Effective Properties of a Composite Beam Subjected to Torsion / Olekhova L.V. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2010. № 2. P. 30-35 [Moscow Univ. Mech. Bulletin. Vol. 72, N 2, 2017. P. 38-42].

The problem of finding the effective characteristics of a  rectilinear beam under pure torsion is considered. The problem can be reduced to determining the torsional stress function from the solution of a boundary-value problem in a 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 volume fraction is analyzed.

Key words: effective characteristics, beam torsion, composite material, stress function.