Variational Scheme for Analysis of Torsion of Embedded Nonuniform Elastic Bars

This paper develops a novel solution scheme for the analysis of the transfer of an axially symmetric torque from a nonuniform elastic bar into a layered elastic halfspace. The torsional deformation of the bar is specified by a set of kinematically admissible functions that are indeterminate to within a set of arbitrary constants. The embedded bar-elastic halfspace system is represented by extended halfspace and a fictitious bar. The fictitious traction distribution on the extended half-space due to a specified displacement field is determined by a discretization procedure. The results of the analysis is used to develop the total potential energy functional for the bar-elastic halfspace loading system. The minimization of the functional determines explicitly the torsional deformation field. The numerical results presented in the paper illustrate the manner in which the torsional stiffness of the bar is influenced by its nonuniformity and its relative rigidity.