轴向载荷作用下双矩形橡胶圈结构的有限变形分析

Finite Deformation Analysis of Structures of Two Rectangular Rubber Rings Subjected to Axial Loads

研究了具有双矩形橡胶圈结构的装置在端部轴向载荷压缩作用下的有限变形问题。首先针对由不可压缩neo-Hookean材料组成的该类结构的有限变形问题,建立了相应的数学模型,利用材料的不可压缩条件和逆解法等求出了问题的隐式解。进而讨论了轴向载荷和结构参数对橡胶圈变形的影响,并分析了轴向压缩率的变化。最后给出了数值模拟,得到了系列有意义的结果:轴向载荷越大、橡胶圈径向越薄或轴向越宽,其径向外表面的膨胀率越大;轴向压缩率在橡胶圈的中间位置最小而在两端最大,轴向压缩率同样受轴向载荷及结构参数的影响。

In this paper, the problem of finite deformation of a structure which has two rectangular rubber rings is examined, where the rings are compressed by axial loads on their axial outer ends. Firstly, a reasonable mathematical model is proposed for the structure composed of an in- compressible neo - Hookean material, and a system of implicit solutions is derived by using the incompressibility condition of material and the inverse method. Then, the influences of axial loads and structure parameters on the deformation are discussed, as well as the change of the axial compression ratio. Numerical simulations are given to illustrate some meaningful conclusions. For example, the expansion ratio of the radial lateral surface of the rubber rings become larger and larger with the increasing axial load, or the decreasing ratio of inner and outer radii, or the increasingaxial width of the rings. It is proved that the axial compression ratio is the smallest at the central cross - section of the rings; however, it is the biggest at the two ends. The axial compression ratio is also influenced by axial load and structure parameters.