Tensegrity system dynamics based on finite element method

Shuo Ma, Muhao Chen, Robert E. Skelton

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


This study presents a finite element analysis approach to nonlinear and linearized tensegrity dynamics based on the Lagrangian method with nodal coordinate vectors as the generalized coordinates. In this paper, nonlinear tensegrity dynamics with and without constraints are first derived. The equilibrium equations in three standard forms (in terms of nodal coordinate, member force density, and member force vectors) and the compatibility equation are also given. Then, we present the linearized dynamics and modal analysis equations with and without constraints. The developed approach is capable of conducting the following comprehensive dynamics studies for any tensegrity structures accurately: performing rigid body dynamics with acceptable errors, which is achieved by setting relatively high stiffness for bars in the simulation; simulating FEM dynamics accurately, where bars and strings can have elastic or plastic deformations; dealing with various kinds of boundary conditions, for example, fixing or applying static/dynamic loads at any nodes in any direction (i.e., gravitational force, some specified forces, or arbitrary seismic vibrations); conducting accurate modal analysis, including natural frequency and corresponding modes. Three examples, a double pendulum, a cantilever truss with external force, and a double prism tensegrity tower, are carefully selected and studied. The results are compared with rigid body dynamics and FEM software ANSYS. This study provides a deep insight into structures, materials, performances, as well as an interface towards integrating control theories.

Original languageEnglish
Article number114838
JournalComposite Structures
StatePublished - Jan 15 2022

Bibliographical note

Publisher Copyright:
© 2021 Elsevier Ltd


  • Finite element method
  • Lagrangian method
  • Linearized tensegrity dynamics
  • Nodal coordinate
  • Non-linear dynamics
  • Tensegrity system

ASJC Scopus subject areas

  • Ceramics and Composites
  • Civil and Structural Engineering


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