Computational modelling of the transformation of bistable scissor structures with geometrical imperfections

In many applications structures need to be easily moveable, or assembled at high speed on unprepared sites. For this purpose, preassembled deployable structures, which consist of beam elements connected by hinges, are highly effective. Intended geometric incompatibilities between the members are introduced for instantaneous structural stability after deployment. In such bistable scissor structures, these incompatibilities result in the bending of some specific members that are under compression with a controlled snap-through behaviour. The main goal of this contribution is to qualitatively and quantitatively discuss the behaviour of bistable scissor structures during deployment. To do this, a 3D nonlinear structural model is proposed to simulate the deployment, including explicitly geometrical imperfections in a stochastic approach. The originality of this contribution is (i) the implementation of gravity, (ii) the geometrical imperfections and (iii) the extension of the numerical model to complex deployable structures. Bounds on geometrical tolerances on several uncertain parameters (length of the beams, eccentricity of the pivot points, hinge misalignment and finite hinge stiffness) are proposed based on non-linear finite element simulations on a single module transformation. The computational tool is then applied to structures consisting of multiple modules and the influence of geometrical imperfections is characterized.