| 一类可压缩超弹性材料球体中的空穴分岔 |
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| 引用本文： | 宋涛,刘永花.一类可压缩超弹性材料球体中的空穴分岔[J].山西大学学报(自然科学版),2006,29(3):258-261. |
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| 作者姓名： | 宋涛 刘永花 |
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| 作者单位： | 1. 山东建筑工程学院,人事处,山东,济南,250014
2. 烟台大学,数学与信息科学系,山东,烟台,264005 |
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| 摘 要： | 研究了由一类均匀各向同性的可压缩超弹性材料组成的球体在给定的表面拉伸作用下的球对称变形问题.给出了问题的控制方程和边界条件,进而求得了描述球体径向对称变形的参数型解析解.证明了对任意给定的表面伸长,方程存在一个平凡解.利用能量比较的方法分析了解的稳定性,并讨论了球体发生空穴分岔时的应力的集中和突变现象.最后给出了数值算例.
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| 关 键 词： | 可压缩超弹性材料 球对称变形 空穴分岔 |
| 文章编号： | 0253-2395(2006)03-0258-04 |
| 收稿时间： | 2006-03-16 |
| 修稿时间： | 2006年3月16日 |
Cavitated Bifurcation in Spheres Composed of a Class of Compressible Hyperelastic Materials |
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| SONG Tao,LIU Yong-hua.Cavitated Bifurcation in Spheres Composed of a Class of Compressible Hyperelastic Materials[J].Journal of Shanxi University (Natural Science Edition),2006,29(3):258-261. |
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| Authors: | SONG Tao LIU Yong-hua |
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| Abstract: | A spherical symmetric deformation problem was examined for a solid sphere subjected to a prescribed uniform radial stretch on its surface.The sphere was composed of a class of homogeneous isotropic compressible hyperelastic materials.The governing equation and the boundary conditions of the problem were presented,and the analytic solutions with parametric type that describe radial symmetric edformation of the sphere were obtained.The stability of the solutions was analyzed by using the method of energy comparison,and the stress distribution after cavitation occurs was also discussed.Finally,some numerical examples were presented. |
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| Keywords: | compressible hyperelastic material spherical symmetric deformation cavitated bifurcation |
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