The Application Research Of The Substructure Method In Bridge Structural Analysis

With the rapid development of traffic construction, computer hardware technologies and the theory of finite element method, the calculation of complex structural mechanics problems has experienced revolutionary change. Meanwhile, such development has also brought new vitality to the further development of dynamic substructure method theory. When making an analysis of the vehicle-bridge-track dynamic characteristics, the structural degrees of freedom is accordingly increasing as the scale of structural model is expanding. Therefore, numerous calculation of structure should have to be made. The basic idea of substructure method is to modify before recovery, through reducing the DOFs to simplified calculation, which not merely reduces the order of dynamic equation, improves the calculation efficiency but also ensures the accuracy of structural analysis.The paper first studies ballastless tracks with long embedded sleepers. Based on the theory of static condensation method by Guyan and super-element method of substructure, the paper proposes an efficient sleeper super-element, which can be used in the elaborate vehicle-bridge-track coupling dynamic analysis and dramatically improve the calculation efficiency. The main researches are as follows:①Based on D’Alembert theory,the author derives multi-degree-of-freedom system motion equation; a finite element model of ballastless tracks is established with the finite element method, then the bridge structure vibration differential equation is derived.②Based on Guyan’s theory of the static condensation method, the author builds model of ballastless tracks with long embedded ties, and does static analysis under different conditions. Through comparing the reduced model’s static and dynamic properties with the unreduced one’s, the paper verifies Guyan’s static condensation method’s feasibility in structural static analysis and shortage in dynamic analysis.③In this paper, the author uses MATRIX50element in ANSYS to build reduced model of bridge’s ballastless tracks. By comparing the reduced model’s transient-dynamical property with the unreduced one’s, it shows MATRIX50element’s shortages in horizontal and vertical torsion, because its mass matrix and damping matrix also comes from Guyan’s theory.④With the D’Alembert’s principle,the paper derives mass matrix [M],stiffness matrix [K] and damping matrix [C]of sleeper substructure super-element. Utilizing the MATRIX27unit in ANSYS, the paper simulates and builds the reduced model.Then the paper compares the reduced model with the oringinal one in spatial dynamic response analysis, the results verify the feasibility of sleeper super-element this paper presents.