Folding Simulation of Flat Arrays Using Refined Beam Finite Elements

The shift toward smaller satellites has sparked growing interest in deployable booms that can stow compactly and extend to full length once on-orbit [1]. These booms are typically rolled into a coil and, when released, unroll into slender rods made of thin-walled composite shells, releasing stored strain energy in the process; such mechanisms are common in spaceborne telescopes and other large-aperture payloads [2,3]. Tape springs, thin elastic strips, remain the most prevalent deployable boom. The introduction of carbon-fibre-reinforced-plastic (CFRP) tape springs has further improved stiffness-to-mass ratios [4]. A related concept, the Triangular Rollable and Collapsible (TRAC) boom, links two tape-spring “flanges” along a common “web,” forming a triangular cross-section that offers markedly higher bending stiffness. First developed at the Air Force Research Laboratory by Murphey and Banik [5], metallic TRAC booms flew on NASA’s NanoSail-D solar sail [6]; more recent work has shifted to composite TRAC designs to mitigate temperature-gradient problems seen in metal versions. One high-profile application is Caltech’s Space Solar Power Project (SSPP), which envisions a modular lattice of TRAC longerons and rectangular CFRP battens that supports arrays of multifunctional tiles. These tiles harvest solar energy, convert it to RF power, and beam it to Earth [7]. The SSPP structure consists of bending-stiff trapezoidal strips, arranged in four identical quadrants. The two edges of each strip are formed by composite TRAC longerons, connected by carbon fiber rectangular battens. Accurate simulation is vital for sensitivity studies and for minimizing costly hardware tests. Conventional finite-element analysis often relies on 2-D shell elements to model slender booms, a choice that struggles to capture out-of-plane responses and local effects, especially critical in composite laminates [8]. To overcome these shortcomings, this work employs a Carrera Unified Formulation (CUF)–based finite-element model [9]. CUF enriches one-dimensional beam elements with high-order cross-sectional expansions, allowing three-dimensional and localized behaviours to appear within a low-degree-of-freedom framework. The method has already proven effective for buckling and post-buckling studies of deployable booms [10]; here, it is extended to simulate the full folding and deployment sequence of the SSPP flat-array module.