• 应用研究 •

### 扇形截面杆扭转问题的差分线法

1. 1. 清华大学航天航空学院
2. 南京航空航天大学
• 收稿日期:2010-08-19 修回日期:2010-11-13 出版日期:2011-02-15 发布日期:2011-03-03
• 通讯作者: 吴泽艳

### THE METHOD OF LINES FOR TORSION PROBLEMS OF PRISMATIC BARS WITH SECTOR CROSS-SECTION

2,Wu Zhe2

• Received:2010-08-19 Revised:2010-11-13 Online:2011-02-15 Published:2011-03-03

Abstract: The method of lines is used to deal with torsion problems of prismatic bars with sector cross-section. Firstly, ordinary differential equations are obtained from partial differential equations of the torsion problem of prismatic bars with sector cross-sections, and are solved analytically. Secondly, the torsion stress function is derived semi-analytically. Finally, the torsion stiffness of the sector cross-section is obtained. The special solution of the ordinary differential equations is obtained by means of the double sweep method, and the eigenvalues and eigenvectors of the tridiagonal matrix are solved, without using the inverse matrix, based on a theorem that eigenvectors of a real symmetric matrix are orthogonal. The torsion stiffness is solved by a compound trapezoid formula. The numerical results are in good agreement with the existing results, which show the correctness of the algorithm. This method is a kind of semi-analytical method, and can be applied in design of prismatic bars with sectorial cross-section in engineering.