Comprehensive accuracy analysis for large closed-loop deployable structures based on matrix structure analysis and linear-complementarity-based contact analysis of spatial joint clearances

The surface accuracy of the deployable structure is crucial in determining the electromagnetic performance of the large satellite antenna. This paper proposes a comprehensive accuracy analysis framework for deployable structures considering clearances of spatial joints, geometric deviations, elastic deformations, external loads, and preloads, all of which can affect surface accuracy during the assembly process. Surface accuracy is calculated by combining the global equilibrium analysis of the deployable structure with the local equilibrium analysis of clearance-affected joints. First, a global elastostatic equilibrium analysis of the deployable structure is performed based on a unified mathematical formulation that describes the elasticity of beams and joints. Then, the local equilibrium analysis for the clearance-affected joints is transformed into a quadratic optimization problem through a linear-complementarity-based method. This method avoids the necessity for a combinatorial search for several traditional discontinuous contact configurations. Considering both global and local equilibrium in iterative analysis, the surface accuracy of the antenna is calculated. This integration avoids prior artificial assumptions about contact configurations of the joints. Finally, the proposed method is validated by comparing it with simulations and experimental results.