翻转后的不可压缩neo-Hookean圆柱管的有限变形  

FINITE DEFORMATION OF EVERTED CYLINDRICAL SHELLS COMPOSED OF INCOMPRESSIBLE NEO-HOOKEAN MATERIALS

作　　者：赵巍[1,2] 袁学刚[1,2] 张洪武[1] 任九生[3] 

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,工程力学系,大连116024 [2]大连民族学院理学院,大连116600 [3]上海大学上海市应用数学和力学研究所,上海200072

出　　处：《固体力学学报》2012年第4期404-407,共4页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金(10872045,10772104);教育部新世纪优秀人才支持计划(NCET-09-0096);中央高校基本科研业务费专项基金(DC120101124)资助

摘　　要：研究了由径向横观各向同性不可压缩的neo-Hookean材料组成的圆柱管在翻转后的有限变形问题.利用材料的不可压缩条件和半逆解法对相应的数学模型进行求解,并根据边界条件得到了翻转后的圆柱管的内半径以及轴向伸长率应满足的非线性方程组.通过数值算例讨论了材料参数和结构参数对翻转后圆柱管的内半径以及轴向伸长率变化的影响.结果表明:初始厚度对翻转后圆柱管的内半径与轴向伸长率没有本质上的影响;而径向各向异性参数却有本质上的影响,特别是在轴向伸长率方面.The finite deformation problem is examined for an everted cylindrical shell composed of a class of transversely isotropic incompressible neo-Hookean materials about radial direction.The corresponding mathematical model is solved by using the incompressible condition and the semi-inverse method;moreover,the system of nonlinear equations that the inner radius and the axial stretch rate of the everted cylindrical shell must satisfy is obtained by the boundary conditions.The effects of material and structure parameters on the inner radius and the axial stretch rate of the everted cylindrical shell are discussed by numerical examples.The results show that the effect of initial thickness on the inner radius and the axial stretch rate of the everted cylindrical shell is not essential,but of the radial transversely isotropic parameter,especially on the aspect of axial stretch rate.

关 键 词：横观各向同性 超弹性圆柱管 翻转 轴向伸长率 

分 类 号：O347[理学—固体力学]