Nonlinear analysis of compliant deployable structures: modelling, simulation and experimental validation

Compliant mechanisms are flexible components which can store elastic energy when deformed and then passively release it to produce a motion. Their scope of applications encompasses various domains from robotic orthoses to microscopes and grippers. In this work, the developments focus on compliant mechanisms called tape springs used in deployable space structures.

Tape springs, due to their autonomous deployment capacity from a compact folded configuration, their high stiffness in the deployed equilibrium state and their simplicity of integration, represent efficient alternatives to common motorised hinges for space applications. Thus, they are currently used to deploy appendices on satellites such as solar panels or telescopes and are considered as valuable components in the design of future applications such as solar sails, deployable optics and inflatable structures. However, their structural behaviour is highly nonlinear and quite sensitive to the design parameters and to the various constraints encountered on Earth and in a space environment. The objective of this thesis is thus to develop validated high-fidelity dynamic models of tape springs which can be used to support the design process. The methodology involves the development of advanced finite element models and experimental tests based on an original set-up.

First, a quasi-static model based on shell finite elements is established and used to investigate the nonlinear response of tape springs as well as the influence of various geometric parameters. This model is then exploited for the design of tape springs deploying a reflector based on an automatic optimisation procedure. The study is further extended to dynamic analyses, which are characterised by a self-locking of the tape springs in their final deployed configuration. In order to accurately capture these phenomena, the importance of a suitable representation of the physical structural dissipation in the model is demonstrated and, for metallic tape springs, a Kelvin-Voigt model is retained.

An experimental set-up is then designed in order to validate the model and its capacity to represent the nonlinear phenomena inherent to tape springs which occur during quasi-static and dynamic tests. The experimental data are acquired by the means of an innovative 3D motion analysis system and a force plate. The reproducibility of the tests is assessed and a procedure, involving several elementary tests, is proposed to identify the parameters of the finite element model, in particular, the structural damping. In the end, a fair correlation between the experimental and numerical results is achieved. The proposed methodology, which relies on numerical and experimental methods, thus leads to a dynamic model of tape springs which can be used to predict their behaviour in various conditions.