准静力学双面接触支承问题及其粘弹性材料的非局部摩擦

A·拓亚林

doi:10.3879/j.issn.1000-0887.2010.05.010

准静力学双面接触支承问题及其粘弹性材料的非局部摩擦

doi: 10.3879/j.issn.1000-0887.2010.05.010

A·拓亚林

USTHB 数学系动力系统实验室,BP 32 EL ALIA, 巴布足瓦 16111, 阿尔及利亚

详细信息

中图分类号: O151.25;O343.3
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- 被引次数: 0
出版历程
- 收稿日期: 1900-01-01
- 修回日期: 2009-11-23
- 刊出日期: 2010-05-15

Quasistatic Bilateral Contact Problem With Adhesion and Nonlocal Friction for Viscoelastic Materials

Arezki Touzaline

Laboratoire de Systèmes Dynamiques, Facultéde Mathhmatiques, USTHB, BP 32 EL ALIA, Bab-Ezzouar, 16111, Algérie

摘要

摘要: 建立了描述变形体和基础间接触问题的数学模型．接触是双面的，并采用非局部摩擦定理建模，支承列入计算．粘结场（bonding field）的变化用一个一阶的常微分方程来表示，材料特性用一个非线性粘弹性本构关系建模．导出了该力学问题的变分公式，当摩擦因数充分小时，证明了其弱解的存在性和唯一性．依赖于时间的变分不等式、微分方程和Banach不动点理论，是该证明依据的基础．
- 粘弹性材料 /
- 粘结 /
- 非局部摩擦 /
- 不动点 /
- 弱解
Abstract: A mathematical model which describes a contact problem between a de form able body and a foundation was considered. The contact was bilateral and was modelled with non local friction law in which adhesion was taken in to account. The evolution of the bonding field was described by a firstorder differential equation and the material. s behavior was modelled with an on linear viscoe lastic constitutive law. A variational formulation of the mechanical problem was derived and the existence and uniqueness result of the weak so lution were proved if the coefficien to ffriction was sufficiently small. The proof is based on arguments of time-dependent variationa line qualities, differential equations and Banach fixed-point theorem.
- viscoelastic materials /
- adhesions /
- nonlocal friction /
- fixed point /
- weak solution

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参考文献(18)

[1]	Duvaut G, Lions J-L. Les Inéquations en Mécanique et en Physique[M]. Paris: Dunod, 1972.
[2]	Sofonea M, Han W, Shillor M. Analysis and Approximations of Contact Problems With Adhesion or Damage[M]. Pure and Applied Mathematics.L76.Boca Raton, Florida: Chapman & Hall / CRC Press, 2006.
[3]	Awbi B, Chau O, Sofonea M. Variational analysis of a frictional contact problem for viscoelastic bodies [J]. Int Math J, 2002, 1(4): 333-348.
[4]	Chau O, Fernandez J R, Shillor M, et al. Variational and numerical analysis of a quasistatic viscoelastic contact problem with adhesion[J]. Journal of Computational and Applied Mathematics, 2003, 159(2): 431-465. doi: 10.1016/S0377-0427(03)00547-8
[5]	Chau O, Shillor M, Sofonea M. Dynamic frictionless contact with adhesion[J]. J Appl Math Phys(ZAMP), 2004, 55(1): 32-47. doi: 10.1007/s00033-003-1089-9
[6]	Fernandez J R, Shillor M, Sofonea M. Analysis and numerical simulations of a dynamic contact problem with adhesion[J]. Math Comput Modelling, 2003, 37(12): 1317-1333. doi: 10.1016/S0895-7177(03)90043-4
[7]	Sofonea M, Hoarau-Mantel T V. Elastic frictionless contact problems with adhesion[J]. Adv Math Sci Appl, 2005, 15(1): 49-68.
[8]	Cangémi L. Frottement et adhérence: modèle, traitement numérique et application  l’interface fibre/matrice[D]. PhD Thesis. Aix Marseille I: Univ Méditerranée, 1997.
[9]	Frémond M. Adhérence des solides[J]. J Mécanique Théorique et Appliquée, 1987, 6: 383-407.
[10]	Frémond M. Equilibre des structures qui adhèrent  leur support[J]. C R Acad Sci, Série Ⅱ, 1982, 295: 913-916.
[11]	Raous M, Cangémi L, Cocu M. A consistent model coupling adhesion, friction, and unilateral contact[J]. Comput Meth Appl Mech Engng, 1999, 177(3/4): 383-399. doi: 10.1016/S0045-7825(98)00389-2
[12]	Rojek J, Telega J J. Contact problems with friction, adhesion and wear in orthopeadic biomechanics—Ⅰ: general developements[J]. J Theor Appl Mech, 2001, 39: 655-677.
[13]	Shillor M, Sofonea M, Telega J J. Models and Variational Analysis of Quasistatic Contact[M]. Lecture Notes Physics. Vol 655.Berlin: Springer, 2004.
[14]	Sofonea M, Arhab R, Tarraf R. Analysis of electroelastic frictionless contact problems with adhesion[J]. Journal of Applied Mathematics, 2006: 1-25. ID 64217.
[15]	Nassar S A, Andrews T, Kruk S, et al. Modelling and simulations of a bonded rod[J]. Math Comput Modelling, 2005, 42(5/6): 553-572. doi: 10.1016/j.mcm.2004.07.018
[16]	Brezis H. Equations et inéquations non linéaires dans les espaces vectoriels en dualité[J]. Annales Inst Fourier, 1968, 18(1): 115-175. doi: 10.5802/aif.280
[17]	Cocou M, Rocca R. Existence results for unilateral quasistatic contact problems with friction and adhesion[J]. Math Model Num Anal, 2000, 34(5): 981-1001. doi: 10.1051/m2an:2000112
[18]	Frémond. Non Smooth Thermomechanics[M]. Berlin: Springer, 2002.