圆柱壳的轴对称平面应变弹性动力学解  

A Theoretical Solution of Cylindrical Shells for Axisymmetric Plain Strain Elastodynamic Problems

作　　者：丁皓江[1] 王惠明[2] 陈伟球[1] 

机构地区：[1]浙江大学建工学院土木系,杭州310027 [2]浙江大学力学系,杭州310027

出　　处：《应用数学和力学》2002年第2期128-134,共7页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目 (10 172 0 75 )

摘　　要：给出一种圆柱壳的轴对称平面应变弹性动力学问题的解析方法·　首先通过引入一特定函数将非齐次边界条件化为齐次边界条件 ,然后利用分离变量法将位移减去特定函数的量展开为关于贝塞尔函数和时间函数乘积的级数 ,并由贝塞尔函数的正交性 ,导出时间函数的方程 ,容易求得此方程的解·　将两者叠加可得弹性动力学问题的位移解·　运用此方法 ,可以避免积分变换 。A method is developed for the transient responses of axisymmetric plain strain problems of cylindrical shells subjected to dynamic loads. Firstly, a special function was introduced to transform the inhomogeneous boundary conditions into the homogeneous ones. Secondly, using the method of separation of variables, the quantity that the displacement subtracts the special function was expanded as the multiplication series of Bassel functions and time functions. Then by virtue of the orthogonal properties of Bessel functions, the equation with respect to the time variable was derived, of which the solution is easily obtained. The displacement solution was finally obtained by adding the two parts mentioned above. The present method can avoid the integral transform and is fit for arbitrary loads. Numerical results are presented for internally shocked isotropic and cylindrically isotropic cylindrical shells and externally shocked cylinders, as well as for an externally shocked, cylindrically isotropic cylindrical shell that is fixed at the internal surface.

关 键 词：轴对称平面应变 积分变换 柱面各向同性 弹性动力学 圆柱壳 解 

分 类 号：O343.2[理学—固体力学]