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

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