热冲击荷载作用下的含球形空腔的广义热弹性功能梯度球形各向同性体

M·K·戈西; M·卡诺瑞阿

热冲击荷载作用下的含球形空腔的广义热弹性功能梯度球形各向同性体

M·K·戈西¹,
M·卡诺瑞阿²

1.
塞拉姆坡学院数学系,塞拉姆坡,胡里_712 201,印度;2.加尔各答大学应用数学系,加尔各答_700 009,印度

详细信息

中图分类号: O343.6
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出版历程
- 收稿日期: 2008-02-13
- 修回日期: 2008-06-30
- 刊出日期: 2008-10-15

Generalized Thermoelastic Functionally Graded Spherically Isotropic Solid Containing a Spherical Cavity Under Thermal Shock

M. K. Ghosh¹,
M. Kanoria²

1.
Department of Mathematics, Serampore College, Serampore, Hooghly-712 201, India;

摘要

摘要: 在带两个松弛时间参数的广义热弹性线性理论(Green和Lindsay理论)意义上，研究含一个球形空腔的功能梯度球形各向同性无限大弹性介质中，热弹性位移、应力和温度的求解方法．空腔表面无应力，但承受一个随时间变化的热冲击荷载作用．在Laplace变换域中，给出了一组矢量-矩阵微分方程形式的基本方程，并用特征值方法求解．应用Bellman方法进行数值逆变换．计算了位移、应力和温度，并给出相应的图形．结果表明，材料热物理性质的变化，对荷载响应的影响非常强烈．并与对应的均匀材料进行了比较和分析．
- 广义热弹性 /
- 功能梯度材料（FGM） /
- Green-Lindsay理论 /
- 矢量-矩阵微分方程 /
- Bellman方法
Abstract: The determination of thermoelastic displacement,stresses and temperature in a functionally graded spherically isotropic infinite elastic medium having a spherical cavity in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters(Green and Lind-say theory)are concerned with.The surface of the cavity is stress free and is subjected to a time dependent thermal shock.The basic equations were written in the form of a vecto-rmatrix differential equation in the Laplace transform domain which was then solved by eigenvalue approach.The numerical inversion of the transforms was carried out using Bellman method.The displacement,stresses and temperature were computed and presented graphically.It is found that the variation of thermo-physical properties of a material strongly influences the response to loading.A comparative study with the corresponding homogeneous material has also been made.
- generalized thermoelasticity /
- functionally graded material(FGM) /
- Green-Lindsay theory /
- vector-matrix differential equation /
- Bellman method

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参考文献(36)

