*** Featuring a foreword by Pritzker Prize Winner Shigeru Ban ***

Bringing together experts from research and practice, Shell Structures for Architecture: Form Finding and Optimization presents contemporary design methods for shell and gridshell structures, covering form-finding and structural optimization techniques. It introduces architecture and engineering practitioners and students to structural shells and provides computational techniques to develop complex curved structural surfaces, in the form of mathematics, computer algorithms, and design case studies.

• Part I introduces the topic of shells, tracing the ancient relationship between structural form and forces, the basics of shell behaviour, and the evolution of form-finding and structural optimization techniques.

• Part II familiarizes the reader with form-finding techniques to explore expressive structural geometries, covering the force density method, thrust network analysis, dynamic relaxation and particle-spring systems.

• Part III focuses on shell shape and topology optimization, and provides a deeper understanding of gradient-based methods and meta-heuristic techniques.

• Part IV contains precedent studies of realised shells and gridshells describing their innovative design and construction methods.

chapter |4 pages


BySigrid Adriaenssens, Philippe Block, Diederik Veenendaal, Chris Williams

part |51 pages

Shells for architecture

chapter |8 pages

Exploring shell forms

ByJohn Ochsendorf, Philippe Block

chapter |6 pages

Shaping forces

ByLaurent Ney, Sigrid Adriaenssens

chapter |12 pages

What is a shell?

ByChris Williams

chapter |12 pages

Physical modelling and form finding

ByBill Addis

chapter |11 pages

Computational form finding and optimization

ByKai-Uwe Bletzinger, Ekkehard Ramm

part |83 pages

Form finding

chapter |12 pages

Force density method

Design of a timber shell
ByKlaus Linkwitz

chapter |18 pages

Thrust network analysis

Design of a cut-stone masonry vault
ByPhilippe Block, Lorenz Lachauer, Matthias Rippmann

chapter |14 pages

Dynamic relaxation

Design of a strained timber gridshell
BySigrid Adriaenssens, Mike Barnes, Richard Harris, Chris Williams

chapter |12 pages

Particle-spring systems

Design of a cantilevering concrete shell
ByShajay Bhooshan, Diederik Veenendaal, Philippe Block

chapter |16 pages

Comparison of form-finding methods

ByDiederik Veenendaal, Philippe Block

chapter |9 pages

Steering of form

ByAxel Kilian

part |96 pages

Structural optimization

chapter |14 pages

Nonlinear force density method

Constraints of force and geometry
ByKlaus Linkwitz, Diederik Veenendaal

chapter |14 pages

Best-fit thrust network analysis

Rationalization of freeform meshes
ByTom Van Mele, Daniele Panozzo, Olga Sorkine-Hornung, Philippe Block

chapter |10 pages

Discrete topology optimization

Connectivity for gridshells
ByJames N. Richardson, Sigrid Adriaenssens, Rajan Filomeno Coelho, Philippe Bouillard

chapter |14 pages

Multi-criteria gridshell optimization

Structural lattices on freeform surfaces
ByPeter Winslow

chapter |16 pages


Structural patterns on modal forms
ByPanagiotis Michalatos, Sawako Kaijima

chapter |14 pages

Homogenization method

Distribution of material densities
ByIrmgard Lochner-Aldinger, Axel Schumacher

chapter |12 pages

Computational morphogenesis

Design of freeform surfaces
ByAlberto Pugnale, Tomás Méndez Echenagucia, Mario Sassone

part |34 pages


chapter |8 pages

The Multihalle and the British Museum

A comparison of two gridshells
ByChris Williams

chapter |12 pages

Félix Candela and Heinz Isler

A comparison of two structural artists
ByMaria E. Moreyra Garlock, David P. Billington

chapter |12 pages

Structural design of free-curved RC shells

An overview of built works
ByMutsuro Sasaki

chapter |3 pages

Conclusion The congeniality of architecture and engineering

The future potential and relevance of shell structures in architecture
ByPatrik Schumacher