A modified fourier series method for the torsion analysis of bars with multiply connected cross sections

modified Fourier series method is proposed for the torsion analysis of prismatic bars with multiply connected cross sections. The key feature in the present approach is the combined use of polynomials and Fourier series solutions unlike in the existing approaches which use the Fourier series only. The replacement of the zeroth harmonic terms in the Fourier series solutions by carefully selected polynomials resolves the major problem of functional dependence which the direct Fourier series method may pose. The polynomials and Fourier series solutions are selected to satisfy the governing equation exactly so that the numerical calculation is minimal. The effectiveness and generality of the present method is verified through numerical examples. c 1997 Elsevier Science Ltd.