材料各向异性对热弹性接触问题的影响

S·P·马瑞克; M·卡诺瑞; P·K·乔德辉

材料各向异性对热弹性接触问题的影响

1.
戈巴丹格欣达学院数学系,西孟加拉邦,印度;2.加尔各答大学应用数学系,加尔各答_700009,印度

详细信息

中图分类号: O343.3；O343.6
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出版历程
- 收稿日期: 2007-10-15
- 修回日期: 2007-12-31
- 刊出日期: 2008-04-15

Effect of Anisotropy on Thermoelastic Contact Problem

1.
Departmemt of Mathematics, Gobardanga Hindu College, Khantura, 24-Parganas(N), West Bengal, India;

摘要

摘要: 研究一个绝热刚性冲头和各向异性弹性传热半空间之间的稳态平面接触问题．由于冲头在半空间表面上的滑移，在接触区域内摩擦生热，并且热辐射到接触区域之外的区域．利用Fourier积分变换，将问题简化为两个奇异积分方程构成的方程组．利用Gauss-Jacobi梯形求积公式，数值地求解该方程组．给出了各向异性和热效应的图例．
- 横观各向同性介质 /
- Fourier变换 /
- 摩擦热 /
- 冲头 /
- 热辐射 /
- 奇异积分方程 /
- Fredholm积分方程
Abstract: The stationary plane contact of an insulated rigid punch and a half-space which is elastically anisotropic but thermally conducting are concerned with.The frictional heat generation inside the contact region due to the sliding of the punch over the half-space surface and the heat radiation outside the contact region are taken into account.With the help of Fourier integral transform the problem was reduced to a system of two singular integral equations.The equations were solved numerically by using Gauss-Jacobi and trapezoidal-rule quadratures.The effects of anisotropy and thermal effects were shown graphically.
- transversely isotropic medium /
- Fourier transform /
- frictional heating /
- punch /
- heat radiation /
- singular integral equation /
- Fredholm integral equation

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参考文献(37)

