A Lagrangian method for constrained dynamics in tensegrity systems with compressible bars

Hsu, Shao‐Chen; Tadiparthi, Vaishnav; Bhattacharya, Raktim

doi:10.1007/s00466-020-01924-z

Cited by 9 publications

(4 citation statements)

References 40 publications

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“…The software documentation and the manuscript (S.C. Hsu & Bhattacharya, 2018) comprehensively cover the functionality and the theory behind the Lagrangian formulation and the novel constraint correction method implemented in the package. We shall seek to incorporate techniques introducing control of dynamic tensegrity systems in future versions of the software.…”

Section: Discussionmentioning

confidence: 99%

STEDY: Software for TEnsegrity DYnamics

Tadiparthi¹,

Hsu²,

Bhattacharya³

2019

JOSS

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Section: Discussionmentioning

confidence: 99%

STEDY: Software for TEnsegrity DYnamics

Tadiparthi¹,

Hsu²,

Bhattacharya³

2019

JOSS

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“…Such a snap behavior is an obvious effect of the soft modes that are inherent in the structure. Other prominent works that discussed statics and dynamics of tensegrities include (Murakami and Nishimura 2001a;Oliveto and Sivaselvan 2011;Ashwear and Eriksson 2014;Li et al 2016;Hsu et al 2020).…”

Section: Mathematics Of Stable Tensegrity Structuresmentioning

confidence: 99%

Mathematics of stable tensegrity structures

Harish¹,

Nandurdikar²,

Deshpande³

et al. 2023

Journal of Theoretical, Computational and Applied Mechanics

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Tensegrity structures have been extensively studied over the last years due to their potential applications in modern engineering like metamaterials, deployable structures, planetary lander modules, etc. Many of the form-finding methods proposed continue to produce structures with one or more soft/swinging modes. These modes have been vividly highlighted and outlined as the grounds for these structures to be unsuitable as engineering structures. This work proposes a relationship between the number of rods and strings to satisfy the full-rank convexity criterion as a part of the form-finding process. Using the proposed form-finding process for the famous three-rod tensegrity, the work proposes an alternative three-rod ten-string that is stable. The work demonstrates that the stable tensegrities suitable for engineering are feasible and can be designed.

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“…For "bars-only" tensegrities, a series of works [23][24][25][26][27][28] develop specialized non-minimal formulations which use the nodal coordinates of two endpoints and a bar length constraint, i.e. six coordinates and one constraint, to uniquely define the dynamics of a 3D rigid bar, and thereby resolve those difficulties.…”

Section: Introductionmentioning

confidence: 99%

A Unified Framework for Dynamic Analysis of Tensegrity Structures with Arbitrary Rigid Bodies and Rigid Bars

Luo¹,

Wu²,

Xu³

2022

Preprint

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This paper develops a unified framework to study the dynamics of tensegrity systems with any arbitrary rigid bodies and rigid bars. The natural coordinates are adopted as a completely non-minimal modeling approach to describe both rigid bodies and rigid bars in terms of different combinations of basic points and base vectors. Various coordinate combinations are then unified into polymorphic expressions that succinctly encompass Class-1-to-k tensegrities. Then, the Lagranged'Alembert principle is employed to derive the dynamic equation, which has a constant mass matrix and is free from trigonometric functions as well as centrifugal and Coriolis terms. For numerical analysis of nonlinear dynamics, a modified symplectic integration scheme is derived, accommodating non-conservative forces and boundary conditions. Additionally, formulations for statics and linearized dynamics around static equilibrium states are derived to help determine cable actuation values and calculate natural frequencies and mode shapes, which are commonly needed for structural analyses. Numerical examples are given to demonstrate the proposed approach's abilities in modeling tensegrity structures composed of Class-1-to-k modules and conducting dynamic simulations with complex conditions, including slack cables, gravity loads, seismic grounds, and cable-based deployments. Finally, two novel designs of tensegrity structures exemplify new ways to create multi-functional composite structures.

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A Lagrangian method for constrained dynamics in tensegrity systems with compressible bars

Cited by 9 publications

References 40 publications

STEDY: Software for TEnsegrity DYnamics

STEDY: Software for TEnsegrity DYnamics

Mathematics of stable tensegrity structures

A Unified Framework for Dynamic Analysis of Tensegrity Structures with Arbitrary Rigid Bodies and Rigid Bars

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