Art and Engineering: testing he boundaries of the physical world: allowing large deformations

Structural engineers envision, design, and construct the bridges and long‐span buildings people depend on daily. Traditionally, the structural engineer’s approach has been to control and limit the stress levels, deflections, and natural frequency in structural systems. While the structural engineering discipline rarely challenges this dogma of limitation and control, this is a fundamental question in art. Many artifacts show that testing the boundaries of the physical world is an inherent part of a successful artwork.  Drawing inspiration from the large deformations achieved in the Pore rubber dance/sculpture installations (Miami Art Basel, Martha Friedman, 2015), our research showed in several lines of inquiry how allowing excessive deformations can also benefit the structural performance of flexible structural system [1,2].

Large deforming rubber sheet in Pore sculpture (Martha Friedman, Miami, 2015)

For instance, we investigated how polyester rope, a product of local home‐spun industries, can be an alternative to steel cable in suspended footbridges because of its low weight, low cost, low creep rate, and durability.

The only existing largely-deforming polyester rope suspended bridge (Ait‐Bayoud, Morocco, 2016 image credit: Engineers Without Borders Columbia University)

However, polyester’s low material stiffness – its Young’s modulus is 70 times smaller than that of steel – results in large static bridge deformations and increased walking slopes. We found that when relaxing traditional bridge deflection limits, the polyester rope’s low stiffness leads to large deflections that give rise to a nonlinear increase in the bridge’s geometric stiffness and, beneficially, leads to high levels of safety against overloading.  This overload capacity has great potential for bridges in the context of resource-constrained environments where larger walking slopes are acceptable.

We established its static and dynamic behavior of the Ait-Bayoud bridge and performed our physical testing on it. (image credit: Ted Segal)

In the future, the Form Finding Lab will continue to envision and develop structural systems by drawing on approaches and phenomena found in art, craft, and nature. This line of scholarship is aligned with the STEAM vision (Science, Technology, Engineering, Art, and Mathematics). In this context, we would like to bring the following Symposium to your attention: “Living at the Intersection” (April 12-13, 2018 on the Princeton University campus). It will engage participants in the exploration of “living at the intersection” of engineering and the arts with thought leaders, researchers, artists, faculty, students, and professionals who create at or near this intersection. More about this symposium later.

[1] E. Segal, L. Rhode-Barbarigos, S. Adriaenssens and R. Filomeno Coelho, ‘Multi-objective optimization of polyester-rope and steel-rope suspended footbridges’, Engineering Structures, vol. 99, pp. 559-567, doi:10.1016/j.engstruct.2015.05.024, 2015.

[2] E. Segal, L. Rhode-Barbarigos, R. Coelho, and S. Adriaenssens, ‘An Automated Robust Design Methodology for Suspended Structures’, Journal of the International Association of Shell and Spatial Structures, vol. 56, pp. 221-229, no.4, 2015.





What I am thinking: structure-inspired artist Lancelot Coar

Lancelot Coar is an Associate Professor in the Department of Architecture at the University of Manitoba, specializing in undergraduate and masters level design studio and construction technology lecture courses and is a researcher at the Centre for Architectural Structures and Technology (CAST). His research includes the development of building systems using fabric formed concrete, fabric reinforced concrete, fabric reinforced ice structures, bending active fiberglass frames and post-tensioned wood. For more information about the projects referenced here and Lancelot’s other work, check out

Sigrid Adriaenssens: What is the relationship between material and design in your work? 

Lancelot Coar: For the way I work, material governs design, not only as an outcome, but as a process. It guides the design and construction methods I develop in order to provoke material to achieve a mutually agreed upon result. I say mutual because I view the will of material as a source of intelligence, a collaborator and guide if you will. Because of this, choosing what material to work with directly impacts my design approach, so that I can respond to that material’s nature.

Fabrigami (2016), a fabric formed origami ice shell (with C. Mueller, L. De Laet, J. Hare, K. Wiese) being pulled into tension prior to application of water onto fabric (photo by N. Bava).

Since all matter provides a distinct territory for force to move through, as well as a unique response to that force, selecting what material to work with is effectively choosing what type of forces I want work with in a design process. For example, membranes and shells offer a 2-dimensional field for stresses that demand very particular approaches to designing; one dealing with tension and the other predominantly compression. While slender elastic materials in bending active systems, like fiberglass bars, give rise to a very different set of design constraints that result in establishing equilibrium through a network of pure bending. And working with phase changing liquid-to-solid materials (like concrete, ice, resin, etc.) requires negotiating a material that is able to change from being formless, animate and highly susceptible to the influence of forces, to becoming rigid and resistant to stress in the form it hardens in.

