摩擦接触问题的比例边界等几何B可微方程组方法

薛冰寒; 林皋; 胡志强; 庞林

doi:10.6052/0459-1879-15-329

摩擦接触问题的比例边界等几何B可微方程组方法

大连理工大学建设工程学部, 大连 116024

基金项目: 国家自然科学基金资助项目(5113800.

详细信息

通讯作者:
薛冰寒,博士研究生,主要研究方向:接触问题、工程结构抗震.E-mail:xuebinghan@mail.dlut.edu.cn

中图分类号: O343
计量
- 文章访问数: 976
- HTML全文浏览量: 104
- PDF下载量: 876
出版历程
- 收稿日期: 2015-08-31
- 修回日期: 2015-11-02
- 刊出日期: 2016-05-17

ANALYSIS OF FRICTIONAL CONTACT PROBLEMS BY SBIGA-BDE METHOD

Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, China

摘要

摘要: 摩擦接触问题是计算力学领域最具挑战性的问题之一,接触系统的泛函具有非线性、非光滑的特点,导致接触算法的收敛性与精确性难以保证.因此将比例边界等几何分析(scaled boundary isogeometric analysis,SBIGA)与B可微方程组(B dierential equation,BDE)相结合,提出了求解二维摩擦接触问题的比例边界等几何B可微方程组方法.在比例边界等几何坐标变换的基础上,通过虚功原理推导了关于边界控制点变量的接触平衡方程,表示成B可微方程组形式的接触条件可被严格满足,求解B可微方程组的算法的收敛性有理论保证.此比例边界等几何B可微方程组方法(SBIGA-BDE)只需在接触体边界进行等几何离散,使问题降低一维,能精确描述接触边界,并可通过节点插入算法进行真实接触区域的识别.此外,由于几何建模和数值分析使用相同的基函数,节约了划分网格的时间.以赫兹接触问题和悬臂梁摩擦接触问题为例,通过与解析解及数值计算软件ANSYS计算结果进行对比,验证了该方法求解二维摩擦接触问题的有效性及高精度等特点.
- 弹性摩擦接触问题 /
- 比例边界等几何分析方法 /
- 比例边界有限元 /
- B可微方程组 /
- 数值模拟
Abstract: Frictional contact analysis is one of the most challenging problems in computational mechanics. The functional system of the contact problem is not only nonlinear, but also non-smooth, so in general the convergence and accuracy of contact algorithms are di cult to be guaranteed. For 2D elastic frictional contact problem, the scaled boundary isogeometric analysis combined with B di erential equation method (SBIGA-BDE method) is developed. Based on the scaled boundary isogeometric transformation, the contact equilibrium equation is derived by using virtual principle. The contact conditions are formulated as B di erential equation and satisfied rigorously. The convergence of the algorithm to solve the B di erential equation is guaranteed by the theory of mathematical programming. In the proposed method, only the outer boundary including the contact boundary need to be discretized isogeometrically, which reduces the spatial dimension by one and the boundary are represented accurately. The real contact length can be detected by the knot insertion algorithm. In addition, as the interpolatory functions used in geometry modeling and numerical analyzing are the same, the time costs in mesh generation is saved. The numerical examples, including Hertz contact problem and cantilever beams frictional contact problem, are presented and compared with analytic solution and ANSYS results. It validates the e ectiveness and accuracy of the proposed method in solving 2D elastic frictional contact problem.
- elastic frictional contact problem /
- scaled boundary isogeometric analysis /
- scaled boundary finite element method /
- B dierential equation /
- numerical modeling

HTML全文

参考文献(30)

1 孙林松, 王德信, 谢能刚. 接触问题有限元分析方法综述. 水利水电科技进展, 2001, 21(3): 18-20 (Sun Linsong, Wang Dexin, Xie Nenggang. A summary of finite element analysis for contact problems. Advances in Science and Technology of Water Resources,2001, 21(3): 18-20 (in Chinese))

2 赵兰浩, 李同春, 牛志伟. 有初始间隙摩擦接触问题的有限元混合法. 岩土工程学报, 2006, 28(11): 2015-2018 (Zhao Lanhao, Li Tongchun, Niu Zhiwei. Mixed finite element method for contact problems with friction and initial gap. Chinese Journal of Geotechnical Engineering, 2006, 28 (11) : 2015-2018 (in Chinese))

