一种各向同性不可压超弹性材料球体的空穴分岔问题的研究  

On Problems of Bifurcation for a Solid Sphere Composed of Isotropic Incompressible Hyper-elastic Materials

作　　者：宋玉娥[1] 

机构地区：[1]北京工业职业技术学院,北京100042

出　　处：《北京工业职业技术学院学报》2008年第4期6-10,共5页Journal of Beijing Polytechnic College

摘　　要：研究了各向同性不可压超弹性材料球体在表面均匀拉伸死载荷作用下的空穴分岔问题,得到了描述球体内部的空穴生成和增长的空穴分岔方程,证明了空穴分岔方程的平凡解支上存在唯一的分岔点,并给出了分岔的辨别条件;利用奇点理论给出了空穴分岔方程在分岔点的等价正规形,并利用最小势能原理讨论了空穴分岔方程的稳定性。In this dissertation, problems of bifurcation for a solid sphere composed of isotropic incompressible hyperelastic materials, subjected to a surface tensile dead load, are examined. The cavitated bifurcation equation that describes cavity formation and growth in interior of the sphere is obtained. It is proved that there exists a unique bifurcation point on the trivial solution of the cavitated bifurcation equation, and the distinguished conditions of right - bifurcation are carried out. Equivalent normal forms of the cavitated bifurcation equation at the bifurcation point were presented by using singularity theory. Stability of solutions of the cavitated bifurcation equation is discussed in each region by using the minimal potential principle, and the catastrophic phenomenon of cavity formation is explained.

关 键 词：各向同性不可压超弹性材料 应变能函数 空穴分岔 能量分析 

分 类 号：O343.7[理学—固体力学]