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基于经典弹性理论,利用欧拉方程组推导了橡胶筒承受径向载荷时的平面问题位移解析解,推导过程中未采用体积不可压缩假设,考虑了泊松比的影响,得到平面问题径向刚度。利用变型贝塞尔函数导出了有限长橡胶筒端面解除约束后径向位移的改变量,叠加平面应变时的径向位移得到有限长橡胶筒径向刚度的精确解。结果表明泊松比在0.48-0.5的范围内取值不同对平面应变时的径向刚度影响非常大。有限长橡胶筒径向刚度精确解与试验数据是一致的。
Based on the classical elasticity theory, Euler equations are used to deduce the analytical solutions of the displacement of a rubber cylinder subjected to radial load. The volume invariance assumption is not used in the derivation. The Poisson's ratio is taken into account to obtain the radial stiffness . The modified Bessel function is used to derive the change of the radial displacement after the restraint of the finite length rubber cylinder end surface. The radial displacement of the finite length rubber cylinder can obtain the exact solution of the radial stiffness of the rubber cylinder with finite length. The results show that the different values of Poisson's ratio in the range of 0.48-0.5 have a great influence on the radial stiffness of plane strain. The exact solution of the finite length rubber cylinder radial stiffness is consistent with the experimental data.