3 刘永健, 姚振汉. 三维弹性体移动接触边界元法的一类新方案. 工程力学, 2005, 22(1): 6-11 (Liu Yongjian, Yao Zhenhan. A new scheme of BEM for moving contact of 3D elastic solid. Engineering Mechanics , 2005, 22 (1): 6-11 (in Chinese))

4 杨霞, 肖宏, 陈泽军. 基于轴承边界元法的轧机圆锥滚子轴承的载荷研究. 应用力学学报, 2014, 31(1): 137-143 (Yang Xia, Xiao Hong, Chen Zejun. Analysis of the distribution of mill conical roller bearing boundary element method, Chinese Journal of Applied Mechanism, 2014, 31 (1): 137-143 (in Chinese))

5 Lorenzis LD, Wriggers P, Hughes TJR. Isogeometric contact: a review. GAMM-Mitteilungen , 2014, 37 (1): 85-123

6 Hughes TJR, Cottrell JA, Bazilevs Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics & Engineering,2005, 194: 4135-4195

7 吴紫俊,黄正东,左兵权等. 等几何分析研究概述. 机械工程学报,2015, 51 (5): 114-129 (Wu Zijun, Huang Zhengdong, Zuo Bingquan,et al. Perspectives on isogeometric analysis, Journal of Mechanical Engineering, 2015, 51 (5): 114-129 (in Chinese))

8 Hughes TJR, Reali A, Sangalli G. Efficient quadrature for NURBSbased isogeometric analysis. Computer Methods in Applied Mechanics & Engineering, 2010, 199 (5): 301-313

9 Lorenzis LD, Wriggers P, Zavarise G. A mortar formulation for 3D large deformation contact using NURBS-based isogeometric analysis and the augmented Lagrangian method. Computational Mechanics,2011, 49 (1): 1-20

10 Dimitri R, De Lorenzis L, Scott MA, et al. Isogeometric large deformation frictionless contact using T-splines. Computer Methods in Applied Mechanics & Engineering, 2014, 269 (1): 394-414

11 Temizer I, Wriggers P, Hughes TJR. Three-dimensional mortarbased frictional contact treatment in isogeometric analysis with NURBS. Computer Methods in Applied Mechanics & Engineering,2012, 209 (1): 115-128

12 Temicer I, Wiggrs P, Hughes TJR. Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS. Computer Methods in Applied Mechanics & Engineering, 2012, 209 (1):115-128

13 Song CM, Wolf JP. Consistent Infinitesimal finite-element cell method: three-dimensional vector wave equation. International Journal for Numerical Methods in Engineering, 1996, 39 (13):2189-2208 3.0.CO;2-P">

14 Deeks A J,Wolf J P. A virtual work derivation of the scaled boundary finite-element method for elastostatics. Computational Mechanics,2002, 28 (6): 489-504

15 Liu J Y, Lin G, Li XC, et al. Evaluation of stress intensity factors for multiple cracked circular disks under crack surface tractions with SBFEM. China Ocean Engineering, 2013, 27 (3): 417-426

16 Li C, Song C, Man H, et al. 2D dynamic analysis of cracks and interface cracks in piezoelectric composites using the SBFEM. International Journal of Solids & Structures, 2014, 51: 2096-2108

17 张勇, 林皋, 胡志强等. 基于等几何分析的比例边界有限元方法. 计算力学学报, 2012, 29 (3): 433-438 (Zhang Yong, Lin Gao, Hu Zhiqiang, et al. Scaled boundary finite element based on isogeometric analisys. Chinese Journal of Computational Mechanics, 2012,29 (3): 433-438 (in Chinese))

18 Lin G, Zhang Y, Hu ZQ, et al. Scaled boundary isogeometric analysis for 2D elastostatics. Science China Physics, Mechanics and Astronomy, 2014, 57 (2): 286-300

19 张勇, 林皋, 胡志强. 比例边界等几何分析方法I:波导本征问题. 力学学报, 2012, 44 (2): 382-392 (Zhang Yong, Lin Gao, Hu Zhiqiang. Scaled boundary isogeometric analysis and its application I: eigenvalue problem of waveguide. Chinese Journal of Theoretical and Applied Mechanics, 2012, 44 (2): 382-392 (in Chinese))

20 Natarajan S, Wang J, Song C, et al. Isogeometric analysis enhanced by the scaled boundary finite element method. Computer Methods in Applied Mechanics and Engineering, 2015, 283: 733-762

