Traction Boundary Conditions for Shell Elements

Abstract

Previous authors have reported difficulty in modeling the free warping torsion of slit cylindrical shells using flat triangular shell elements. During the current study it has been determined that the theoretical basis for traction boundary conditions, rigid body motion characteristics of the finite element model, and kinematic mode singularities are all contributing factors to the finite shell element difficulties with the slit cylinder problem. The scope of this paper is concerned with the formal derivation of the thin cylindrical shell traction boundary conditions and their relation to the finite element analysis of the slit cylinder subjected to warping torsion. It is shown that with the foregoing cumbrances resolved, the flat and shallow shell finite elements respond very accurately for cylindrical shell warping problems.