A multiscale modeling method with updatable ABD shells for laminated flexible solar arrays

Abstract

The flexible solar array is an innovative deployable system to provide electrical power for space stations, satellites, and other spacecrafts. Due to the advantages of lightweight, large area, and high power, it has received considerable attention and applications. However, the intricate multilayer configuration, nonlinear material behavior, and low stiffness characteristic of the array have made it always challenging to accurately predict the morphology and frequencies. This paper presents a numerical nonlinear multiscale method called PWL FE2 for large-scale flexible solar arrays. The proposed method is implemented in Abaqus with Python scripts and Micromechanics plugin. Its fundamental procedure is as follows: at microscale, the nonlinear constitutive model is piecewise linearly interpolated, followed by ABD stiffness and mass homogenizations of each segment; at macroscale, material properties of general ABD shells are updated based on section forces. Benchmark tests on substrate tension show that the error between PWL FE2 and direct numerical simulation (DNS) is less than 5 %. The refined shell model with PWL FE2 algorithm proves to be computationally efficient and convergence-friendly for morphology and frequency analysis of the array. For the single array undergoing strong nonlinearity, the computational efficiency of PWL FE2 is nine times that of DNS. The out-of-plane displacement reaches up to 210 mm, and the differences in reaction forces and deformations between nonlinear and linear simulations exceed 20 %. For the global array subjected to 84 N tensile loads, the array remains planar, and the first four modes are clustered around 0.2 Hz.