Homogenization-based multivariable element method for pure torsion of composite shafts

Application of the hybrid stress element to torsion of composite shafts is restricted, if the volume fraction of reinforcement is very large. The homogenization method is the most suitable for such problems because it gives not only the equivalent material properties but also detailed information of local fields with less computational cost. In this paper, the extension of the homogenization method to the pure torsion of composite shafts with reinforcing fibers aligned along its axis and the application of high performance multivariable elements are studied. The incompatible element based on a modified potential principle and the enhanced-strain element based on the Hu–Washizu principle are appropriate for the analysis of the representative unit cell, whereas the hybrid stress element is appropriate for the macro-homogenized problem. Numerical examples are provided and discussed.