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.

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Journal Journal of Engineering Mechanics
Selvadurai, A.P.S., & Rajapakse, N. (1987). VARIATIONAL SCHEME FOR ANALYSIS OF TORSION OF EMBEDDED NONUNIFORM ELASTIC BARS. Journal of Engineering Mechanics, ll3(l0).