摘要
根据有限变形动力学理论,研究了一个不可压超弹性材料组合球体在突加表面均布拉伸载荷作用下空穴的动态生成问题· 当外加载荷超过其临界值时,除一个平凡解外,还有一个包含着球体内部生成的空穴的分叉解;证明空穴随时间的演化是周期性的非线性振动;同时给出了空穴生成时的临界载荷值、空穴振动的相图。
The dynamical formation of cavity in a hyper_elastic sphere composed of two materials with the incompressible strain energy function, subjected to a suddenly applied uniform radial tensile boundary dead_load, was studied following the theory of finite deformation dynamics. Besides a trivial solution corresponding to the homogeneous static state, a cavity forms at the center of the sphere when the tensile load is larger than its critical value. An exact differential relation between the cavity radius and the tensile land was obtained. It is proved that the evolution of cavity radius with time displays nonlinear periodic oscillations. The phase diagram for oscillation, the maximum amplitude, the approximate period and the critical load were all discussed.
出处
《应用数学和力学》
EI
CSCD
北大核心
2004年第11期1117-1123,共7页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助项目(10272069)
上海市重点学科建设资助项目
关键词
组合不可压超弹性材料
有限变形动力学
空穴的动态生成
非线性周期振动
composed incompressible hyper-elastic material
finite deformation dynamics
cavity formation
nonlinear periodic oscillation
