一类周期对称问题的柱坐标FEM解法

CYLINDRICAL COORDINATES FEM SOLUTION TO PERIODIC SYMMETRIC PROBLEM WITH A ROTATING CENTER

对具有旋转中心的一类周期对称问题，采用柱坐标有限元法求解，避免了在直角坐标系下求解该类问题时必须而复杂的坐标变换，从而使有限元列式及编程得以简化，提高了计算效率。具体推导了柱坐标下的有限元列式，并给出了周期对称边界条件的处理方法。最后，以厚壁圆筒为例，验证了有限元列式及程序的正确性。

The periodic symmetric problem which has a center of rotation is solved by FEM coupled with cylindrical coordinates.The results have the advantages of avoiding the coordinates transformation which is essential when problem is solved by FEM coupled with Cartesian coordinates, thus the FEM formula and code are simplified. FEM formula in the cylindrical coordinates system is derived and the methods of dealing with the periodic symmetric boundary coordinates are given.The formula andFEM program are proved to be correct by a thick-walled cylinder numerical experiments.