Improved multi-body rope approach for free-form gridshell structures using equal-length element strategy

Gridshell roofing constructions are favoured in modern engineering and architecture for their capacity to produce expansive, lightweight roofs using slender main structural elements, yet their complex and costly fabrication limits broader adoption. The Multi-body Rope Approach (MRA) is effective in computing structurally efficient geometries in gridshells, emphasizing the need to optimize design configurations for minimal internal stresses. This paper presents two strategies, Multiple Order MRA (MO-MRA) and Repulsive Nodes MRA (RN-MRA), to improve the MRA and streamline gridshell construction by reducing the necessary types of structural components. These approaches are combined in an improved MRA (i-MRA), reducing manufacturing costs and increasing efficiency in construction management. The i-MRA was implemented in Matlab and tested on four case studies of increasing complexity, demonstrating its effectiveness.