不可压缩橡胶圆柱的空穴和分叉  

Cavity and bifurcation in an incompressible rubber cylinder

作　　者：王勇[1] 唐立强[1] 杨勇[1] 

机构地区：[1]哈尔滨工程大学建筑工程学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2007年第9期980-984,共5页Journal of Harbin Engineering University

基　　金：黑龙江省自然科学基金资助项目(A20004-08);哈尔滨工程大学基础研究基金资助项目(HEUF04005)

摘　　要：利用Y.C.Gao给出的一类应变能函数,分析了不可压缩橡胶圆柱受静载荷作用时在等温条件下及有温度场分布时空穴产生的问题,给出了存在分叉解的条件,确定了外载荷与空穴半径的函数关系,研究了空穴形成时应力的分布,讨论了本构参数和温度对极限载荷和应力分布的影响.结果表明:当本构参数满足0<n<1时,橡胶圆柱体存在分叉解;由Neo-Hooken材料构成的圆柱体将会很稳定而不存在分叉解;本构参数n越大,材料越不容易发生孔洞化不稳定现象;温度越高,材料越不稳定.With the strain energy function propoesd by Y. C. Gao, the advent of cavity was analysed in the incompressible rubber cylinder subjected to static load along with the the existenee of isothermal condition or temperature field. The condition under which a bifurcated solution existed was given. The relationship between external load and cavity radius was determined. The stress distribution when the cavity formed was studied. The effects of constitutive constants and the temperature on the critical load and the stress distribution were discussed. The results indicate that the rubber cylinder has a bifurcation solution when the constitutive parameter is 0〈n〈1 . The rubber cylinder made up of Neo-Hooken material is quite stable and does not have a bifurcation solution. The bigger the constitutive parameter is, the more difficultly the unstable phenomena occurrs for this material,the higher the temperature is, the more unstable the material is.

关 键 词：不可压缩 橡胶圆柱 分叉 应变能函数 

分 类 号：O34[理学—固体力学]