A Theory for the Design of Multi-Stable Morphing Structures
Multi-stable structures can provide desired reconfigurability and require relatively simple actuation. This paper considers general bar and plate structures connected by frictionless hinges that are to be made locally stable in a set of chosen target configurations by attaching extensional and rotational, linear-elastic springs to the structure. The unstressed lengths and angles of the springs, as well as their stiffnesses, are the unknown design parameters to be determined. A set of equilibrium and stability conditions to be satisfied in each of the target configurations of the structure are derived. Solutions of these equations provide specific values of the spring properties that correspond to local energy minima in all of the target configurations. The formulation is fully general and is applicable to structures of any complexity. A simple example is used to illustrate the design process for a bi-stable origami structure and a physical prototype is also presented.
© 2019 Published by Elsevier. Received 5 August 2019, Revised 23 October 2019, Accepted 23 October 2019, Available online 25 October 2019. Discussions with Professor Kaushik Bhattacharya and the team of the AFOSR MURI project Universal Electromagnetic Surface: Exploiting active electronics and active origami to generate a programmable electromagnetic response are acknowledged. This paper is based upon work supported by the Air Force Office of Scientific Research under award number FA9550-18-1-0566 directed by Dr Ken Goretta. Research Data: Matlab codes for the example in Section 6 can be downloaded from Supplementary material. Download all files and put them in the same folder. Run the script "RUN_ME_miura_phi0" in Matlab and the design parameters (rest angles for the torsional springs) will be computed. Declaration of Competing Interest: None.
Supplemental Material - 1-s2.0-S0022509619307628-mmc1.zip