Multi-body Rope Approach for the Form-Finding of Shape Optimized Grid Shell Structures

Abstract

Over the past decades, different approaches, physical and geometrical, were implemented to identify the optimal shape, reducing the internal stresses, of grid shells and vaults. As far as their original organic shape is concerned, the design of grid shell structures inspired architects and structural engineers worldwide and in any time. The method, here presented, is developed and extended, from its original formulation, employing a self-made code based on the dynamic equilibrium, ensured by the d'Alembert principle, of masses interconnected by rope elements in the space-time domain. The equilibrium corresponding the optimized shape to be defined, is obtained through an iterative process in the falling masses connected by a net for the definition of the 'catenary surface' coinciding with the best shape of the shell (form minimizing the bending moment) according to the conditions of zero velocities and accelerations of the nodes. The implementation of the method is realized in MATLAB and set up for Python in an interpreted high-level general-purpose programming language. By the use of this code as well as its object-oriented architecture the MRA Python code will be linked to the Grasshopper environment for the direct visualization of the shapes and their fastparametrization phase.