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We investigate the geometric properties of quadrilateral gridshell units composed of straight rods capable of deploying onto target surfaces of predefined uniform Gaussian curvature. The arrangement of these rods is determined by a novel differential geometry-based procedure that applies the law of cosines for non-Euclidean spaces to ensure that the deformed configuration matches a predetermined target surface, whether spherical or hyperbolic. The proposed design methodology is validated by finite element and tabletop models.

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Investigating Modular Geodesic Gridshells: A Differential Geometry-Based Design Approach

  • 会议论文

  • 发表日期：

    2026年

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  • Davide Pellecchia,
  • Francesco Marmo,
  • Luciano Rosati

摘要

We investigate the geometric properties of quadrilateral gridshell units composed of straight rods capable of deploying onto target surfaces of predefined uniform Gaussian curvature. The arrangement of these rods is determined by a novel differential geometry-based procedure that applies the law of cosines for non-Euclidean spaces to ensure that the deformed configuration matches a predetermined target surface, whether spherical or hyperbolic. The proposed design methodology is validated by finite element and tabletop models.