Corotational 3D joint finite element tailored for the simulation of bistable deployable structures

Abstract

The 3D deployable frames studied in this work are structures composed of elastic beam elements connected by complex joints. During transformation a controlled snap-through allows the instantaneous stabilization of the structure in an open and in a closed, compact configuration. The mechanics of the transformation is highly nonlinear, since it relies on finite rotations of the structural elements. It is also strongly influenced by geometrical features required for a manufacturing-ready design, such as the finite size of structural elements and sufficient spacing between the beams. These features are generally disregarded in the usual wireframe-based design, but they are taken into account in this work by applying a tailor-made corotational 3D joint finite element, developed to incorporate naturally finite joint size, finite nonlinear joint stiffness and friction effects. The formulation of the proposed joint FE is presented and the performance of the numerical implementation is verified using computational benchmarks. The joint FE is then applied to the numerical investigation of the transformation response of bistable deployable structures from a single module case to large, complex structures. Among other findings, it is shown that the incorporation of finite joint size and beam spacing in the numerical model leads to a different snap-through mechanism that significantly reduces the peak force required for transformation, which could be a basis for future design strategies. Additionally the performance of structures applying the bistable structural pattern on the whole structure or following an entirely modular design (interconnected single modules) is also compared, as a function of the structural size.