Bounds for the torsional rigidity of inhomogeneous cylindrical bars

The object of this paper is the uniform torsion of inhomogeneous, isotropic, linearly elastic cylindrical bar. The aim is to give lower and upper bounds for the torsional rigidity of the bar with doubly connected cross section. The outer and inner boundary curves of cross section are similar curves. The level lines of the function which gives the change of the shear rigidity on the cross section are also similar curves to the boundary curves. The application of derived bounding formulae is illustrated by examples. An approximated formula to determine the shear stresses is also presented.