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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2206.06221 |
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| _version_ | 1866929478319472640 |
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| author | Luo, Jiahui Xu, Xiaoming Wu, Zhigang Wu, Shunan |
| author_facet | Luo, Jiahui Xu, Xiaoming Wu, Zhigang Wu, Shunan |
| contents | This paper proposes a unified approach for dynamic modeling and simulations of general tensegrity structures with rigid bars and rigid bodies of arbitrary shapes. The natural coordinates are adopted as a non-minimal description in terms of different combinations of basic points and base vectors to resolve the heterogeneity between rigid bodies and rigid bars in three-dimensional space. This leads to a set of differential-algebraic equations with a constant mass matrix and free from trigonometric functions. Formulations for linearized dynamics are derived to enable modal analysis around static equilibrium. For numerical analysis of nonlinear dynamics, we derive a modified symplectic integration scheme which yields realistic results for long-time simulations, and accommodates non-conservative forces as well as boundary conditions. Numerical examples demonstrate the efficacy of the proposed approach for dynamic simulations of Class-1-to-$k$ general tensegrity structures under complex situations, including dynamic external loads, cable-based deployments, and moving boundaries. The novel tensegrity structures also exemplify new ways to create multi-functional structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_06221 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Unified Approach for Dynamic Analysis of Tensegrity Structures with Arbitrary Rigid Bodies and Rigid Bars Luo, Jiahui Xu, Xiaoming Wu, Zhigang Wu, Shunan Computational Engineering, Finance, and Science This paper proposes a unified approach for dynamic modeling and simulations of general tensegrity structures with rigid bars and rigid bodies of arbitrary shapes. The natural coordinates are adopted as a non-minimal description in terms of different combinations of basic points and base vectors to resolve the heterogeneity between rigid bodies and rigid bars in three-dimensional space. This leads to a set of differential-algebraic equations with a constant mass matrix and free from trigonometric functions. Formulations for linearized dynamics are derived to enable modal analysis around static equilibrium. For numerical analysis of nonlinear dynamics, we derive a modified symplectic integration scheme which yields realistic results for long-time simulations, and accommodates non-conservative forces as well as boundary conditions. Numerical examples demonstrate the efficacy of the proposed approach for dynamic simulations of Class-1-to-$k$ general tensegrity structures under complex situations, including dynamic external loads, cable-based deployments, and moving boundaries. The novel tensegrity structures also exemplify new ways to create multi-functional structures. |
| title | A Unified Approach for Dynamic Analysis of Tensegrity Structures with Arbitrary Rigid Bodies and Rigid Bars |
| topic | Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2206.06221 |