Publication | Multibody System Dynamics Journal 2020
A low order, torsion deformable spatial beam element based on the absolute nodal coordinate formulation and Bishop frame
In this paper we introduce a new singularity-free beam element for large deformation analysis of beam finite elements.
Download publicationAbstract
A low order, torsion deformable spatial beam element based on the absolute nodal coordinate formulation and Bishop frame
Mehran Ebrahimi, Adrian Butscher, Hyunmin Cheong
Multibody System Dynamics Journal 2020
Heretofore, the Serret–Frenet frame has been the ubiquitous choice for analyzing the elastic deformations of beam elements. It is well-known that this frame is undefined at the inflection points and straight segments of the beam where its curvature is zero, leading to singularities and errors in their numerical analysis. On the other hand, there exists a lesser-known frame called Bishop which does not have the caveats of the Serret–Frenet frame and is well-defined everywhere along the beam center-line. Leveraging the Bishop frame, in this paper, we propose a new spatial, singularity-free low order beam element based on the absolute nodal coordinate formulation for both small and large deformation applications. This element, named ANCF14, has a constant mass matrix and can capture longitudinal, transverse (bending) and torsional deformations. It is a two-noded element with 7 degrees of freedom per node, which are global nodal coordinates, nodal slopes and their cross-sectional rotation about the center-line. The newly developed element is tested through four complex benchmarks. Comparing the ANCF14 results with theoretical and numerical results provided in other studies confirms the efficiency and accuracy of the proposed element.
Related Resources
2024
What’s in this LCA Report? A Case Study on Harnessing Large Language Models to Support Designers in Understanding Life Cycle ReportsExploring how large language models like ChatGPT can help designers…
2023
Generating Pragmatic Examples to Train Neural Program SynthesizersUsing neural networks is a novel way to amortize a synthesizer’s…
2014
Draco: Bringing Life to Illustrations with Kinetic TexturesDraco is a prototype sketch-based interface from that allows artists…
2019
Project Discover: Workflow for Generative Design in ArchitectureThis project involves the integration of a rule-based geometric…
Get in touch
Something pique your interest? Get in touch if you’d like to learn more about Autodesk Research, our projects, people, and potential collaboration opportunities.
Contact us