横观各向同性圆柱体端部问题的三维弹性理论解

End Problem Solution of Transversely Isotropic Circular Cylinder with Three Dimensional Elasticity Theory

从位移的通解出发，用分离变量法得到横观各向同性圆柱体的位移和应力的特征函数展开式，并把位移势函数的解用付里叶积分的形式表示。利用留数运算，该积分解可以转换成类似于特征函数的展开式。通过混合端部边界问题，得到与特征函数解成双正交关系的另一组函数。利用这种双正交关系，可以处理不同的端部边界问题。

In this paper, based upon the general solutions of displacements, the eigen functions expansion of displacements and stresses of the transversely isotropic circular cylinder are obtained by using the seperated variable method, and the solution of displacement potentical is expressed as the form of Fourier integration. By using the calculation of residues, the fourier integration can be transferred as the similar expansion of eigenfunctions. Through the solutions of two mixed end problems, a set of bi orthogonal function relations will be obtained. These relations can be used to solve all the problems of different boundary conditions.