
The Airshell Prototype
This paper by Alessandro Liuti, Sofia Colabella, and Alberto Pugnale, presents the construction of Airshell, a small timber gridshell prototype erected by employing a pneumatic formwork.
Design of Self-supporting Surfaces
Self-supporting masonry is one of the most ancient and elegant techniques for building curved shapes. Because of the very geometric nature of their failure, analyzing and modeling such strutures is more a geometry processing problem than one of classical continuum mechanics.
This paper uses the thrust network method of analysis and presents an iterative nonlinear optimization algorithm for efficiently approximating freeform shapes by self-supporting ones.
The rich geometry of thrust networks leads us to close connections between diverse topics in discrete differential geometry, such as a finite-element discretization of the Airy stress potential, perfect graph Laplacians, and computing admissible loads via curvatures of polyhedral surfaces.
This geometric viewpoint allows us, in particular, to remesh self-supporting shapes by self-supporting quad meshes with planar faces, and leads to another application of the theory: steel/glass constructions with low moments in nodes.
Vaulted masonry structures are among the simplest and at the same time most elegant solutions for creating curved shapes in building construction. For this reason they have been an object of interest since antiquity; large, non-convex examples of such structures include gothic cathedrals. They continue to be an active topic of research today.
Our paper is concerned with a combined geometry+statics analysis of self-supporting masonry and with tools for the interactive modeling of freeform self-supporting structures. Here “self-supporting” means that the structure, considered as an arrangement of blocks (bricks, stones), holds together by itself, with additional support present only during construction.
Our approach is twofold: We first give an overview of the continuous case of a smooth surface under stress, which turns out to be governed locally by the Airy stress function. This mathematical model is called a membrane in the engineering literature and has been applied to the analysis of masonry before.
The surface is self-supporting if and only if stresses are entirely compressive. For computational purposes, stresses are discretized as a fictitious thrust network [Block and Ochsendorf contained in the masonry structure; this network is a system of forces in equilibrium with the structure’s deadload.
While previous work in architectural geometry was mostly concerned with aspects of rationalization and purely geometric sideconditions which occur in freeform architecture, the focus of this paper is design with statics constraints.
Conclusion. This paper builds on relations between statics and geometry, some of which have been known for a long time, and connects them with newer methods of discrete differential geometry, such as discrete Laplace operators and curvatures of polyhedral surfaces.
We were able to find efficient ways of modeling selfsupporting freeform shapes, and provide architects and engineers with an interactive tool for evaluating the statics of freeform geometries.
The self-supporting property of a shape is directly relevant for freeform masonry. The actual thrust networks we use for computation are relevant e.g. for steel constructions, where equilibrium of deadload forces implies absence of moments.
This theory and accompanying algorithms thus constitute a new contribution to architectural geometry, connecting statics and geometric design.
This paper by Alessandro Liuti, Sofia Colabella, and Alberto Pugnale, presents the construction of Airshell, a small timber gridshell prototype erected by employing a pneumatic formwork.
In this paper by Gregory Charles Quinn, Chris J K Williams, and Christoph Gengnagel, a detailed comparison is carried out between established as well as novel erection methods for strained grid shells by means of FE simulations and a 3D-scanned scaled physical model in order to evaluate key performance criteria such as bending stresses during erection and the distance between shell nodes and their spatial target geometry.
In this paper by Frederic Tayeb, Olivier Baverel, Jean-François Caron, Lionel du Peloux, ductility aspects of a light-weight composite gridshell are developed.
In this paper by Julian Lienhard, Holger Alpermann, Christoph Gengnagel and Jan Knippers structures that actively use bending as a self forming process are reviewed.
Parametric Tools for Architects & Designers @2025
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