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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., SCOPUS: ar.j, info:eu-repo/semantics/published

Pre-assembled scissor structures can be transformed from a compact bundle of elements to a fully deployed configuration, offering a considerable volume expansion. Intended geometrical incompatibilities during transformation can be introduced as a design strategy to obtain bistability, which allows instantaneously achieving some structural stability in the deployed state. Because of these incompatibilities, some specific members bend during transformation, resulting in a controlled potentially tunable snap-through behaviour. Geometric design methodologies were proposed in the literature to obtain a compatible geometry (i.e. with all of the beams straight) in the folded and the deployed configurations. However, most of these approaches do not consider finite hub sizes or introduce extra incompatibilities in the geometry by adding hub legs. In this contribution, deployability conditions are derived taking the finite hub size, i.e. the spacing between the connections of the different beams to the hub, into account to make triangulated bistable scissor modules fully geometrically compatible in the folded and the deployed configuration, SCOPUS: ar.j, info:eu-repo/semantics/published

Mobile deployable scissor structures are transportable and can be transformed rapidly from a compact folded state offering a huge volume expansion. Intended geometrical incompatibilities during transformation can be introduced as a design strategy to obtain bistability, which allows instantaneously achieving some structural stability in the deployed state. In such bistable deployable structures, these incompatibilities result in the elastic bending of some specific members that are under compression with a controlled snap-through behaviour. Attempts to optimally design deployable bistable structures remain scarce, since the underlying structuralmechanical concepts are complex. Furthermore, the requirement of flexibility during deployment while ensuring some structural stability in the deployed state prevents the use of simple design methodologies relying on the structural behaviour under service loads only. In this contribution, the trends and challenges of using computational tools in the structural analysis and design process of deployable bistable structures are discussed. Computational tools are crucial for the geometrical and structural design, for the definition of a rigorous design methodology and for a deeper understanding of the complex transformation behaviour of these structures., SCOPUS: ar.j, info:eu-repo/semantics/published

Preassembled scissor structures are transportable and can be transformed rapidly while offering a huge volume expansion. Intended geometrical incompatibilities between the members during transformation can be introduced as a design strategy to obtain bistability, which allows instantaneously achieving some structural stability in the deployed state. In such bistable scissor structures, these incompatibilities result in the bending of some specific members that are under compression with a controlled snap-through behavior. This contribution investigates the nonlinear structural behavior of bistable scissor structures during transformation using finite element models. Attempts to model the complete transformation cycle of bistable scissor structures remain scarce, partially because the underlying phenomena and modeling concepts are complex. The main goal of this contribution is to propose a 3D nonlinear structural model for the simulation of the deployment of bistable scissor structures including geometrical imperfections., info:eu-repo/semantics/published

In many applications structures need to be easily moveable, or assembled at high speed on unprepared sites. Forthis purpose, preassembled deployable structures, which consist of beam elements connected by hinges, arehighly 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., SCOPUS: ar.j, info:eu-repo/semantics/published

Two algorithms for the stress update (i.e., time integration of the constitutive equation) in large-strain solid mechanics are compared from an analytical point of view. The order of the truncation error associated to the numerical integration is deduced for each algorithm a priori, using standard numerical analysis. This accuracy analysis has been performed by means of a convected frame formalism, which also allows a unified derivation of both algorithms in spite of their inherent differences. Then the two algorithms are adapted from convected frames to a fixed Cartesian frame and implemented in a small-strain finite element code. The implementation is validated by means of a set of simple deformation paths (simple shear, extension, extension and compression, extension and rotation) and two benchmark tests in non-linear mechanics (the necking of a circular bar and a shell under ring loads). In these numerical tests, the observed order of convergence is in very good agreement with the theoretical order of convergence, thus corroborating the accuracy analysis., Peer Reviewed, Postprint (author’s final draft)