A comparative study of geometrical curvature expressions for the large displacement analysis of spatial absolute nodal coordinate formulation Euler–Bernoulli beam motion

While the geometrical curvature expressions have become widely used in the beams based on absolute nodal coordinate formulation, they have not yet been compared and sufficiently verified, particularly for the spatial beam motion. In this paper, two geometrical curvature expressions for the large displacement analysis of spatial beam motion are compared and their fundamental differences are highlighted: the exact curvature model and general curvature model. In order to examine numerically the ability of two curvature expressions in the large displacement analysis, a three-dimensional absolute nodal coordinate formulation Euler–Bernoulli beam element is selected as the candidate. Several static and dynamical benchmarks are performed to assess their accuracy and differences. It is shown that the exact curvature model can be effectively and efficiently used in static applications, particularly in the highly nonlinear static analysis. In dynamics problems, the accuracy of two curvature models is equivalent, while the exact curvature model is more time-consuming. These conclusions can be a recommendation for the choice of geometrical curvature expressions in some certain practical examples.