Hamiltonian System Of Bending-torsion Coupling Of Thin-walled Curved Beams Improved Analysis

The thin-walled curved beam bridge has the advantages of large torsional rigidity,light weight and beautiful appearance.It is a structural type widely used in urban viaducts,urban overpasses and highway railway bridges.However,due to the influence of the curvature of the thin-walled curved beam,the bending-torsional coupling effect occurs in the curved beam under the action of external force,so the analysis of the curved beam becomes more complicated than the linear beam.In the past,the research on thin-walled curved beams mostly ignored the influence of shear deformation during bending and the secondary shear deformation when the closed-section curved beam was twisted,which caused errors in the research and analysis results of thin-walled curved beams.It is very meaningful to analyze the bending and torsion analysis of curved beam bridges.The shear deformation in bending and the secondary shear deformation in torsion are considered in this article.On the basis of Timoshenko beam theory,the total potential energy of the bending-torsion coupling of thin-walled curved beams is derived directly from the assumptions of Vlasov,KURL Bruner-Hardin and plane cross-section in bending,and the shear strain curvature correlation term in the strain field is taken into account.The corresponding Lagrangian function and Lagrangian equation are derived.Dual variables are introduced by Lelander transformation,and the Hamiltonian dual solution system for bending-torsion coupling of thin-walled curved beams with arbitrary cross-section is obtained.In this paper,a suitable example is selected to verify the feasibility of the proposed theory.The theory of this paper is compared with the other two thin-walled curved beam bending and torsion problems analysis theory.The calculation results of the three theories under the same working conditions in the same example are compared and analyzed and summarized.The difference between the theories is a certain improvement on the theory of bending and torsion analysis of thin-walled curved beams.