Saint-Venant torsion of orthotropic bars with inhomogeneous rectangular cross section

This work presents an exact solution of the Saint-Venant torsion of a straight bar with an orthotropic and inhomogeneous rectangular cross section whose material properties obey the exponential law in one direction. An approximate solution is also obtained for the material properties being arbitrarily distributed in one direction by using a layerwise model, in which the inhomogeneous rectangle is simulated by a composite rectangle composed of multiple rigidly connected homogeneous rectangular regions. The warping function, stresses and torsional rigidity are analytically expressed in terms of Fourier series for both solutions, in which the hyperbolic functions are not directly employed to avoid numerical difficulties. Some numerical examples are finally presented to verify the proposed method and the parametrical study is also performed.