Geometrically conforming and directionally enriched finite element method for three dimensional slender members

Abstract

Analysis of spatially curved and twisted slender members with arbitrary cross‐sections, under general loads, is challenging as it requires accurate representation of the geometry and design of effective models for solution of the boundary‐value problem of thermo‐elasticity. Classical models miss the three‐dimensional nature of the solution in the vicinity of boundaries, loading zones, re‐entrant corners, cut‐outs, and defects. The current work provides a novel framework, to efficiently and accurately solve the problem of spatially curved, twisted beam‐like structures. The novelty of the method is two‐fold. First, it uses the finite element framework to capture the geometry of curved, extruded slender members with any desired accuracy adaptively. Secondly, it incorporates directionally enriched higher order basis functions along with appropriate mesh refinement separately in the longitudinal direction and cross‐section, to efficiently capture the cross‐sectional and longitudinal characteristics of the displacement field. The efficacy of the method is established through numerical examples.