A finite beam element framework for variable stiffness structures

Recently, interest in using spatially variable structural properties has increased significantly due to the perceived benefits associated with composite and functionally graded materials. However, the increased variability of structural properties can exacerbate numerical errors resulting from the modelling assumptions originally derived for prismatic structures. This work is the first of a series we are conducting with the aim to achieve accurate 3D displacement, strain and stress fields using computationally cheap 1D beam elements to model spatially variable wind turbine blades. The strategy developed for this purpose is split into two parts. The first concerns the automated generation of refined linear beam elements and the second considers the extension of the co-rotational framework in order to provide a straightforward means of using these elements in non-linear analyses. In this paper we focus on the former and propose two enhancements to conventional beam elements. First, a framework for the automated generation of beam elements with a variable number of nodes is developed. Second, an integration scheme designed to take into account spanwise variations of structural properties along the beam element length is introduced. The influence of the proposed improvements on the displacements and strains accuracy of a statically loaded wind turbine blade is presented. Results suggest that this new method successfully improves the accuracy of strain predictions while lowering the number of nodes required in order to reach a converged strain field.