Session: 01-12-02: Spacecraft Structures 2

Paper Number: 152593

152593 - Rotation, Folding and Deployment Simulation of a Solar Array Structure Made of Ultra-Thin Composites Using One-Dimensional Finite Elements 

Over the past few decades, deployable structures in space engineering have predominantly been made from thin and ultra-thin composite materials. These structures have played a key role in various space missions, supporting solar sails, photovoltaic panels, antennas, and other large-scale components [1].

Triangular Rollable and Collapsible (TRAC) boom longerons are widely used deployable structures in space applications. TRAC longerons are composed of two composite tape springs, each 85 μm thick, bonded along one edge. These longerons offer key advantages such as low mass, high packing efficiency, and ease of deployment. To enhance stiffness while maintaining a minimal weight, carbon fiber-reinforced plastic is employed. This combination of lightweight materials and compact design makes TRAC longerons ideal as components of large structures in space, such as solar arrays and antennas, where mass and volume constraints are critical.

This study investigates a hierarchical structure where TRAC longerons are joined with transverse components, known as battens, to create a structural frame for the Space Solar Power Project (SSPP) spacecraft [2]. The structure analyzed consists of two pairs of TRAC longerons, measuring 0.4 and 0.6 meters in length. The deployment process is simulated in several stages: (a) frame rotation, (b) longerons pinching, (c) folding, and (d) structure deployment.

Numerical analyses are carried out using the Carrera Unified Formulation (CUF) [3], which allows for the development of a mathematical model using only one-dimensional finite elements. The model incorporates linear, quadratic, and cubic beam finite elements, along with high-order expansion functions, to accurately represent the structure's three-dimensional (3D) geometry. Lagrange elements are used to describe cross-sectional deformation, enabling a precise 3D representation without the aspect-ratio limitations of traditional shell and 3D finite elements, which is a common issue in thin structures. Additionally, out-of-plane strains and stresses are evaluated, employing full Green-Lagrange strain functions to derive geometrically nonlinear governing equations without introducing approximations.

The simulation utilizes an implicit quasi-static approach, which is well-suited for capturing the gradual folding and controlled deployment of this space structure. This method is coupled with the Newton-Raphson constant linearization scheme to iteratively solve the nonlinear equations, ensuring convergence even in the presence of significant nonlinearities. A displacement control method is employed to manage the stepwise progression of the simulation.

In addition to addressing geometric nonlinearities inherent in large deployable structures, the simulation also models the complex contact interactions between structural components. These interactions are represented through nonlinear springs acting at predefined node pairs, effectively simulating the mechanical response during contact events. A polynomial contact law governs the behavior of these springs, providing an accurate model of the forces exchanged between the components as they come into contact. This combination of techniques allows for a detailed and realistic simulation of the deployment process, accounting for both the structural and contact-related nonlinearities that are critical for the performance of large space structures.

References

[1] F. Royer and S. Pellegrino. Ultralight ladder-type coilable space structures. In 2018 AIAA Spacecraft Structures Conference, page 1200, (2018).

[2] Gdoutos, E., Truong, A., Pedivellano, A., Royer, F. and Pellegrino, S., 2020. Ultralight deployable space structure prototype. In AIAA Scitech 2020 Forum (p. 0692).

[3] Carrera, E., Cinefra, M., Petrolo, M., Zappino, E.: Finite Element Analysis of Structures Through Unified Formulation. Wiley, Amsterdam (2014)

Presenting Author: Riccardo Augello Politecnico di Torino

Presenting Author Biography: Riccardo Augello is a Postdoctoral Fellow under the Marie Sktodowska-Curie Actions, which is a researcher mobility programme funded by the European Commission.

Augello received his Ph.D. in Mechanical Engineering at Politecnico di Torino, Italy, in February, 2021. His research project focused on the development of advanced mathematical theories based on nonlocal mechanics for the geometrical nonlinear analysis of composite structures. Augello joined Caltech in March 2023 as a part of his European research project “NOnlinear analysis for VIrTual design of composite deployAble Space booms and membranes” (NOVITAS). The project aims to generate novel advances in the mathematical modelling of ultra-thin deployable and foldable composite structures.