Fabrigami following the icing of the fabric.

Despite the diverse ways that materials relate to stresses, the nature of materials is always revealed in how they seek equilibrium. Therefore, I find it important to witness the event of materials seeking equilibrium. These observations are what guide my understanding about them, my approach to designing, methods for making, and ideas for how they may be useful in producing efficient building systems. In some projects, I have attempted to incorporate the active participation of multiple materials with very different natures to yield exciting and productive results.

An example of this can be seen in a recent project, entitled “Ice Bloom”, carried out in January 2017 with Dr. Sigrid Adriaenssens and Michael Cox (Princeton University), Dr. Lars de Laet (Vrije Universiteit Brussels), and Mark West (University of Washington). This project tested how three highly dynamic material systems (fabric formwork, shell construction, and bending active frames) could work together to create a synergistic building system that builds off of the efficiencies and nature of each material in it. This project involved the creation of an 8m x 8m x 4m fabric formed ice vault, shaped by a bending active frame covered in a fabric formwork and sprayed with water in the extreme winter climate of Winnipeg, Manitoba in Canada.

Ice Bloom (2017) during the watering of the fabric formwork, supported by a bending active frame (photo by N. Bava).

This project provided an opportunity for three material systems to influence the formation of each other in order to produce a materially and structurally efficient result, otherwise impossible to achieve with a single material system alone. For example, the elastica geometries formed by a fiberglass rebar bending active frame was discovered to be capable of following the principal stress patterns of the vault design, thus a construction method was developed to guide the fiberglass bars to follow that pattern. Once erected the elastic frame supported a fabric formwork textile to create a ribbed pattern that followed the topology of the bars supporting the fabric. The result was that when the water was applied, the saturated fabric deformed following the bar patterns and collected more water in the concave valleys between the bars. This allowed for the ice to not only form a contiguous structural shell over all of the fabric, but to also create thickened ice beams along the principal compression pathways of the vault shell. The self-organizing behaviour of each of these materials resulted in the creation of an integrated building system that aided in the design process, intelligently organized material massing, and generated an efficient structural form as a result.

Ice Bloom after a 2cm snowfall onto the freshly frozen ice shell. The ribbed pattern of the snow reveals the valleys of the principal stress lines created by the bending active frame.

SA: What is your preferred material and why?

LC: Flexible and wet materials, mainly because they are expressive and animate, both qualities I am trying to better understand and use in form-generation and the construction processes.

For a long time (even before pre-industrialization), building materials have been conceived of and treated as silent agents of our design will. Their characteristics have been muted and generalized by the massiveness of how we use them in construction. Because we largely wish our structures to be static (even though they never truly are), we have established our design processes, methods of analysis, definition of failure, and construction tolerances to all infer a predilection for rigidity. This frame of thinking has impacted how we have come to think about materials as instruments of stasis and not as mediums possessing expressive and dynamic characteristics that might perhaps be useful.

Pre-stressed wood research exploring deployable expanding frame systems (2008, with D. Blouw).

Even the tools we use to shape building materials are designed to control the characteristics of matter in the name of geometric dominance; namely the industrial single-axis machines that are used to cut, press, and roll prismatic “sticks” and “sheets”. Because of this, our design practices, construction traditions and even our teaching of material sciences has passed down this presumption of rigidity to new generations of engineers and architects, including myself. So, by working with expressive materials, I am in essence inviting matter to help me decouple my preconceptions about materials from their actual expressive nature in order to explore how they might become active participants in our quest to shape them.

What is your design process?

Left: Heated wax modeling table used to create fabric formed wax shells through improvisation and scalable construction methods (2009, with Z. Lebel). Right: Once a design is finished, the heat is turned off and a rigid fabric and wax model is formed.

For the most part, I begin by playing. Play is a vital part of the decoupling process I was speaking about. It is one of the few ways I know how to have my presumptions confront the realities of material behaviour, and be forced to reconcile what I assume with what I am witnessing. Playing is an act of improvised negotiation between the unconscious (intuitive) and the conscious (intellectual) through direct experience. By playing, in this case with materials, we are discovering them on many levels, and thereby actively re-forming our intuition about them. As many past masters have reminded us, from Nervi to Maillart, structural intuition is an important part of designing if we are to understand the fullest essence of structural behaviour. When speaking about our awareness and fascination with complex geometries, Nervi points out that although we observe innumerable examples of form resistant structures in nature and everyday life, resistance through geometry is not a part of our heritage of study, analysis or representational traditions. As a result, it has not yet become a part of the intuitive structural language we draw from to design structures. “In other words, we are not yet used to thinking structurally in terms of form.” I would extend this to also include us not yet being able to think structurally in terms of behaviour.

