Grid-shell design and analysis via reciprocal discrete Airy stress functions

Abstract

This research paper introduces a theoretical framework for the design and analysis of compression-and-tension grid-shells in static equilibrium where the states of self-stress function as design freedoms. This is based on a synthesis of reciprocal discrete Airy stress functions in the context of graphic statics and the Force Density Method (FDM). Specifically, the former is a direct method for generating 2-dimensional global static equilibrium whereas the latter allows for its 3-dimensional implementation. As a result, creative design explorations can take place directly within the equilibrium space without the need for iterative convergence algorithms to obtain equilibrium. The use of reciprocal Airy stress functions in conjunction with the lower bound theorem gives insight and explicit control with regards to the states of self-stress as design and analysis freedoms which can define the structural form and its load path.