Bending-torsion Coupling Analysis Of Open Thin-walled Bar With Stiffening Members

With the advance of sustainable development, thin-walled bar is becoming more and more popular in all industries because its light quality, high strength, and can be made full use of material. Compared with the closed section thin-walled bars, the open thin-walled ones are relatively easier to be produced with lower costs as they’re one-step forming. Open thin-walled bars normally have a single symmetry axes only, the torsion stiffness is smaller, and vulnerable to bending and twisting instability. And by opening set in stem a lateral ties, the warping of the opening sections and the resistance to twist stiffness can be greatly enhanced. The deformation characteristics of the open thin-walled bar with stiffening members, is between the open section and closed section.In this paper, the system is divided into strength members and a open thin-walled bar in the analysis of the open thin-walled bar with stiffening members. By Vlasov’s classical theory and Kollbrunner-Hajdin’s longitudinal warping displacement assumption, as well as strengthening the component, the use of continuous and the continuous two assumptions, two kinds of different calculation models of analysis of the bars are established.Based on the Hamilton’s principle and the precise integration method, from energy variational principle, by opening of a thin-walled bar in strengthening the component of continuous and continuous assumption respectively, a Hamiltonian dual system for the reinforced open thin-walled bar with stiffening members is constituted by introducing dual variables. And second order analysis of the bars on the basis of the continuous treatment strengthen component function. Then by a precise integration method of two end boundaries, and the establishment of corresponding MATLAB language program, the pole pieces of generalized displacements and generalized forces are solved. Finally the numerical example verification, shows the correctness of this method.This method has higher precision. The calculating process is simple and clean. A new way of bending-torsion coupling analysis of open thin-walled bar with stiffening members is provided.