中文摘要：

本文推导粘弹介质中圆孔孔径时变时的应力和位移。由粘弹解与弹性解的对应关系得到粘弹时变应力解。用直接解方程法求径向位移,最终归结为求解关于待定函数的l阶非齐次微分方程。将半径时变函数泰勒展开,用幂级数解法得到一般情况下的解。在寻找定解条件时,采用了对待定函数的光滑化处理,认为在t=0的微小邻域内函数仍满足微分方程,通过积分得到与待定系数数目相同的定解条件,从而获得本问题径向位移解析解。对Maxwell粘弹模型的求解证明了该法的可靠性。文中解适用于任意粘弹模型和孔径任意时变的情况。

英文摘要：

For general viscoelastic model, the displacement and stress during the hole expanding were analyzed by using time-varying mechanics method. First, the viscoelastic time-varying stress solution was obtained by corresponding principle of time-varying mechanics. Then, the displacement in r-direction was derived by solving equations directly, which is a mathematical problem of solving l-order non-homogeneous differential equation. Taylor expand the function of time-varying radius, positive series method can be use to solve this differential equation. Smooth treatment of undetermined function in point t -- 0 was processed in order to find the initial conditions. Considering that undetermined function is satisfied the differential equation in neighborhood of t -- O, initial conditions whose number is equal to the undetermined coefficients were obtained by integration. So the analytical solution of displacement suit for general viscoelastic model was presented. The solution of Maxwell model testifies the reliability of this method.