Analysis Of Plane Strain Pure Bending Curved Beam With Unified Strength Theory

The curved beam is broadly used in engineering structure because of its streamline shape and good mechanical properties. Many scholars have paid great attentions to the research of curved beam. The elastic-plastic analysis of pure bending curved beam is an important part in curved beam’s research. It includes the solutions of the stresses, strains and displacements in different stages, and also includes the solutions of the critical load. The analysis of the plane strain elastic-plastic pure bending of a linear strain hardening curved beam is conducted. The elastic-plastic unified solutions suitable for all kinds of materials is obtained based on the unified yield criterion (UYC) and unified strength criterion (USC).The solution based on the UYC considers the influence of the intermediate principal stress on material’s yield strength, it can be used for the materials whose tensile and compressive strength is identical. Based on the derived theoretical solution, the influences of the intermediate principal stress and poison’s ratio on the elastic-plastic critical load, the interface radii between the elastic and plastic regions and the displacement distribution of the curved beam are discussed. Due to the assumption of plastic incompressibility, the USC that consider the strength-differential effect and intermediate principal stress effect can also be used in curved beam’s elastic-plastic bending analysis. Compared with the solution based on UYC, the solution on the basis of USC can be more widely used. At the same time, based on the theoretical solution in USC, the influences of the intermediate principal stress and strength-different on the elastic-plastic critical load, the interface radii between the elastic and plastic regions and the displacement distribution of the curved are discussed. According to the above two discussions, intermediate principal stress and strength-different have significant influence on the plane strain pure bending of the curved beam. The influence of the intermediate principal stress and strength-different cannot be ignored in curved beam’s elastic-plastic bending analysis, the choice of the yield criterion is of great importance for the accuracy of the result.The ABAQUS FEM is also used to simulate curved beam’s plane strain elastic-plastic bending. Compared with the theoretical solution in each elastic-plastic bending stage, we can obtain that the result we get in this paper is similar to the FEM result.