Elastic torsional analysis of prismatic shafts by differential quadrature method

✍ Scribed by Zhong, Hongzhi

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 166 KB
• Volume: 14
• Category: Article
• ISSN: 1069-8299
• DOI: 10.1002/(sici)1099-0887(199803)14:3<195::aid-cnm131>3.0.co;2-i

✦ Synopsis

The governing equation of an elastic prismatic shaft is the two-dimensional Poisson equation de®ned on the cross-sectional area of the shaft. In this paper, the dierential quadrature method (DQM) is employed to solve the Poisson equation on some non-rectangular domains. Singularities, which may appear in the expression of stress components or boundary conditions at a degenerated point of the grid, are removed by means of the Taylor expansion. The results of three examples are compared with the exact solutions. It is shown that accurate results can be achieved by the DQM. In addition, three geometric transformations are conducted in the third example so that the eect of mapping on the convergence and accuracy of results is investigated. It is found that rapid convergence can be ful®lled if the degenerated point of the mesh falls on a Dirichlet boundary. The approach addressed in the paper can be extended to other potential problems governed by either the Poisson equation or the Laplace equation.