D-Nets on rotational surfaces : Equilibrium gridshell layout, symmetric to the principal stress directions

Abstract

This paper presents a novel topology for gridshells symmetric to the principal stress directions. This diagonal layout (D-Net) allows to distribute forces evenly across neighbouring members and create equilibrium states for compression- (or tension-) only gridshells, through its orthotropic behaviour. We derive a formula for the D-Net directions and present a computational workflow to calculate their paths on NURBS surfaces under given loads and supports. The workflow is conducted using isogeometric analysis (IGA) that continuously evaluates the stress field over the smooth geometry. In this initial investigation, we focus on rotational surfaces for compression-only and mixed (compression and tension) gridshells. The results are verified with a series of archetypical design shapes and Finite Element analysis. We compare the structural behaviour of three gridshells, equilateral, principal-stress and D-Net, evaluating the holistic load-bearing behaviour under four load-cases. Finally, we discuss the practical challenges for D-Net design and its potential for architecture. The research gives a holistic assessment of theory, design and structural behaviour, and opens the doors to a novel topology for gridshell design, that naturally follows the flow of forces.