BENDING-TORSION COUPLING ANALYSIS OF THE COMPOSITE SECTION THIN-WALLED BAR STRUCTURE

Based on the consistency theory of restrained torsion, the coupled bending-torsion problem of composite section thin-walled bar structures consisting of some thin-walled bars is studied in this paper. The total potential energy of thin-walled bar structure with bending-torsion coupling and its corresponding Lagrange function are obtained on the basis of Vlasov’s rigid-frame assumption, Kollbrunner-Hajdin’s longitudinal warping displacement assumption and the plane-section assumption of bending. By introducing dual variables, a Hamiltonian dual system for the static analysis of a composite section thin-walled bar structure is constituted, then Hamiltonian canonical equations are derived for the analysis of bending-torsion coupling. High accuracy numerical solutions are obtained using a precise integration method of two end boundaries. The method proposed in this paper is applicable for the bending-torsion coupling analysis of thin-walled bar structures of open sections, closed sections and mixed sections. And it is the application of Hamiltonian mechanics in the bending-torsion coupling analysis of a composite section thin-walled structure. It is highly accurate and easy to accept with a simple and clear mathematic derivation as well as efficient numerical algorithms.