Mesnil R., Douthe C., Baverel O.
This paper investigates the potential offered by non-regular patterns for the design of gridshell structures focusing on two aspects: fabrication and structural performance. Studies on non-regular patterns are scarce, with a few notable exceptions . We propose a framework for shape generation in real-time of gridshells with non-standard patterns with planar facets and the assessment of the proposed grid patterns. The possibilities of the framework are demonstrated through a detailed study on the kagome grid pattern, which is made of hexagons and triangles.
We propose two intuitive methods to generate kagome gridshells with planar facets. The first method is based upon the marionette technique, a method for shape generation inspired by descriptive geometry and proposed by the authors in . The marionette technique constitutes the most general framework for the shape generation of gridshells with planar facets. We re-interpret this method with an algorithm of conversion from Planar-Quadrilateral (PQ) mesh to a Planar-Kagome (PK) mesh.
We study then the structural performance of the kagome grid patterns by comparing the linear buckling load of gridshells covered with quadrangular or kagome grid pattern. We summarized the main results of a parametric study presented in  for various geometries and grid densities showing that the linear buckling load of kagome gridshells can be up to twice as high as the one of quadrangular gridshells. Finally, we propose a method of homogenization inspired by Winslow  for the evaluation of the stiffness of non-standard periodic patterns.