefang fa neng gou you xiao de shi jia jie chu tiao jian 、mo ni jie chu wen ti 。
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论文详细介绍
论文作者分别是来自大连理工大学的胡清元，发表于刊物大连理工大学2019-04-22论文，是一篇关于等几何论文,拟协调论文,网格畸变论文,闭锁论文,接触问题论文,大连理工大学2019-04-22论文的文章。本文可供学术参考使用，各位学者可以免费参考阅读下载，文章观点不代表本站观点，资料来自大连理工大学2019-04-22论文网站，若本站收录的文献无意侵犯了您的著作版权，请联系我们删除。