Nonuniform Torsion of Composite Bars by Boundary Element Method

In this paper a boundary element method is developed for the nonuniform torsion of composite bars of arbitrary constant cross section. The composite bar consists of a matrix surrounding a finite number of inclusions. The materials have different elasticity and shear moduli and are firmly bonded together. The bar is subjected to an arbitrarily concentrated or distributed twisting moment while its edges are restrained by the most general linear torsional boundary conditions. Because warping is prevented, besides the Saint-Venant torsional shear stresses, the warping normal stresses are also computed. Two boundary-value problems with respect to the variable along the beam angle of twist and to the warping function at the shear center are formulated and solved employing a boundary element method approach. Both the warping and the torsion constants are computed by employing an effective Gaussian integration over domains of arbitrary shape. Numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy. The contribution of the normal stresses caused by restrained warping is investigated.