[1]	Comez I,Birinci A,Erdol R. Double receding contact problem for a rigid stamp and two elastic layers[J].European J Mech A Solids,2004,23(6):909-924. doi: 10.1016/j.euromechsol.2004.05.008
[2]	Chaudhuri P K,Ray S.Receding contact between an orthotropic layer and an orthotropic half-space[J].Archives of Mechanics,1998,50(4):743-755.
[3]	Chaudhuri P K,Ray S.Receding axisymmetric contact between a transversely isotropic layer and a transversely isotropic half-space[J].Bull Calcutta Math Soc,2003,95(2):151-164.
[4]	El-borgi S,Abdelmoula R,Keer L.A receding contact plane problem between a functionally graded layer and a homogeneous substrate[J].Internat J Solids and Structures,2006,43(12):658-674. doi: 10.1016/j.ijsolstr.2005.04.017
[5]	Jing H S,Liao M L.An improved finite element scheme for elastic contact problems with friction[J].Computers and Structures,1990,35(5):571-578. doi: 10.1016/0045-7949(90)90385-F
[6]	Fabrikant V I.Elementary solution of contact problems for a transversely isotropic layer bonded to a rigid foundation[J].Z Angew Math Phys,2006,57(3):464-490. doi: 10.1007/s00033-005-0041-6
[7]	Shvets R M,Martynyak R M,Kryshtofovych A A. Discontinuous contact of an anisotropic half-plane and a rigid base with disturbed surface[J].Internat J Engrg Sci,1996,34(2):183-200. doi: 10.1016/0020-7225(95)00091-7
[8]	Barik S P,Kanoria M,Chaudhuri P K. Contact problem for an anisotropic elastic layer lying on an anisotropic elastic foundation under gravity[J].J Indian Acad Math,2006,28(1):205-223.
[9]	Adams C G,Barber J R,Ciavarella M,et al.A paradox in sliding contact problems with friction[J].J Appl Mech,2005,72(1):1-3. doi: 10.1115/1.1795221
[10]	Barber J R. Some thermoelastic contact problems involving frictional heating[J].Quart J Mech Appl Math,1976,29(1):1-13. doi: 10.1093/qjmam/29.1.1
[11]	Ciavarella M,Johansson L,Afferrante L,et al.Interaction of thermal contact resistance and frictional heating in thermoelastic instability[J].Internat J Solids and Structures,2003,40(21):5583-5597. doi: 10.1016/S0020-7683(03)00313-5
[12]	Ciavarella M, Barber J R. Stability of thermoelastic contact for a rectangular elastic block sliding against a rigid wall[J].European J Mech A Solids,2005,24(3):371-376. doi: 10.1016/j.euromechsol.2004.10.008
[13]	KE Liao-liang,WANG Yue-sheng.Two dimensional sliding frictional contact of functionally graded materials[J].European J Mech A Solids,2007,26(1):171-188. doi: 10.1016/j.euromechsol.2006.05.007
[14]	Grilitskii D V,Pauk V I.The plane contact problem of steady thermoelasticity taking heat generation into account[J].J Appl Math Mech,1997,61(6):1007-1012. doi: 10.1016/S0021-8928(97)00129-9
[15]	Gwarny M,Pauk V J. Plane contact problem involving frictional heating for a thermoelastic wedge[J].J Thermal Stresses,2002,25(6):573-583. doi: 10.1080/01495730290074306
[16]	Hills D A,Barber J R.Steady motion of an insulating rigid flat-ended punch over a thermally conducting half-plane[J].Wear,1985,102(1/2):15-22. doi: 10.1016/0043-1648(85)90087-0
[17]	Hills D A,Barber J R. Steady sliding of a circular cylinder over a thermally conducting half-plane[J].Internat J Mech Sci,1986,28(9):613-622. doi: 10.1016/0020-7403(86)90076-7
[18]	Yevtushenko A A,Pauk V J. The non-stationary contact problem for rough bodies taking heat generation by friction into account[J].J Appl Math Mech,1996,60(4):687-692. doi: 10.1016/S0021-8928(96)00086-X
[19]	Yevtushenko A A,Pauk V J. Steady state frictional heat generation on the periodical sliding contact[J].Mathematical Methods and Physicomechanical Fields,1999,42(1):95-99.
[20]	Jang Y H.Effects of thermal contact resistance on transient thermoelastic contacts for an elastic foundation[J].J Appl Mech,2005,72(6):972-977. doi: 10.1115/1.2042485
[21]	Matysiak S J,Pauk V J.Plane contact problem for periodic laminated composite involving frictional heating[J].Archive of Applied Mechanics,1995,66(1):82-89.
[22]	Ma L F,Korsunsky A M. Fundamental formulation for frictional contact problems of coated systems[J].Internat J Solids and Structures,2004,41(11/12):2837-2854. doi: 10.1016/j.ijsolstr.2003.12.022
[23]	Lekhnitskii S G.Theory of Elasticity of an Anisotropic Body[M].Moscow:Mir Publishers,1981.
[24]	Pauk V J. Plane contact problem involving heat generation and radiation[J].J Theory Appl Mech,1994,32(4):829-839.
[25]	Pauk V J. Plane contact problem for a layer involving frictional heating[J].Internat J Heat and Mass Transfer,1999,42(14):2583-2589. doi: 10.1016/S0017-9310(98)00330-5
[26]	Pauk V. Contact problem involving frictional heating for rough half-space[J].J Appl Mech,2004,71(2):287-290. doi: 10.1115/1.1687793
[27]	Pauk V,Wozniak M.Frictional heating effects in the plane contact of a layer and a rigid flat punch[J].J Tech Phys,2003,44(3):237-244.
[28]	Pauk V,Zastrau B. 2D rolling contact problem involving frictional heating[J].Internat J Mech Sci,2002,44(12):2573-2584. doi: 10.1016/S0020-7403(02)00193-5
[29]	Pauk V J,Yevtushenko A. A frictional heating in a sliding contact of two thermoelastic bodies[J].Internat J Solids and Structures,1997,34(12):1505-1516. doi: 10.1016/S0020-7683(96)00091-1
[30]	Marzeda J,Pauk V,Wozniak M.Contact of a rigid body flat punch with a wedge supported by the winkler foundation[J].J Theory Appl Mech,2001,39(3):563-575.
[31]	Dhaliwal R S,Singh A.Dynamic Coupled Thermoelasticity[M].India:Hindustan Publishing Co,1980.
[32]	Vorovich I I,Aleksandov V A,Babeshko A.Non-Classical Contact Problem of Elasticity[M].Moscow:Nauka,1974.
[33]	Timoshenko S P,Goodier J N.Theory of Elasticity[M].Maidenhead:McGrag-Hill,1934.
[34]	Abramowitz M,Stegun I.Handbook of Mathematical Functions[M].New York:National Bureau of Standards,1964.
[35]	Krenk S. On quadrature formulas for singular integral equations of the first and the second kind[J].Quart Appl Math,1975,33(3):225-232.
[36]	S·P·马瑞克，M·卡诺瑞，P·K·乔德辉.无限横观各向同性弹性圆柱中刚性圆盘的扭转振动[J].应用数学和力学,2006,27(7):799-804.
[37]	Noda N, Ashida F. Transient thermoelastic fields in a transversely isotropic infinite solid with a penny-shaped crack[J].J Appl Mech,1987,54(4):854-860. doi: 10.1115/1.3173128