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<p>Inflatable space structures have gained significant research interest owing to their high packaging efficiency, low areal density, and reduced launch cost. In these systems, a torus functions as the principal supporting frame, providing the necessary boundary stiffness and structural support for the central reflector membrane or sunshield. This work presents a finite element analysis of the inflation mechanics of a torus fabricated from flat Kapton membranes, following the actual manufacturing process by initialising the structure as a planar, stress-free annular membrane to capture the characteristic linear elastic behaviour of Kapton during deployment. The transition from a flat annulus to a toroidal shape was numerically simulated, and the resulting torus radii were verified against the theoretical benchmark, establishing close agreement. A systematic comparison of reduced-integration S4R and fully integrated <i>S4</i> shell elements revealed that <i>S4R</i> elements produced unacceptable artificial energy ratios across all mesh densities and pressure levels, while <i>S4</i> elements achieved both artificial and kinetic energy ratios below 1% of the internal energy without any stabilization, confirming their suitability for this class of thin-membrane deployment problem. Root mean square error (RMSE) analysis was conducted to quantify the geometric deviation of the deployed cross-section from the theoretical reference profile across varying pressure levels and membrane thicknesses. The non-dimensional inflation parameter is introduced as a preliminary scaling guide for any linear elastic flat-sheet toroidal inflatable structure, with the critical deployment threshold corresponding to 0.0192 for the present model.</p>

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High-Fidelity Finite Element Investigation of the Deployment of a Flat Toroidal membrane

  • 期刊论文

  • 发表日期：

    2026年6月18日

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  • Amiy Chandraul,
  • V. Murari,
  • Satish Kumar

摘要

Inflatable space structures have gained significant research interest owing to their high packaging efficiency, low areal density, and reduced launch cost. In these systems, a torus functions as the principal supporting frame, providing the necessary boundary stiffness and structural support for the central reflector membrane or sunshield. This work presents a finite element analysis of the inflation mechanics of a torus fabricated from flat Kapton membranes, following the actual manufacturing process by initialising the structure as a planar, stress-free annular membrane to capture the characteristic linear elastic behaviour of Kapton during deployment. The transition from a flat annulus to a toroidal shape was numerically simulated, and the resulting torus radii were verified against the theoretical benchmark, establishing close agreement. A systematic comparison of reduced-integration S4R and fully integrated S4 shell elements revealed that S4R elements produced unacceptable artificial energy ratios across all mesh densities and pressure levels, while S4 elements achieved both artificial and kinetic energy ratios below 1% of the internal energy without any stabilization, confirming their suitability for this class of thin-membrane deployment problem. Root mean square error (RMSE) analysis was conducted to quantify the geometric deviation of the deployed cross-section from the theoretical reference profile across varying pressure levels and membrane thicknesses. The non-dimensional inflation parameter is introduced as a preliminary scaling guide for any linear elastic flat-sheet toroidal inflatable structure, with the critical deployment threshold corresponding to 0.0192 for the present model.