Elasto-Plastic Large Deformation Bend Forming Process Analysis Of Beams Using Coupling Cross-Section Finite Element Technique

Bending structural members with constant cross-section find wide applications in construction, machinery, railway, transport and other areas. They are usually manuafactured through bending forming of straight bars. Numerical models are widely used to simulate the highly nonlinear bending forming process and provide important forming parameters for the rational design of the forming process. It is well known that performing nonlinear analysis is usually very time consuming. In order to improve the analysis efficiency, it is highly desirable to make good use of the characteristic of the forming process to reduce the model size if possible.When a constant cross-sectional beam is subject to circular pure bending deformation, the material in the same cross-sectional plane of the beam before deformation will remain to be in the same plane after deformation, and the deformation field of all cross-sections will be identical. These deformation features can be used to implement the finite element simulation of beam bending forming process based on a typical thin slice of the beam geometry. Accurate boundary conditions can be formulated and applied to the artificial cross-sectional boundaries of the thin slice geometric model. By doing so, the size of the finite element model can be significantly reduced, thus the running time can also be substantially reduced.The analysis of a rectangular bar was first carried out using the slice finite element model developed. For linear or elastic perfectly plastic pure bend analysis, the numerical results such as bending moment-curvature relationship, springback and stress distribution were validated with available theoretical analytical solutions. Then the analyses were extended to the large deformation elastic-plastic bending processes of bars with circular cross-section and I-section beams. Finally the modelling methodology has been further extended to analyze periodic beam structures by modeling a typical periodic unit of the beam. As an example of the periodic beams, the bending process of a steel I-section bar with corrugated web has been simulated.