A tutorial on simulating nonlinear behaviors of flexible structures with the discrete differential geometry (DDG) method
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908320708689920 |
|---|---|
| author | Huang, Weicheng Hao, Zhuonan Li, Jiahao Tong, Dezhong Guo, Kexin Zhang, Yingchao Gao, Huajian Hsia, K. Jimmy Liu, Mingchao |
| author_facet | Huang, Weicheng Hao, Zhuonan Li, Jiahao Tong, Dezhong Guo, Kexin Zhang, Yingchao Gao, Huajian Hsia, K. Jimmy Liu, Mingchao |
| contents | Flexible elastic structures, such as beams, rods, ribbons, plates, and shells, exhibit complex nonlinear dynamical behaviors that are central to a wide range of engineering and scientific applications, including soft robotics, deployable structures, and biomedical devices. While various numerical methods have been developed to simulate these behaviors, many conventional approaches struggle to simultaneously capture geometric and material nonlinearities, as well as nonlinear external interactions, particularly in highly deformable and dynamically evolving systems. The Discrete Differential Geometry (DDG) method has emerged as a robust and efficient numerical framework that intrinsically preserves geometric properties, accommodates material nonlinearity, and accurately models interactions with external environments and fields. By directly discretizing geometric and mechanical quantities, DDG provides an accurate, stable, and efficient approach to modeling flexible structures, addressing key limitations of traditional numerical methods. This tutorial provides a systematic introduction to the DDG method for simulating nonlinear behaviors in flexible structures. It covers DDG theory, simulation frameworks, and MATLAB implementation, with examples spanning dynamic systems, geometric and material nonlinearities, and external interactions like magnetics and fluids, culminating in practical insights and future directions. By offering a comprehensive and practical guide, together with open-source MATLAB code, this tutorial aims to facilitate the broader adoption of DDG-based numerical tools among researchers and engineers in computational mechanics, applied mathematics, and structural design. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_11417 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A tutorial on simulating nonlinear behaviors of flexible structures with the discrete differential geometry (DDG) method Huang, Weicheng Hao, Zhuonan Li, Jiahao Tong, Dezhong Guo, Kexin Zhang, Yingchao Gao, Huajian Hsia, K. Jimmy Liu, Mingchao Soft Condensed Matter Flexible elastic structures, such as beams, rods, ribbons, plates, and shells, exhibit complex nonlinear dynamical behaviors that are central to a wide range of engineering and scientific applications, including soft robotics, deployable structures, and biomedical devices. While various numerical methods have been developed to simulate these behaviors, many conventional approaches struggle to simultaneously capture geometric and material nonlinearities, as well as nonlinear external interactions, particularly in highly deformable and dynamically evolving systems. The Discrete Differential Geometry (DDG) method has emerged as a robust and efficient numerical framework that intrinsically preserves geometric properties, accommodates material nonlinearity, and accurately models interactions with external environments and fields. By directly discretizing geometric and mechanical quantities, DDG provides an accurate, stable, and efficient approach to modeling flexible structures, addressing key limitations of traditional numerical methods. This tutorial provides a systematic introduction to the DDG method for simulating nonlinear behaviors in flexible structures. It covers DDG theory, simulation frameworks, and MATLAB implementation, with examples spanning dynamic systems, geometric and material nonlinearities, and external interactions like magnetics and fluids, culminating in practical insights and future directions. By offering a comprehensive and practical guide, together with open-source MATLAB code, this tutorial aims to facilitate the broader adoption of DDG-based numerical tools among researchers and engineers in computational mechanics, applied mathematics, and structural design. |
| title | A tutorial on simulating nonlinear behaviors of flexible structures with the discrete differential geometry (DDG) method |
| topic | Soft Condensed Matter |
| url | https://arxiv.org/abs/2504.11417 |