He goes on to say that “In order to develop this kind of intuition, form-resistance should be studied in our schools of architecture through the critical analysis of structures, and above all through models” (Nervi, 1956). Despite this statement being made over a half-century ago, we have only begun to find ways of working that invite us to understand structures through form and behaviour in our recent efforts to link computational modeling systems with physical prototypes.

A superimposed photograph of a load test of a post-tensioned bending active spline (2017, with J. Piper and V. Jiang; photo by J. Piper).

In reference to my design process, I would point out that each material system presents a unique set of constraints, opportunities, and roles for the designer to take in shaping that system. What I mean by this is that with self-organizing or parametric material systems (i.e. bending actives frames, fabric formwork, etc.) a designer/builder does not shape the structure, they establish boundary conditions within which a material finds equilibrium through form. Therefore, the conventional approach of design being provided by the will of the designer does not apply here. With these systems, a designer is only one half of the equation, material will is the other half. As a result, in each project I become interested in playing with the design constraints of the site, construction sequence and assembly techniques that compel the material to arrive at a desired result.

SA: What is the importance of ‘making’?

LC: Making is central to my research. Typically, I begin exploring a material by examining and testing full-scale samples to see its characteristics. From that I try to find an analogous material to test in model form. Although at a smaller size, the selected material is chosen so that its behaviour is scaled, and thus the model itself performs at “full scale”. I always use physical modeling to begin research, but then I turn to digital modeling tools (like Rhino/Kangaroo, FEA, etc.) to provide computational insight not provided by physical models. Yet, while digital tools are able to produce curated depictions of material systems, they can never render their full nature, nor can they provide insight into constructability (both in terms of sequence and technique). Therefore, digital tools are a discrete and important part of the work, but not the complete work.

Left: Digital models of a bending active frame with a bar pattern following the principal stresses of a vault. Center: Physical model of the frame used to verify construction sequence and methods. Right: Completed frame erected in place at the Centre for Architectural Structures and Technology (CAST) (2017, images and photos by V. Jiang, J. Piper).

Form-finding is a term used quite often in recent years, most often referring to the results of producing a form through working with a parametric design or material system. In form-finding processes like the ones I describe here, I am primarily interested in the act of forming itself, and the formal results secondarily. By working with physical models at multiple sizes, the act of negotiation between the construction acts of the builder and the behavioural response of the material establish the methodology, construction techniques, and construction sequences required to arrive at a congruent construction logic. Once this is established, the final forms can then be explored. Unless the dance of action/reaction and designer will/material response is understood, the intention of the designer inevitably becomes in conflict with the will of the material. The goal is to avoid this conflict as much as possible. This avoidance is the key to construction and material efficiency, and if lucky, structural efficiency as well.

Left: Testing a construction technique to produce an origami geometry using a tension net. Right: applying a fabric formwork to the tension net to create an origami form.

Another result of aligning the work of the designer/builder with the material systems is that the formal language of a resulting structure often is unexpected and not based solely on the predilections of the designer. Besides efficiency, another aim of this work is to uncover new structural and architectural formal languages that are not necessarily based in the industrial design traditions of our training, but instead from the lexicon of the natural world.

Shadow patterns created by a bending active frame and fabric skin structure for On the Road/en Route (2010).
Fabric formed paraffin wax shell and black sand (2014).

SA: What is your greatest achievement and why?

LC: Personally, of course being a father.

Professionally, I would say sustaining a high degree of fun in my work. Although this may seem frivolous, I believe that finding pleasure in one’s work is essential to being productive and encouraging imagination and persistent curiosity.

Coar and J. Hare attempting to put point loads on to Fabrigami once the tension net was released and the fabric and ice shell was freestanding (photo by D. Rey).

SA: What question do you never get asked and would like to be asked? What would be the answer?

LC: “Why build in this way?”

Primarily because of our need for significant improvements in building efficiency.

We are living in increasingly unstable environments resulting from centuries of unrestrained energy and material consumption. At the same time, large populations and entire communities are being forced into migration due to food scarcity, conflict and a changing climate. If we are to respond to these pressing challenges in a meaningful way, our buildings cannot continue to rely only on the assumption of stasis, nor the requirement for large quantities of energy, material or expense in order to be realized.  While iterative improvements to the industrial building trade are continually being made, I believe that we should at the same time, be exploring radically alternative approaches to design and construction. These approaches might instead emerge from the inherent efficiencies of the material world to achieve new directions toward minimal construction energy, reduced material mass, and simplified construction methods. These methods are not intended to replace our existing technologies in construction, but to instead expand our ability to respond to a greater range of human needs and situations, and to align more closely with the living systems of our world, of which we are an influential part.


