Equivalence Relation of Curved Beam Pure Bending and Its Experimental Verification

Abstract

The pure bending process of the plane curved beam is one of the most important parts in the field of solid mechanics.However,because of exist of the initial curvature,it is difficult to give the accurately analysis result.Relatively,the bending process of the straight beam can be easily predicted.To simplify the analytical model of plane curved beam bending,according to the feature of small deformation in small curved beam bending process,the equivalence relation of curved beam pure bending is given by introducing the linear distribution assumption of the bending strain.Based on the feature of four-point bending process,and relying on the measuring equipment with high precision,the experimental results prove the feasibility of equivalence relation by the ways of different plank stuff and different technological parameter.The final results suggest the absolute error is less than 5×10–5,the relative error is less than 4.5%,when using the addition curvature instead the bending result of the curved beam.