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

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, for example, 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 nonlinear analyses for which hp-FE methods are often not readily applicable. The aim of this paper is, therefore, to derive a corotational FE formulation for enriched three-, four-, and five-noded beam elements, suitable for nonlinear hp-FE refinement. To this end, the mathematical formulation is derived to incorporate enriched elements within the corotational FE beam framework. The proposed formulation is then validated against multiple nonlinear benchmark problems and an experimental case study.