Buckling of elastic shallow arches using the theory of a cosserat point

The numerical solution of problems of curved rods can be formulated using rod elements developed within the context of the theory of a Cosserat point. It is well known that the buckling of shallow arches presents a formidable challenge to theoretical models because it necessarily requires accurate modeling of the nonlinear coupling of membrane and bending effects as well as the accurate prediction of prebuckled deformations. This paper shows that the Cosserat theory predicts buckling loads and deformed shapes of elastic clamped circular arches which are in excellent agreement with the experiments over the full range of arch geometries that were tested. This success suggests that the Cosserat theory can be used to obtain reliable results for nonlinear deformations of curved elastic rods. Moreover, the analysis of these experiments indicates that variations in the thicknesses of shallow arch structures due to standard tolerances have a strong influence on buckling loads and should be measured and controlled in accurate buckling experiments.