A low order, torsion deformable spatial beam element based on the absolute nodal coordinate formulation and Bishop frame

2020-11-16

Multibody system dynamics

AI Summary

To address the low modeling accuracy and high computational cost associated with torsion–bending coupling in large-deformation simulations of highly flexible spatial beams, this paper proposes a novel three-dimensional Absolute Nodal Coordinate Formulation (ANCF) beam element based on the Bishop parallel frame. Unlike the conventional Serret–Frenet frame, the Bishop frame decouples curvature and torsion, avoids Euler-angle singularities, and enables geometrically exact, singularity-free torsion-deformable modeling. By integrating the Bishop frame into the ANCF framework for the first time—combined with continuum mechanics-based formulation and finite-element discretization—the proposed element achieves significantly improved simulation accuracy for problems involving strong spatial bending–torsion coupling and large torsional deformations, while reducing the number of degrees of freedom by over 30%. Dynamic response errors are reduced by an order of magnitude compared to conventional ANCF beam elements.

Technology Category

• Computer Vision: 3D Computer Vision
• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Problem

• Beam Models
• Serret-Frenet Coordinate System
• Elastic Deformation Analysis

Innovation

• ANCF14 beam element
• Bishop coordinate system
• accuracy and superiority in deformation analysis