Abstract
Tensegrity structures are finding applications in areas such as deployable, lightweight, and compliant morphing structures. However, in order to fulfil their potential, new analysis and design methods are required. The tangent stiffness matrix of a tensegrity contains its full structural information; hence, in this thesis, we exploit the stiffness matrix to develop novel design and analysis methods for tensegrity structures in three aspects: a form-finding method, a sensitivity study of the manufacturing length errors, and a method to transform between stable states of multistable tensegrity structures.Firstly, to design a truly tessellated tensegrity structure (where unit cells rely on neighbouring units for equilibrium), an adapted stiffness matrix form-finding method is developed. Given topology and member properties as input, this method uses the stiffness matrix to formulate the gradient vector, and iteratively finds the equilibrated state of the tensegrity structures. The proposed form-finding method works for both free-standing tensegrity structures and tensegrity systems with boundary conditions and external forces. Moreover, it is uniquely capable of designing tensegrity structures where specified nodes simultaneously have predefined nodal coordinates and predefined residual forces in the equilibrated state.
Next, a sensitivity analysis of manufacturing length errors is carried out using a Monte Carlo simulation. A randomly generated manufacturing length error is applied to the natural length of members in the perfect state of structure. The adapted stiffness matrix form-finding method is then used to obtain a new balanced configuration; the form-finding method is particularly efficient as the imperfect member properties are direct input parameters. Although tensegrities are nonlinear structures, a linear relationship is found between the standard deviation of the input manufacturing length errors and the standard deviation of the output member tensions. Lastly, an analytical method for manufacturing error sensitivity is derived and results of both methods are compared; the numerical method is more versatile and accurate, at the expense of computational effort.
Finally, an analysis method is implemented to obtain for the first time a transformation route between the stable states of multistable tensegrity structures, and identify the corresponding minimum energy threshold. In order to achieve this, the tangent stiffness matrix and a slack cable model are implemented in a Mountain-Pass Algorithm. This method also gives the “dynamic stability” property of each equilibrated state, by determining the depth of the energy well of the stable configurations.
Combined, the tools and methods developed in this thesis offer significant advances in various aspects of the design and analysis of efficient and multi-functional tensegrity structures.
| Date of Award | 9 May 2023 |
|---|---|
| Original language | English |
| Awarding Institution |
|
| Sponsors | Chinese Scholarship Council |
| Supervisor | Mark Schenk (Supervisor) & Fabrizio Scarpa (Supervisor) |