Obtainment of the Envelope Graph of Bending Moments of the Solid Model of Slab Ballastless Track

When designing and calculating through ANSYS software, there exist many solid models that are unable to be simplified as the beam or shell. In order to obtain the distribution of internal force of these structures to guide the optimization design, the paper puts forward a method to obtain the envelope graph of bending moments of solid models through the secondary development of ANSYS software on the basis of the principles of the finite element internal force method. The method is applied to CRTSIballastless track structure on subgrade to analyze the longitudinal and transverse envelope graph of the bending moments under the action of the design wheel load or the common wheel load with temperature gradient. The method is useful for the optimization design of the ballastless track structure and can be applied to obtain the envelope graph of bending moments, shear or axial force of structures in other fields, which can’t be simplified as the beam or shell element. Introduction When analyzing the stress of various engineering structures through the application of the finite element method, we can make judgments based on the calculated stress state, which is accurate and reasonable theoretically. But in many cases, in addition to comprehending the stress state of structures, we need to determine reliability and make structural designs according to the axial forces, shear forces and bending moments of certain dominative cross-sections of structures [1]. Therefore, it’s of great significance to obtain the structure internal force diagram. Ballastless track is usually emulated and simulated by the beam-solid model and beam-shell model. It’s convenient to develop the beam-shell model and the boundary conditions are relatively simple, but the model often can’t reflect the actual stress of ballastless track. When calculating the warping stress under temperature gradient, or considering the influence of cracks, concrete creep and other factors, the solid model has to be used. ANSYS is the universal finite element software, which has favorable openness and provides various ways of the secondary development. The users can extend the function and inherit the system in the standard ANSYS version according to their own needs [2]. Ref. [3] obtains the average effect of the internal force of each section by the method of obtaining the internal force through the secondary development of ANSYS. When the difference of the internal force in the cross-section is not distinct, the method is feasible; on the contrary, the structure internal force diagram is needed to get the most unfavorable position to guide the structure design. The paper uses the finite element software ANSYS as a platform, it obtains the longitudinal and transverse envelope graph of bending moments of the track board in different load conditions based on the principle of finite element internal force method [4-6] through the secondary development of the APDL language, which makes certain guiding significance for the design of ballastless track structure. The Obtainment of The Envelope Graph of Bending Moments of Ballastless Track Board Calculation Model. Taking CRTSI slab ballastless track as the research object [7-10], the refined model in Fig. 1 is established through ANSYS and the convex block station is neglected in order to 6th International Conference on Electronic, Mechanical, Information and Management (EMIM 2016) © 2016. The authors Published by Atlantis Press 1753 control the mesh easily, meanwhile, the size effect of the fastener is considered, namely, the nodes on the rail are connected with the corresponding nodes in the size range of fasteners on the track board so as to eliminate stress concentration. The rail is simulated by beam188 element, the track board, CA mortar and base board are simulated by solid185 element and the fasteners and subgrade are both simulated by combination14 element. Figure 1. The finite element model of CRTSIslab ballastless track Load Conditions. The design wheel load or common wheel load with temperature gradient are the main forces for the reinforcement design for the element slab ballastless track on subgrade. According to this, this paper uses two kinds of load conditions (Table 1), the train loads are loaded as a single wheelset, which are loaded on the rail successively from the end of the track board, the midpoint of adjacent fasteners to the top of the fasteners. Table 1 The design loads of CRTSIslab ballastless track on subgrade Conditions Condition 1 Condition 2 Items design wheel load common wheel load with temperature gradient Values 300kN 150kN -5°C~+10°C The Envelope Graph of Bending Moments of Ballastless Track Board in Condition 1. Fig. 2 illustrates that the longitudinal positive bending moments along the length of the board change with alternating peaks and troughs in condition 1, which reach the peak on the cross-sections of the track board below the fasteners and drop about 60 percent to the trough between the fasteners. When the train loads are acted on the rail above the middle fastener, the bending moments reach its maximum value of 22.454kN·m/m and the longitudinal positive bending moments along the width of the board are relatively small on the end and middle of the board with the value of 10.907kN·m/m and 8.565kN·m/m. As for the longitudinal negative bending moments, they vary smoothly along the width and tend to be stable along the length after increasing from the end of the board to the second fastener, which reach its maximum value of 3.743kN·m/m on the cross-sections of the board below the fourth and the fifth fastener when the rail above the end fastener is loaded. Fig. 3 illustrates that the transverse positive bending moments along the length of the board change with alternating peaks and troughs, which reach the peak on the cross-sections of the track board below the fasteners and drop about 40 percent to the trough between the fasteners. When the train loads are acted on the rail above the end fastener, the bending moments reach its maximum value of 20.238kN·m/m on the corresponding cross-section. Along the width, there exist sections of 0.28B(B is the width of the track board)with the value of approximate zero of the bending moments near the center of the board. As for the transverse negative bending moments, when the train loads are acted on the rail at the end of the board, the bending moments reach its maximum value of 7.366kN·m/m and there exist sections of 0.32B with the value of approximate zero of the bending moments near the end of the board.