Nervi, P. L., 1956. Structures. 1st Edition ed. Ann Arbor: F.W. Dodge Corp.


HyparGate: Italian researchers reviving the ancient art of stereotomy

Italian architects of the New Fundamentals Research Group (Polytechnic University of Bari) and engineers from Roma Tre University are designing and constructing innovative reinforced stone shells and reviving stereotomy, the ancient art of cutting stones.

(Image: S.N.B.R.)

Using advanced modeling and analysis software, and robotic fabrication, the team, coordinated by Prof. Giuseppe Fallacara, has designed the HyparGate, the first discrete hyperbolic paraboloid made of stone. The HyparGate covers a free area of 22 square meters thanks to the cantilever morphology of the shell. The hypar is a well-known ruled surface that has been used in the last decades for many structural applications related to reinforced concrete shells. The full-scale construction is located in France, representing the entrance portal to the headquarters of the French company S.N.B.R.. The main idea is to replace reinforced concrete with pre-stressed stone in order to reduce the use of artificial materials in architecture as much as possible.

Focusing on the hypar’s morphological properties, an aspect of considerable importance in terms of structural analysis and fabrication is that it can be easily described in an analytic way as a parametric surface. The mathematical description allows the direct calculation of some geometric quantities that characterize the structural behaviour. Furthermore, it is one of the most famous ruled surfaces: it may be generated using two families of line segments called “generatrices.” This feature is particularly important in this case because it implies a simple way of dividing the stone into modules, and above all, it permits the use of post-tensioning with rectilinear steel bars in order to eliminate residual tensions along the generatrices.

The main intent is to establish an innovative connection between shape, structure, and fabrication, and to generate a series of new self-supported vaulted morphologies through integrated parametric analyses. This computational approach underlines the potential of robotic fabrication in architectural fields, making possible the fabrication of optimized voussoirs modelled using parametric software. The fabrication process includes the use of robotic arms in combination with CNC manufacturing techniques like circular saw cutting, milling, and diamond wire cutting. The whole research aims to demonstrate that by seamlessly combining digital fabrication tools, architectural design, and mechanical analysis, it is possible to develop innovative structural morphologies with intrinsically high aesthetic value and a high degree of sustainability.

Title: HyparGate

Concept & design: Prof. Dr. Giuseppe Fallacara

3D drafting and optimization: Giuseppe Fallacara, Nicola Martielli, Maurizio Barberio, Bertrand Laucournet

Structural analysis (prestressed reinforced stone): Prof. Ing. Nicola Rizzi, Valerio Varano, Daniele Malomo

Fabrication and construction: S.N.B.R. Société Nouvelle Le Batiment Régional

Location: SNBR Bureaux – 2 Rue Alcide de Gasperi, 10300 Sainte-Savine, Troyes (France)

Chronology (design, fabrication and construction): 2014 – 2016

Stone type: Armenian travertine

Structures in the Low Countries: Port House, Antwerp

The third interesting structure we discuss in the series Structures in the Low Countries is the Port House in the city of Antwerp, Belgium.  This building, designed by Zaha Hadid, is the brand new Port House. It was opened 6 months after Zaha’s sudden death  and the population of Antwerp is still making up their mind whether they like it or not.  In any case, we liked it a lot. As the Antwerp-based graphic designer, Stephanie Specht,  says

“Bateau c’est un batiment sur l’eau” 

The Diamond Ship (Zaha Hadid) with the Ark (bOb Van Reeth) in the forground

The president of the Port of Antwerp, Marc Van Peel, has called it a “Diamond Ship” which refers to the context of Antwerp being famous for its diamond trade and the site location right in the middle of the Antwerp Port.

In 2008 Zaha and her office entered a design competition with hundred other design teams to upgrade and expand an existing early 20th century fire station into an office building for the port authority. The original brick building, which is a copy of a 16th century Hanseatic building, has a historic designation and had in the original design drawings an eye-catching spire which was never built.

Original drawing of the Hanseatic fire station, Antwerp, Early 20th century. City Archives

The addition of the triangulated glass volume seems to defy gravity and is a signature piece, like the spire was meant to be. This four story volume of offices is supported on a sculptural column, holding the fire escape, and on an elevator core that rises up from the original courtyard.

