Coupled Sizing, Shape and Topology Optimisation of Bistable Deployable Structures

Bistable scissor structures, consisting of beams connected by hinges, are transportable and can be transformed from a compact to a deployed configuration. Geometric incompatibilities can be introduced during transformation to obtain a bistable structural response which enforces some instantaneous structural stability in the deployed state. The design of bistable scissor structures requires assessing both the non-linear transformation behaviour, as well as the service state, since a proper structural design has to provide stiffness in the deployed state as well as flexibility during transformation. These contradicting requirements were formulated previously in Arnouts et al. [1] as a multi-objective shape and sizing optimisation (SSO). The originality of this contribution is the elaboration of a design methodology coupling a novel topology optimisation (TO) to SSO and demonstrating its performance for the design of a bistable deployable wall. In this novel step, the number of bistable deployable modules (BDM) of the structure is optimised at low computational cost by finding the location of BDM, yielding mixed structures composed of BDM and non-bistable modules (NBDM) of lower weight and complexity than structures entirely built from BDM. TO is incorporated and assessed in the design methodology prior or subsequent to the SSO step. It is shown that the mixed structures combining BDM and NBDM resulting from the new coupled TO-SSO approach outperform pure BDM based structures.