Hamiltonian System Of Bending-torsional Coupling Of Thin-walled Curved Box Girders

Thin walled curved beams are widely used in bridge structures due to their adaptability to terrain changes,saving building space and good structural performance.The box and groove section thin-walled structures are most widely applied,which meets the needs of modern bridges.The "bending and torsion coupling" effect of the thin-walled curved beam makes the force of the bridge become quite complex,so it is very necessary to study the bending and torsion coupling of the thin-walled curved beam.The study of thin-walled curved beams is mainly based on the theory of thin-walled members.However,the shear deformation of the thin-walled curved beams will be increased to a certain extent by neglecting the shear deformation of the thin-walled curved beams.If the two shear stress is ignored in the closed section,the two shear deformation will make the mechanical properties of the thin-walled curved beam rare and accurate and objective.The study on the bending and torsion coupling problem of a curved beam with arbitrary section is based on the following three points: first,the shear deformation of the bending of the beam is considered;secondly,the influence of the two shear stress on the torsional deformation is considered;and third,the total potential energy is calculated directly by the strain field.The specific process is as follows: under the assumption of the runo lasoff's periphery,under the assumption of the kURL Bruner Hardin theory for the longitudinal warping displacement and the assumption of the flat section in the bending,the total potential energy of the structure of an arbitrary section and thin-walled bar under the coupling of bending and torsion is obtained,and the corresponding Lagrange's function is obtained.In this paper,a Hamiltonian dual system is established for the analysis of the bending and torsion coupling of a curved beam with arbitrary section,and the Hamiltonian regular equation for the bending and torsion coupling analysis is derived.Using the precise integration method of the boundary value problem at both ends,we use Matlab programming to get the high-accuracy numerical solution.This method is the application of Hamilton mechanics to the bending and torsion coupling of thin-walled curved beams.The mathematical derivation is simple and has a mature and efficient numerical algorithm.The method is clear,high precision and easy to accept.Finally,according to the internal force and deformation produced by the bending and torsion coupling of the thin-walled curved beam,the analysis and comparison are carried out,and the applicable scope and the degree of the actual calculation structure are judged reasonably.