A nonlinear algorithm for large deformations of multi-stepped variable-section flexible solar arrays

Abstract

Aerospace solar arrays serve as the primary means for spacecraft to collect energy. Flexible solar arrays have the advantages of a high deployment ratio, light weight, a large span, and high specific power. Currently, they are primarily used on space stations. Ultra-thin, multi-stepped variable-section flexible solar arrays are a novel design solution. Due to extremely low stiffness, flexible solar arrays exhibit nonlinear behavior such as large deformations under bending during the deployment process driven by external forces, which is the main topic of this paper. To quickly obtain the morphology of the flexible solar array after unfolding and improve design efficiency, this paper first transforms the unfolding morphology of the flexible solar array into a nonlinear large deflection problem of a fourth-order discontinuous variable-section composite beam and gives the equivalent methodology. Subsequently, an efficient nonlinear difference algorithm is proposed. A set of differential equations for large deflections of multi-stepped variable-section beams under complex loading conditions is derived. The finite difference method is employed to discretize this system, and four different categories of node processing methods are derived in detail. Newton's iterative technique is used to solve for the curvature of each point, and explicit formulas to calculate the point coordinates, strain, and stress are developed. Ground deployment experiments, numerical simulations of on-orbit deployment, and comparisons with benchmark examples are used to verify the validity of the ND algorithm. Finally, the morphological analysis of the on-orbit deployment of the flexible solar array is performed, and some design advice is given.