Approximate Torsional Analysis of Multi-layered Tubes with Non-circular Cross-Sections

In this paper an approximate formulation for torsional analysis of tubes with multi-layered non-circular cross-sections is presented. A previously presented method based on Bredt's theory is extended to achieve these formulas. Layers are assumed to be isotropic and may possess different thicknesses and material properties. The obtained formulas for shear stress and angle of twist are applicable to thin to moderately thick closed cross-sections. It is shown that depending on the properties of the layers, maximum shear stress does not necessarily happen on the outer boundary. Furthermore, the effect of different cross-sectional shapes on torsional response is studied. Using the presented method, one can achieve desirable shear stresses and angles of twist for a polygonal multi-layered tube with a proper choice of bluntness. The method can be extended for torsion problem of FGM tubes as well. The presented formulas for torsion problem are relatively accurate and suitable to be implemented in optimization programs.