MATHEMATICS

Numerical solution of Saint-Venant's problem about torsion of a shaft with two-connected domain section by the method of conformal mapping

V. V. Sobolev, A. A. Molchanov

Don State Technical University

Abstract: A numerical method for solving the Saint-Venant problem about torsion of a shaft with an arbitrary two-connected section domain was developed. This method is based on preliminary building of a conformal mapping of this domain onto a circle ring followed by the solution of the reduced boundary Dirichlet problem. The testing of this method with employment of computer programs demonstrates its sufficiently high efficiency and precision.

Keywords: Saint-Venant problem, shaft torsion, Dirichlet boundary problem, harmonic function, two-connect domain, conformal mapping, numerical method, computer program.

UDC: 519.632+531.262

Received: 29.10.2010