Effective properties of a composite beam subjected to torsion

The problem of finding the effective characteristics of a rectilinear beam under pure torsion is considered. The problem is reduced to finding the torsional stress function determined from the solution of a boundary-value problem in the cross section of the beam for a partial differential equation with variable coefficients. Two special boundary-value problems are formulated to find the effective characteristics. It is shown that the effective coefficients are reciprocal in the case of torsion of a layer with nonuniform thickness. In the two-dimensional case, the problem is solved by a finite element method. The cases of a square beam with single and multiple inclusions are discussed. The dependence of the effective characteristics on the inclusion's volume fraction is analyzed.