21 Lin G, Zhang Y, Wang Y, et al. Coupled isogeometric and scaled boundary isogeometric approach for earthquake response analysis of dam-reservoir-foundation system. Lisbon: 2012

22 Rahman MU, Rowlands RE, Cook RD, et al. An iterative procedure for finite-element stress analysis of frictional contact problems. Computers and Structures, 1984, 18 (6): 947-954

23 钟万勰. 弹性接触问题的参数变分原理及参数二次规划求解. 计算结构力学及其应用, 1985, 2(1): 1-9 (Zhong Wanxie. Parameter variational principle and parameter quadratic programming method for elastic contact problem. Computational Structural Mechanics and Application, 1985, 2 (1): 1-9 (in Chinese))

24 Klarbring A. A mathematical programming approach to threedimensional contact problems with friction. Computer Method in Applied Mechanics Engineering, 1986, 58 (2): 175-200

25 Leung AYT, Chen GQ, Chen WJ. Smoothing Newton method for solving two-and three-dimensional frictional contact problem. International Journal Numerical Methods in Engineering, 1998, 41 (6): 1001-1027 3.0.CO;2-A">

26 Li XW, Ai-Kah Soh, Chen WJ. A new nonsmooth model for three dimensional frictional contact problem. Computational Mechanics,2000, 26 (6): 528-535

27 Christensen P, Klarbring A, Pang JS, et al. Formulation and comparison of algorithm for frictional contact problems. International Journal Numerical Methods in Engineering, 1998, 42 (1): 145-173 3.0.CO;2-L">

28 Piegl L, TillerW. The NURBS Book. Berlin: Springer-Verlag, 1997

29 Song C, Wolf JP. Body loads in scaled boundary finite-element method. Computer Methods in Applied Mechanics & Engineering,1999, 180 (1-2): 117-135

30 Pang JS. Newton's method for B-differentiable equations. Mathematics of Operations Research, 1990, 15 (2): 311-341

施引文献(19)

期刊类型引用(13)

1.	陈琼，崔德山，张扬景皓，朱俊峰. 一种新型环剪仪的研制及其应用. 地质科技通报. 2025(01): 205-215 . 百度学术
2.	张先盼，唐朝波，杨建广，刘将，朱强，黄天曦，叶文龙. 剪切强化苯胺与软锰矿浸出工艺研究. 矿冶工程. 2024(06): 125-128 . 百度学术
3.	朱强，杨建广，周远林，汪文超，南天翔，唐朝波，曾伟志. 剪切强化针铁矿沉铁过程晶体生长规律研究. 过程工程学报. 2022(02): 186-194 . 百度学术
4.	梅江洲，马刚，邹宇雄，王頔，周伟，常晓林. 颗粒断层泥黏滑运动的研究进展. 中国科学:技术科学. 2022(07): 984-998 . 百度学术
5.	许志洋，孟凡净，丁昊昊. 表面摩擦因数对颗粒螺旋输送动力学特性的影响. 机床与液压. 2022(14): 136-140 . 百度学术
6.	刘静香，孟凡净，董娜. 输运物料参数对螺旋输送机输运影响的力学机制. 河南工学院学报. 2022(05): 5-9 . 百度学术
7.	孟凡净，刘华博，花少震. 颗粒间摩擦对颗粒流润滑影响的力学机制. 工程力学. 2021(04): 221-229+246 . 百度学术
8.	谭援强，肖湘武，张江涛，姜胜强. 尼龙粉末在SLS预热温度下的离散元模型参数确定及其流动特性分析. 力学学报. 2019(01): 56-63 . 本站查看
9.	张耀文，吴迪. 黏性土的残余强度及试验方法研究. 工程技术研究. 2019(24): 147-148+226 . 百度学术
10.	孟凡净，刘焜，吴华伟. 颗粒流润滑剪切膨胀的力学机制研究. 工程力学. 2018(08): 236-244 . 百度学术
11.	修晨曦，楚锡华. 基于微形态模型的颗粒材料中波的频散现象研究. 力学学报. 2018(02): 315-328 . 本站查看
12.	王嗣强，季顺迎. 考虑等效曲率的超二次曲面单元非线性接触模型. 力学学报. 2018(05): 1081-1092 . 本站查看
13.	宋朝阳，宁方波. 弱胶结类岩石细观结构参数与其宏观力学行为的关联性研究进展. 金属矿山. 2018(12): 1-9 . 百度学术