非均匀温度场中组合热超弹性球体的动态孔穴生成

程昌钧; 梅波

非均匀温度场中组合热超弹性球体的动态孔穴生成

程昌钧^1,2,
梅波^1,2

1.
上海大学力学系,上海 200072;2.上海市应用数学和力学研究所上海市应用数学和力学研究所,上海 200072

基金项目: 国家自然科学基金资助项目(10272069);上海市重点学科建设项目(Y0103)

详细信息

作者简介:
程昌钧(1937- ),女,重庆人,教授、博士生导师(联系人.Tel:+86-21+56331454;Fax:+86-21-36033287;E-mail:chjcheng@mail.shu.edu.cn)

中图分类号: O343
计量
- 文章访问数: 2570
- HTML全文浏览量: 139
- PDF下载量: 593
- 被引次数: 0
出版历程
- 收稿日期: 2004-06-30
- 修回日期: 2005-12-11
- 刊出日期: 2006-04-15

Dynamical Formation of Cavity for Composed Thermal Hyperelastic Spheres in Non-Uniform Temperature Fields

CHENG Chang-jun^1,2,
MEI Bo^1,2

1.
Department of Mechanics, Shanghai University, Shanghai 200072, P. R. China;

摘要

摘要: 在有限变形动力学的框架下，研究了在非均匀温度场中组合热超弹性球体，在表面均布拉伸死载荷作用下的动态孔穴的生成和增长问题．首先建立了相应的非线性数学模型，利用换元积分方法求得了孔穴半径与外加载荷之间的一个精确的微分关系，并进行了数值计算，得到了不同温度下球体中孔穴生成时的临界载荷和分叉曲线．考察了参数对孔穴生成与增长的影响,并与相应的静态结果进行了比较．结果表明孔穴是以一个有限的半径突然出现的,且随时间的演变孔穴半径呈现周期性的非线性振动；当温度升高,临界值降低,同时在相同的条件下动态临界载荷低于静态临界载荷．
- 组合热超弹性球体 /
- 非均匀温度场 /
- 动态的孔穴生成和增长 /
- 非线性的周期振动 /
- 温度的影响
Abstract: Dynamical formation and growth of cavity in a sphere composed of two incompressible thermal-hyperelastic Gent-Thomas materials are discussed under the case of a non-uniform temperature field and surface dead loading.The mathematical model was first presented based on the dynamical theory of finite deformations.An exact differential relation between the void radius and surface load was obtained by using the variable transformation method.By numerical computation,critical loads and cavitation growth curves were obtained for different temperatures.The influence of the temperature and material parameters of the composed sphere on the void formation and growth are considered and compared with that for static analysis.The results show that the cavity occurs suddenly with a finite radius and its evolvement with time displays a non-linear periodic vibration and that the critical load decreases with the increase of temperature and also the dynamical critical load is lower than the static critical load under the same conditions.
- composed thermal-hyperelastic sphere /
- non-uniform temperature field /
- dynamical formation and growth of cavity /
- nonlinear periodic vibration /
- influence of temperature

HTML全文

参考文献(16)

[1]	朱兆祥.材料和结构的不稳定性[M].北京：科学出版社,1994.
[2]	Gent A N,Lindley P B.Internal rupture of bonded rubber cylinders in tension[J].Proc R Soc London Ser A,1958,249:195—205.
[3]	Williams M L,Schapery R A.Spherical flaw instability in hydrostatic tension[J].Internat J Fracture,1965,1(1):64—71. doi: 10.1007/BF00184154
[4]	Ball J M.Discontinuous equilibrium solutions and cavitations in nonlinear elasticity[J].Phil Trans R Soc Lond,Ser A,1982,306:557—610. doi: 10.1098/rsta.1982.0095
[5]	Horgan C O,Abeyaratne R.A bifurcation problem for a compressible nonlinearly elastic medium:growth of a micro-viod[J].J Elasticity,1986,16(1):189—200. doi: 10.1007/BF00043585
[6]	Horgan C O,Polignone D A.Cavitation in nonlinear elastic solids: A review[J].Appl Mech Rev,1995,48:471—485. doi: 10.1115/1.3005108
[7]	Knowles J K.On a class of oscillations in the finite deformation theory of elasticity[J].J Appl Meth,1962,29(2):283—286.
[8]	Guo Z H,Solecki R.Free and forced finite amplitude oscillations of an elastic thick-walled hollow sphere made of incompressible material[J].Arch Mech Stos,1963,15:427—433.
[9]	Calderer C.The dynamical behavior of nonlinear elastic spherical shells[J].J Elasticity,1983,13(1):17—47. doi: 10.1007/BF00041312
[10]	Chou-Wang M-S,Horgan C O.Cavitation in nonlinear ealstodynamic for neo-Hookean materials[J].Internat J Engng　Sci,1989,27:967—973.
[11]	REN Jiu-sheng, CHENG Chang-jun. Dynamical formation of cavity in transversely isotropic hyper~elastic spheres[J].Acta Mechanica Sinica,2003,19(3)：320—323. doi: 10.1007/BF02487808
[12]	任九生，程昌钧.超弹性材料中空穴的动态生成[J].固体力学学报，2004,25(1)：42—46.
[13]	Casey J.Abeyaratne R.Finite Thermoelasticity[M]. The American Society of Mechanical Engineers,1999.
[14]	Nicholson D W,Nelson N.Finite element analysis in design with rubber elasticity[J].Rubber Chem Technol,1990,63:358—406.
[15]	Nicholson D W,Lin B.Theory of thermoelasticity for bear-incompressible elastomers[J].Acta Mech,1996,116(1):15—28. doi: 10.1007/BF01171417
[16]	Eringen A C.Mechanics of Continua[M].Second Edition.New York: Robert E Krieger Publishing Cpmpany,1980.(中译本：程昌钧，俞焕然译，戴天民校.连续统力学[M].，北京：科学出版社，1990.)

施引文献

资源附件(0)

访问统计

计量

文章访问数: 2570
HTML全文浏览量: 139
PDF下载量: 593
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

非均匀温度场中组合热超弹性球体的动态孔穴生成

作者简介:
程昌钧(1937- ),女,重庆人,教授、博士生导师(联系人.Tel:+86-21+56331454;Fax:+86-21-36033287;E-mail:chjcheng@mail.shu.edu.cn)

计量

Dynamical Formation of Cavity for Composed Thermal Hyperelastic Spheres in Non-Uniform Temperature Fields

计量

目录

留言板

非均匀温度场中组合热超弹性球体的动态孔穴生成

作者简介: 程昌钧(1937- ),女,重庆人,教授、博士生导师(联系人.Tel:+86-21+56331454;Fax:+86-21-36033287;E-mail:chjcheng@mail.shu.edu.cn)

计量

出版历程

Dynamical Formation of Cavity for Composed Thermal Hyperelastic Spheres in Non-Uniform Temperature Fields

计量

出版历程

目录

作者简介:
程昌钧(1937- ),女,重庆人,教授、博士生导师(联系人.Tel:+86-21+56331454;Fax:+86-21-36033287;E-mail:chjcheng@mail.shu.edu.cn)