Computational Design and Optimization of Discrete Shell Structures Made of Equivalent Members

This paper presents a computational design method for generating discrete shell structures using sets of equivalent discrete members. This study addresses the challenge of reducing the geometrical variety in discrete shell elements by introducing a method to design and optimize constituent members considering their similarity, approximation of the double-curved architectural surface, and buildability. First, we employed a relaxation-based computational form-finding method to generate a discrete topology with planar quad faces and an approximated smooth, double-curved surface. Then, we perform clustering and optimization based on face similarities concerning the minimization of deviations from the smooth surface approximation, and the dihedral angle between the planes of neighboring elements and their optimal intersection plane. The proposed approach can reduce the geometrical differences in discrete shell elements while satisfying the user-defined error threshold. We demonstrated the viability of our method on various structured topologies with different boundary conditions, support settings, and total face counts, while explicitly controlling inter-element facing angles for assembly ready contacts. This enables mold-based prefabrication with repeatable components.