Corotational Finite Element Formulation for Static Nonlinear Analyses with Enriched Beam Elements

Abstract

The increasing reliance of aerospace structures on numerical analyses encourages the development of accurate, yet computationally efficient, models. Finite element (FE) beam models have, in particular, become widely-used approximations during preliminary design stages and to investigate novel concepts, e.g. aeroelastic tailoring. Over the last 50 years, developments in hp-FE methods based on elements of variable size (h) and polynomial degree (p) have helped reduce the computational cost of numerical analyses. Concurrently, many structures, including aircraft wings and wind turbine blades, have gradually increased in length, slenderness, and complexity. As a result, modern blades and wings regularly operate beyond the range of linear deformation, requiring non-linear analyses for which hp-FE methods are often not readily applicable. The aim of this paper is, therefore, to derive a co-rotational finite element formulation for enriched 3-, 4-and 5-noded beam elements, suitable for non-linear hp-FE refinement. To this end, we derive the mathematical formulation to incorporate enriched elements within the co-rotational FE beam framework. The proposed formulation is then validated against multiple non-linear benchmark problems and an experimental case study.

Comparison of blade optimisation strategies for the IEA 15MW reference turbine

“…In this work, it was found that a damping ratio of 6% was required for stable simulations when using the modal beam with 15 modes. However, a few trial simulations using ATOM's non-linear beam model [20] appeared to be stable with a damping ratio of 0.5%. Thus, a question mark remains over the stability analysis of large blades and more accurate methods of assessing stability are required.…”

A co-rotational formulation for quasi-steady aerodynamic nonlinear analysis of frame structures

“…Regarding the nonlinear geometric analysis of wind turbine blades, the linearized equations of motion were solved in [16] , obtaining a good level of agreement between the exact beam theory and formulations using shell elements. In [11] , [29] , static co-rotational formulations were used to simulate morphing or highly flexible wings, highlighting the computational efficiency to validate experimental results. However, the performance of a formulation considering consistent inertial terms and aerodynamic forces using the co-rotational framework, has not been reported.…”