On the Design of Torsion-Free Gridshells

Connection nodes are usually the costliest elements of gridshells because of their geometrical complexity. Their fabrication might be significantly simplified if they have no geometrical torsion. Literature has therefore focused on developing geometrical structures with null torsion, such as conical and circular meshes, and on associated generation methods. The meshes are closely linked with principal curvature and therefore give limited freedom to the designer. This paper investigates two approaches which allow for the design of torsion-free or quasi torsion-free gridshells for any planar quad mesh. The first approach is based on the theory of parallel transformation to define a torsion free layout. It tries then to fit nodal axes with surface normals. The second approach accounts for fabrication tolerances and use this additional freedom to build quasi torsion-free layout aligned with surface normal. It is based on the theory of conical meshes and is aimed at helping designers quantify torsion a priori. Especially, the freedom offered by tolerances for deviating a quadrangular pattern from principal curvature nets is quantified and illustrated in two case studies.