Hamel's field variational integrator for simulating dynamics of thin-walled geometrically exact beams with warping effects

Chen, Ju; Huang, Ziheng; Tian, Qiang

doi:10.1016/j.mechmachtheory.2023.105462

Mechanism and Machine Theory

2023

DOI: 10.1016/j.mechmachtheory.2023.105462

|View full text |Cite

Hamel's field variational integrator for simulating dynamics of thin-walled geometrically exact beams with warping effects

Ju Chen,

Ziheng Huang,

Qiang Tian

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

2025

Publication Types

Select...

Article5

Relationship

Self Cite0

Independent5

Authors

Journals

Cited by 5 publications

References 51 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Constraint Realization‐Based Hamel Field Integrator for Geometrically Exact Planar Euler–Bernoulli Beam Dynamics

Wang,

Shi,

2024

Numerical Meth Engineering

View full text Add to dashboard Cite

In this article, we first introduce a Hamel field integrator designed for a geometrically exact Euler–Bernoulli beam with infinite‐dimensional holonomic constraints, constructed using a Lagrange multiplier. This method addresses the complexities introduced by constraints, but the additional multiplier introduces a new degree of freedom and hence results in a system with mixed‐type partial differential equations. To address this issue, we further propose a constraint realization method based on perturbation theory for infinite‐dimensional mechanical systems within the framework of Hamel's formalism. This method circumvents the use of additional Lagrange multiplier, significantly reducing the computational complexity of modeling problems. Building on this, we construct a perturbed Hamel field integrator optimized for parallel computing and incorporate artificial viscosity to accelerate constraint convergence. While applicable to three dimensions, our method is demonstrated in a simplified context using planar Euler–Bernoulli beam examples to illustrate the effectiveness of the unified mathematical framework.

show abstract

Constraint Realization‐Based Hamel Field Integrator for Geometrically Exact Planar Euler–Bernoulli Beam Dynamics

Wang,

Shi,

2024

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

A spacetime variational integration approach to the full discretization of flexible beams based on absolute nodal coordinate formulation

Zhou,

Ren,

Fan

et al. 2024

Nonlinear Dyn

View full text Add to dashboard Cite

A new variational integrator for constrained mechanical system dynamics

Zhou,

Ren,

Fan

et al. 2025

Applied Mathematical Modelling

View full text Add to dashboard Cite

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Hamel's field variational integrator for simulating dynamics of thin-walled geometrically exact beams with warping effects

Cited by 5 publications

References 51 publications

Constraint Realization‐Based Hamel Field Integrator for Geometrically Exact Planar Euler–Bernoulli Beam Dynamics

Constraint Realization‐Based Hamel Field Integrator for Geometrically Exact Planar Euler–Bernoulli Beam Dynamics

A spacetime variational integration approach to the full discretization of flexible beams based on absolute nodal coordinate formulation

A new variational integrator for constrained mechanical system dynamics

Contact Info

Product

Resources

About