TORSION OF HOLLOW CYLINDERS

In this paper torsion of hollow cylinders of arbitrary cross section is studied using finite element technique and multipoint constraint concept. The requirement that the displacement in the axial direction be single valued and the condition that the Prandtl stress function is a constant along the boundary of each hole give rise to linear multipoint constraints. The present analysis is applied to some of the cross sections for which the results are already available and then to a circular cylinder with a star shaped hole. The analysis for the latter case find its application in the design and analysis of solid propellant launch vehicles. The variation of the torsional rigidity when the star shaped hole is offset from the centre is studied. The lines of shearing stress are drawn for the cylinders with star shaped hole.