Efficient Seismic Response Analysis Method For Suspension Bridge Based On Hybrid-nonlinearity Separated Finite Element Method

Suspension bridge is the most economical,beautiful and competitive bridge type in large-span bridges.Within its service life,it will suffer from different forms of natural disasters,among which the damage and losses caused by earthquakes are more serious.As an important means of simulating the catastrophe mechanism of engineering structures such as suspension bridges,nonlinear finite element method has attracted more and more attention from scholars at home and abroad.The current nonlinear finite element analysis of the suspension bridge structure mainly derives the stiffness matrix and the equilibrium equation by the TL(complete Lagrangian)determinant or the UL(updated Lagrangian)determinant,and solves it by the incremental iteration method.The traditional method needs to continuously update and decompose the tangent stiffness matrix during calculation.However,as the size of the suspension bridge increases and the refined requirements of the finite element model increase,the number of degrees of freedom of the structural analysis model will increase sharply,resulting in a rapid decrease in calculation efficiency.The inelasticity-separated finite element method is a new type of high-efficiency structural nonlinear analysis method proposed in recent years.This method has been developed in many aspects,but for the suspension bridge,the necessary simulation method is still lacking.Based on the nonlinear theory,the hybridnonlinearity separated finite element method for cable-beam composite structures is proposed to achieve efficient seismic response analysis of such structures.The main contents of this paper are as follows:First of all,the basic theory of the two-node catenary clue element that can accurately simulate the cable structure is introduced,and the element stiffness matrix and the cable end reaction force iterative solution method based on the Newton iteration method are proposed in two cases.Aiming at the problem of determining the initial state of cable-beam composite structures such as suspension bridges,an accurate catenary method for shape finding of main cables is introduced,and calculation methods for boom force and shape finding of side cables are proposed.Subsequently,the hybrid-nonlinearity separated finite element method for calculating the seismic response of a cable-beam composite structure is proposed.This method expands and superposes the isolation nonlinear governing equation of the beam structure and the governing equation of the cable structure variable stiffness method to obtain the overall hybrid-nonlinearity separated governing equation.By introducing the approximate Woodbury formula and using the error index to control the update frequency of the correlation matrix,an efficient simulation of the overall geometric nonlinear behavior of the structure and the local material nonlinear behavior can be achieved,and further combined with the Newmark direct integration method,an efficient seismic response analysis of the suspension bridge structure is realized.Finally,taking a cable-beam composite structure as an example,the seismic response analysis results of this method are compared with those of the finite element software ANSYS,which proves the accuracy of this method.Taking a suspension bridge as an example,the application of the method in this paper is introduced from the whole process of model simplification,unit division,determination of initial equilibrium state(shape finding of main cable and side cable),load application and dynamic calculation.The time complexity theory proves that this method is more efficient than the traditional variable stiffness method.