基于偶应力理论的拉格朗日乘子约束的四结点杂交元法

山东大学学报(工学版)

基于偶应力理论的拉格朗日乘子约束的四结点杂交元法

张波¹，王锡平²，李术才¹，杨学英³，　姜晓波⁴，　王敏²，干惠明⁵

1. 山东大学岩土与结构工程研究中心，山东济南250061;2. 山东大学土建与水利学院，山东济南250061;3. 山东城市建设职业学院，山东济南250014;4. 乳山市银滩建设监理有限公司，山东乳山264504;5. 威海市公路管理局，山东威海264200

收稿日期:2007-01-12 修回日期:1900-01-01 出版日期:2007-12-24 发布日期:2007-12-24
通讯作者: 张波

Hybrid finite element method constrained by Lagrange multiplier in couplestress theory

ZHANG Bo¹，WANG Xi-ping²,LI Shu-cai¹，YANG Xue-ying³,JIANG Xiao-bo⁴,WANG Min²，GAN Hui-ming⁵

1. Geotechnical and Structural Engineering Research Center,Shandong University,Jinan 250061,China;2. School of Civil Engineering，Shandong University，Jinan 250061，China；3. Shandong Urban Construction Vocational College

Received:2007-01-12 Revised:1900-01-01 Online:2007-12-24 Published:2007-12-24
Contact: ZHANG Bo

摘要/Abstract

摘要： 在约束转动的偶应力理论中，有微转动和宏观转动相等的约束条件，目前的研究对于此约束条件的引入大都是采用罚函数法，罚函数法与其他引入约束条件的方法相比要求相对弱一点，容易实现，但罚函数值的选择有一定的困难，不利于偶应力理论的推广应用，以拉格朗日乘子来引入此约束条件，避免了罚函数法的缺点.为了满足偶应力问题对单元位移试解的c1连续性要求，采用四结点杂交元来构造有限单元法的基本单元.数值算例验证了本文方法具有精度高和稳定性好的特点.

关键词: 偶应力, 拉格朗日乘子, 杂交元

Abstract: There is a constrained condition, of which macro rotation is equal to the micro rotation in couple-stress theory. The constraint condition is introduced by a penalty function technique in recent researches, which has not only some advantages but!also some disadvantages making the couple-stress theory using difficult. The constrained condition is introduced by Lagrange multiplier method to overcome these disadvantages of the penalty function technique. To meet the special demand of c1 continuity of the couplestress theory, four nodes hybrid element is introduced. The numerical example validates the good accuracy and high efficiency of this method.

Key words: couple-stress, Lagrange multiplier, hybrid element

中图分类号:

O344.3

张波,王锡平,李术才,杨学英,姜晓波,王敏,干惠明5 . 基于偶应力理论的拉格朗日乘子约束的四结点杂交元法[J]. 山东大学学报(工学版), 2007, 37(6): 74-78 .

ZHANG Bo,WANG Xi-ping,LI Shu-cai,YANG Xue-ying,JIANG Xiao-bo,WANG Min,GAN Hui-ming5 . Hybrid finite element method constrained by Lagrange multiplier in couplestress theory[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2007, 37(6): 74-78 .

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