Finite Element Algorithm for Surface Flattening

Document Type : Research Paper

Authors
Department of Mechanical and Energy Engineering, Shahid Beheshti University, Tehran, Iran
Abstract
Membrane and inflatable structures are generally composed of non-developable geometries that must be approximated from planar surfaces. This study proposes a novel finite element–based algorithm for surface flattening, specifically tailored for structural form-finding and analysis. The method regulates edge length and curvature through truss and beam elements, ensuring boundary compatibility during surface flattening. Unlike conventional geometric or mesh-parameterization techniques, the proposed approach is fully integrated into the finite element framework, enabling direct structural simulation. The algorithm has been implemented as an Abaqus plugin, which automatically generates flattened surfaces and reconstructs the final geometry from assembled planar patches. Beyond geometric accuracy, the plugin leverages Abaqus’ nonlinear capabilities to evaluate stresses under applied pressure, providing a unique and practical tool for analyzing the strength and stability of inflatable structures.
Keywords
Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Available Online from 07 November 2025