Uniform Torsion Analysis of Composite Shafts Using Point Collocation Method Based on Pascal Polynomials

Abstract

Torsion bars are important elements in the marine structure applications. The usage of the composite torsion bars has increased recently because it takes advantage of the different material property of each constituent. The current research focuses mainly on the uniform warping analysis of composite torsion shafts by using the point collocation method (PCM). The PCM is based on Pascal's triangle polynomial expansion and coupled with subdomain technique that is indispensable for the analysis of composite bars. In addition to satisfying the field equation (Laplace equation for warping function) and traction-free boundary condition for each component, the continuity conditions in both warping functions and tractions need to be imposed along the interfaces of all components. In this paper, multiple-scale factors are introduced into the polynomial series to improve the numerical stability. The current scheme is easy to be implemented, and the algebraic equations for warping functions can be simply established. This numerical method can effectively calculate the structural responses of the composite shafts. The numerical examples of this study include the composite shafts having elliptical and rectangular cross sections. The structural responses such as warping functions, shear stresses and torsional rigidity are reported. The PCM solutions are compared with the exact solutions and with the finite element solutions obtained from COMSOL. The results show that this simple numerical method can effectively achieve the solutions with a high degree of accuracy.