[1]钟志鹏,万水.考虑裂纹接触摩擦的逐点Lagrange乘子法[J].东南大学学报(自然科学版),2012,42(5):994-999.[doi:10.3969/j.issn.1001-0505.2012.05.035]
 Zhong Zhipeng,Wan Shui.Point-by-point Lagrange multiplier method for modeling interface cracks with contact and friction[J].Journal of Southeast University (Natural Science Edition),2012,42(5):994-999.[doi:10.3969/j.issn.1001-0505.2012.05.035]
点击复制

考虑裂纹接触摩擦的逐点Lagrange乘子法()
分享到:

《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
42
期数:
2012年第5期
页码:
994-999
栏目:
数学、物理学、力学
出版日期:
2012-09-20

文章信息/Info

Title:
Point-by-point Lagrange multiplier method for modeling interface cracks with contact and friction
作者:
钟志鹏 万水
东南大学交通学院,南京 210096
Author(s):
Zhong Zhipeng Wan Shui
School of Transportation, Southeast University, Nanjing 210096, China
关键词:
裂纹 逐点Lagrange乘子法 应力强度因子 接触和摩擦 有限元方法.
Keywords:
crack point-by-point Lagrange multiplier method stress intensity factors contact and friction finite element method
分类号:
O346.1
DOI:
10.3969/j.issn.1001-0505.2012.05.035
摘要:
为了解决裂纹面可能发生的接触摩擦问题,精确求解裂纹尖端附近应力, 提出了一种逐点Lagrange乘子法.将Lagrange乘子逐点转到局部坐标系下,采用Gauss-Seidel迭代法求解法向乘子和切向乘子, 并在求解过程中对切向乘子的约束进行修正,待所有点的乘子求解完成后再将其变换到整体坐标系下迭代求解位移.与传统接触算法相比,该算法无需对总刚度阵求逆,降低了求解规模. 利用该算法计算了压剪作用下中心裂纹板以及纯剪作用下中心界面裂纹板的应力强度因子,计算结果与已有文献结果吻合良好.随后考察了Comninou接触模型在远场纯剪作用下不同摩擦系数对位移场、接触区和裂尖附近应力场的影响,结果表明,接触对裂尖正应力影响较大,忽略裂纹面接触摩擦作用,应力强度因子可能被高估.
Abstract:
In order to solve the stress near the crack tip accurately, a new algorithm—point-by-point Lagrange multiplier method(PLMM)for solving the crack contact problem in an infinite plate is proposed. First, the Lagrange multiplier is transformed to a local coordinate system. Then, the iterative solution of normal and tangential multiplier forces is solved by using the Gauss-Seidel iteration method and the constraint modification of the tangential multiplier is made. After the calculation of all point multiplier forces completed, they are transformed to a global coordinate system to solve displacements iteratively. Compared with the conditional contact algorithms, the PLMM without finding the inverse global stiffness matrix requires less computer storage. The stress intensity factors(SIFs)for the center cracked plate under compression and shear and the center interface crack under shear traction are calculated by the PLMM method, and the calculation results show good agreement with the results in literature. The influences of the friction coefficients on the displacement field, contact zone, and stress fields near the crack tip of the Comninou contact model are studied. The results show that the effect of contact on the distribution of normal stress is great and the SIF may be overestimated without considering crack surface contact.

参考文献/References:

[1] Chen X H,Huang W,Qian Z D.Interfacial behaviors of epoxy asphalt surfacing on steel decks [J].Journal of Southeast University:English Edition, 2007,23(4):594-598.
[2] Rice J R,Sih G C.Plane problems of cracks in dissimilar media [J].Journal of Applied Mechanics,1965,32(2):418-423.
[3] Comninou M,Schmueser D.The interface crack in a combined tension-compression and shear field [J].Journal of Applied Mechanics, 1979,46(2):345-348.
[4] Qian W,Sun C T.A frictional interfacial crack under combined shear and compression [J].Composites Science and Technology, 1998,58(11):1753-1761.
[5] Collombet F,Lalbin X,Bonini J,et al.Contact impact techniques for the study of impacted laminated structures [J].Recent Advances in Contact Mechanics, 2008,28(4/5/6/7/8):171-184.
[6] Bruno D,Greco F,Lonetti P.A coupled interface-multilayer approach for mixed mode delamination and contact analysis in laminated composites [J].International Journal of Solids and Structures, 2003,40(1):7245-7268.
[7] Giner E,Sabsabi M,Fuenmayor F J.Calculation of K in crack face contacts using X-FEM.Application to fretting fatigue [J].Engineering Fracture Mechanics,2011,78(2):428-445.
[8] Nemat-Nasser S,Horii H.Compression-induced nonplanar crack extension with application to splitting,exfoliation and rockburst [J].Journal of Geophysical Research, 1982,87(B8):6805-6821.
[9] Avraham D,Leeslie B S.Shear loaded interface crack under the influence of friction:a finite difference solution [J].International Journal for Numerical Methods in Engineering, 2004,59(13):1749-1780.
[10] 郭小明,赵惠麟.工程结构接触问题的研究及进展[J].东南大学学报:自然科学版,2003,33(5):577-582.
  Guo Xiaoming,Zhao Huilin.Study on contact problems in engineering structures [J].Journal of Southeast University:Natural Science Edition, 2003,33(5):577-582.(in Chinese)
[11] 梁国平.有限元语言[M].北京:科学出版社,2009.
[12] Shi X Q,Zhang X R,Pang H L.Determination of interface fracture toughness of adhesive joint subjected to mixed-mode loading using finite element method [J].International Journal of Adhesion & Adhesives, 2006,26(4):249-260.

相似文献/References:

[1]Bui Manh Tuan,陈云飞.平板表面裂纹应力强度因子和应力分布规律的确定[J].东南大学学报(自然科学版),2014,44(4):728.[doi:10.3969/j.issn.1001-0505.2014.04.009]
 Bui Manh Tuan,Chen Yunfei.Determination of stress intensity factors and stress distribution for surface crack in plates[J].Journal of Southeast University (Natural Science Edition),2014,44(5):728.[doi:10.3969/j.issn.1001-0505.2014.04.009]

备注/Memo

备注/Memo:
作者简介: 钟志鹏(1983—),男,博士生; 万水(联系人),男,博士,教授,博士生导师, wanshui60421@yahoo.com.
基金项目: 国家自然科学基金资助项目(50878048, 50978055).
引文格式: 钟志鹏,万水.考虑裂纹接触摩擦的逐点Lagrange乘子法[J].东南大学学报:自然科学版,2012,42(5):994-999. [doi:10.3969/j.issn.1001-0505.2012.05.035]
更新日期/Last Update: 2012-09-20