A curved beam model with the asymptotic expansion method

Abstract

In our previous work (Ferradi, 2015, 2016) [7,10], a model reduction technique was proposed for straight beams with a constant cross-section, based on the asymptotic expansion method applied to the general 3D equilibrium equations. An iterative scheme was then deduced, where 2D cross section modes, representing the general form of the kinematic, were derived at each order. The following paper is an extension of the work in Ferradi (2015, 2016) [7,10] to the curved beam elements, where in addition to the asymptotic expansion method, the differential geometry tools are used. Thus, a new efficient and locking free beam model is derived from the asymptotic expansion method, capable of representing accurately the full 3D stress and the displacement field of the curved beam, even in the vicinity of external forces. In each example, the results are compared to those from a reference shell model of the same beam geometry.