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

Abstract

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 multilayered 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.

Torsion of tubes with quasi-polygonal holes using complex variable method

“…Nevertheless, Arif Gürel et al’s solution is incapable of predicting warping displacements and stress concentrations at the sharp corners. In our prior work [20], the imaginary strips method [7, 15] has been expanded to analyze the torsional behavior of multi-layered tubes with arbitrarily shaped cross-sections. Also on the torsion of non-homogeneous bars, Ecsedi presented a solution for the Saint-Venant torsion problem of solid and hollow cylindrical non-homogeneous bars with shear modulus being a function of the Prandtl’s stress function of the same cylindrical bars when the material is considered homogeneous [21].…”