Optimal fiber configurations for maximum torsional rigidity

                                   by

                               Robert Lipton
                     Worchester Polytechnic Institute

               INSCC 110, 3:30pm  Monday, March 8, 1999


                                Abstract

Prismatic shafts reinforced with imperfectly bonded fibers are
considered. We consider all configurations of fibers with simply
connected cross section. Among all shafts with the same cross-sectional
area and with the same joint cross-sectional area of fibers we seek the
optimal fiber and shaft configuration that maximizes the torsional
rigidity. When an upper bound on the diameter of the shaft is prescribed, it is
shown that there is a critical boind strength below which the optimal
fiber and shaft configuration is given by a circular shaft reinforced with
a single centered circular fiber. When the bond strength is greater than
critical it is shown that the concentric circular fiber and shaft
configuration is strictly suboptimal.
                          
Request for preprints and reprints to  
       Robert Lipton <lipton@WPI.EDU>

This information can be found at http://www.math.utah.edu/research/