On a method for solving the problem of elastic torsion of cylindrical beams possessing multiply connected cross sections. I. Theoretical considerations. II. Sample numerical results (Q1821587)

The problem of elastic torsion of cylindrical beams is considered in the general case of arbitrary, multiply connected cross sections. A new method for determination of the torsion function is presented basing on conformal mapping of the cross section onto an auxiliary multiply connected domain bounded by circles. Both the mapping function, and the complex torsion function are assumed in form of series, each one containing a power series, as well as a series of rational functions. Determination of the torsion function is reduced to computation of the unknown constant coefficients of the series. Some numerical results are presented.