[1]	Biot M A. Thermoelasticity and irreversible thermodynamics[J].J Appl Phys,1956,27(3):240-253. doi: 10.1063/1.1722351
[2]	Chadwick P.Thermoelasticity,the Dynamical Theory[M].In:Hill R,Sneddon I N,Eds.Progress in Solid Mechanics.Vol 1.Amsterdam: North Holland,1960.
[3]	Lord H，Shulman Y.A generalized dynamical theory of thermoelasticity[J].Mech Phys Solid,1967,15(5):299-309. doi: 10.1016/0022-5096(67)90024-5
[4]	Green A E，Lindsay K A. Thermoelasticity[J].J Elast,1972,2(1):1-7. doi: 10.1007/BF00045689
[5]	Tzou D Y. Experimental support for the lagging behavior in heat propagation[J].J Thermophys Heat Transf,1995,9(4):686-693. doi: 10.2514/3.725
[6]	Mitra K, Kumar S，Vedaverg A. Experimental evidence of hyperbolic heat conduction in processed meat[J].J Heat Transfer,ASME,1995,117(3):568-573. doi: 10.1115/1.2822615
[7]	Chandrasekharaiah D S. Thermoelasticity with second sound, a review[J].Appl Mech Rev,1986,39(3):355-375. doi: 10.1115/1.3143705
[8]	Bahar L, Hetnarski R. State space approach to thermoelasticity[J].J Thermal Stresses,1978,1(1):135-145. doi: 10.1080/01495737808926936
[9]	Ezzat M. Fundamental solution in thermoelasticity with two relaxation times for cylindrical regions[J].Internat J Engrg Sci,1995,33(14):2011-2020. doi: 10.1016/0020-7225(95)00050-8
[10]	Hetnarski R B，Ignaczak J.Generalized thermoelasticity response of semi-space to a short laser pulse[J].J Thermal Stresses,1994,17(3):377-396. doi: 10.1080/01495739408946267
[11]	Bagri A, Eslami M R.Generalized coupled thermoelasticity of disks based on the Lord-Shulman model[J].J Thermal Stresses,2004,27(8):691-704. doi: 10.1080/01495730490440127
[12]	Kar A, Kanoria M.Thermo-elastic interaction with energy dissipation in an unbounded body with a spherical hole[J].International Journal of Solids and Structures,2007,44(9):2961-2971. doi: 10.1016/j.ijsolstr.2006.08.030
[13]	Das N C，Lahiri A. Thermoelastic interactions due to prescribed pressure inside a spherical cavity in an unbounded medium[J].Ind J Pure Appl Math,2000,31(1):19-32.
[14]	Kar A, Kanoria M. Thermoelastic interaction with energy dissipation in a transversely isotropic thin circular disc[J].European Journal of Mechanics, A/Solids,2007，26（6）：969-981. doi: 10.1016/j.euromechsol.2007.03.001
[15]	Ghosh M K，Kanoria M. Generalized thermoelastic problem of a spherically isotropic infinite elastic medium containing a spherical cavity[J].J Thermal Stresses,2008,31(8):665-679. doi: 10.1080/01495730802193872
[16]	Aboudi J, Pindera M J，Arnold S M. Thermo-inelastic response of functionally graded composites[J].International Journal of Solids and Structures,1995, 32(12):1675-1710. doi: 10.1016/0020-7683(94)00201-7
[17]	Wetherhold R C，Seelman S, WANG Jian-zhong. The use of functionally graded materials to eliminate or control thermal deformation[J].Composites Science and Technology,1996,56(9):1099-1104. doi: 10.1016/0266-3538(96)00075-9
[18]	Sugano Y. An expression for transient thermal stress in a nonhomogeneous plate with temperature variation through thickness[J].Ingenieur Archiv,1987,57(2):147-156. doi: 10.1007/BF00541388
[19]	Qian L F， Batra R C. Transient thermoelastic deformations of a thick functionally graded plate[J].J Thermal Stresses,2004,27(8):705-740. doi: 10.1080/01495730490440145
[20]	Lutz M P，Zimmerman R W. Thermal stresses and effective thermal expansion coefficient of a functionally graded sphere[J].J Thermal Stresses,1996,19(1): 39-54. doi: 10.1080/01495739608946159
[21]	Ye G R, Chen W Q，Cai J B.A uniformly heated functionally graded cylindrical shell with transverse isotropy[J].Mechanics Research Communication,2001,28(5):535-542. doi: 10.1016/S0093-6413(01)00206-3
[22]	Chen W Q, Wang X，Ding H J. Free vibration of a fluid-filled hollow sphere of a functionally graded material with spherical isotropy[J].Journal of the Acoustical Society of America,1999,106(5):2588-2594. doi: 10.1121/1.428090
[23]	Ding H J, Wang H M，Chen W Q.Analytical thermo-elastodynamic solutions for a nonhomogeneous transversely isotropic hollow sphere[J].Archive of Applied Mechanics,2002,72(8):545-553. doi: 10.1007/s00419-002-0225-x
[24]	Chen W Q, Ding H J，Wang X. The exact elasto-electric field of a rotating piezoceramic spherical shell with a functionally graded property[J].International Journal of Solids and Structures,2001,38(38/39):7015-7027. doi: 10.1016/S0020-7683(00)00394-2
[25]	Wang B L，Mai Y W. Transient one dimensional heat conduction problems solved by finite element[J].International Journal of Mechanical Sciences,2005,47(2):303-317. doi: 10.1016/j.ijmecsci.2004.11.001
[26]	Shao Z S, Wang T J，Ang K K. Transient thermo-mechanical analysis of functionally graded hollow circular cylinders[J].J Thermal Stresses,2007,30(1):81-104. doi: 10.1080/01495730600897211
[27]	Mallik S H，Kanoria M. Generalized thermo-elastic functionally graded solid with a periodically varying heat source[J].International Journal of Solids and Structures,2007,44(22/23):7633-7645. doi: 10.1016/j.ijsolstr.2007.05.001
[28]	Bagri A, Eslami M R. A unified generalized thermoelasticity formulation; application to thick functionally graded cylinders[J].J Thermal Stresses,2007,30(9/10):911-930. doi: 10.1080/01495730701496079
[29]	Chen W Q. Stress distribution in a rotating elastic functionally graded material hollow sphere with spherical isotropy[J].Journal of Strain Analysis for Engineering Design,2000,35(1):13-20. doi: 10.1243/0309324001513973
[30]	Obata Y, Noda N.Steady thermal stresses in a hollow circular cylinder and a hollow sphere of a functionally graded material[J].J Thermal Stresses,1994,17(5):471-487. doi: 10.1080/01495739408946273
[31]	Ootao Y，Tanigawa Y.Transient thermoelastic problem of a functionally graded cylindrical panel due to nonuniform heat supply[J].J Thermal Stresses,2007,30(5):441-457. doi: 10.1080/01495730601146394
[32]	Das N C, Lahiri A, Sen P K.Eigenvalue approach to three dimensional generalized thermoelasticity[J].Bulletin Calcutta Math Soc,2006,98(4):305-318.
[33]	Nowacki W.Dynamic Problems of Thermoelasticity[M].Warszawa: Polish Scientific Publishers, 1975.
[34]	Wang H M, Ding H J，Chen Y M. Thermoelastic dynamic solution of a multilayered spherically isotropic hollow sphere for spherically symmetric problems[J].Acta Mechanica,2005,173(1/4):131-145.
[35]	Bellman R, Kolaba R E， Lockette J A.Numerical Inversion of the Laplace Transform[M].New York:American Elsevier Pub Co, 1966.
[36]	Dhaliwal R S，Sing A.Dynamic Coupled Thermoelasticity[M].Delhi:Hindustan Publ, 1980.