By off- setting the glass faceted volume from the geometric center of the brick building, the architects created compositional tension while allowing daylight to filter into the courtyard.  In addition, the shape of the glass “diamond” volume seemed to be bent and stretched by invisible forces, generating the feeling of movement.  The glass facade whose edges are beveled and cut, reflects the light during the day time and at night shines as a diamond beacon. This in contrast with the brick building, which seems very grounded and celebrates repetition and symmetry, a exemplary product of early 20th century bricklaying techniques.  The city of Antwerp has been the Diamond City since 1447. 2017 was inaugurated as the ‘Diamond Year’ , the Port House is an excellent icon to celebrate this legacy. This is our last post for this year, we wish you Happy Holidays and inspiration for the new year!  from all of us at the Form Finding Lab

Beveled cut edges in a parametrically designed facade

Thin Vaulting: Rwanda National Cricket Stadium


YorkshireTea_RwandaCricket_25.10.17 - Team Yorkshire Tea playing at the Rwandan Cricket Stadium - credit Jonathan Gregson_preview
Team Yorkshire Tea playing at the Rwandan Cricket Stadium (Photo: Jonathan Gregson)

This project is part of a 5-year collaboration between Light Earth Designs and the Rwanda Cricket Stadium Foundation, which focuses on how Rwanda can transition away from a purely agricultural economy using local home-grown, labour-intensive construction techniques, thereby avoiding imports, lowering carbon, and building a skilled workforce.

The primary enclosure of the cricket stadium, the vaults, adapts ancient Mediterranean tile-vaulting (using compressed soil-cement tiles) to a moderately active seismic area by using geogrid reinforcing in the layers and bearing the springing points of the doubly curved vaults on the ground.  The vaults follow the natural resolution of forces toward the ground, closely mimicking the parabolic geometry of a bouncing ball and evoking the cherished hilly topography of Rwanda. The masonry vaults are completely in compression, allowing the use of a simple layered thin shell composite of low strength tiles.

The tiles, which are hydraulically pressed with a small addition of cement and do not require firing, are produced on site using local soil and a combination of skilled and unskilled local labor. They are laid in layers onto a temporary timber skeleton and span up to 16m. A geogrid (developed by architectural and engineering researchers at Cambridge University) is added to give some seismic protection. The shells are waterproofed and topped with local broken granite (found everywhere across the country) to help the structure blend in with its surrounding as well as to add weight and stability.

Simple, efficient, and thin concrete tables are inserted into the vaults, providing space for the more enclosed functions: the service areas, the changing rooms, an office and a restaurant.  These tables are topped with natural Rwandan agro-waste-fired tiles made of commonly found wetland clay. The open mezzanines -a bar and a clubhouse -enjoy wonderful raised clear panoramic views over the Oval and wetland valley beyond.

Bricks are used to define edges and spaces -often laid in a perforated bond -allowing the breeze and light to filter through. These bricks are sourced from enterprises set up by Swiss NGO SKAT Consulting, and are also low carbon agro-waste-fired bricks manufactured using high efficiency kilns, further reducing embedded energy and carbon.  Waste stone from Rwandan granite flooring and worktops are used for flooring. The plywood rectangles used to press the tiles are reused as countertops while timber and plywood from the vault formwork is made into joinery and doors, ensuring that a maximum of waste material goes into primary production.  Local slate is configured to allow rain water to permeate and infiltrate the soil.  Retaining walls are either local granite boulders or are hollow to encourage planting.

The building grows out of the cut soil banking that was formed as the pitch was levelled, thus becoming part of the landscape. The banking creates a wonderful natural amphitheater with great views to the pitch and the wetland valley beyond.  Whilst the language of the building speaks about progression and dynamism through extreme structural efficiency, the materials speak of the natural, the hand made, and the human. It is a building made by Rwandans using Rwandan materials.

The design builds on vault design and research by Michael Ramage at the University of Cambridge Centre for Natural Material Innovation alongside Ana Gatóo and Wesam Al Asali, and extends the work of Ramage with John Ochsendorf (MIT) and Matt DeJong (Cambridge).

30- Rwanda_National_Cricket_Stadium-Credit Paul Broadie_Yorkshire Tea
(Photo Paul Broadie)

Peter Rich Architects with Michael Ramage and John Ochsendorf pioneered soil tiled vaulting at the Mapungubwe Interpretation Centre (SA).  Light Earth Designs (Tim Hall, Ramage, and Rich) continued with the Earth Pavilion (UK), FR2 offices for Joseph Ritchie (Chicago, USA) and have undertaken research in the application of geogrids in seismic zones conducted at the University of Cambridge.

The vault construction proposes a mix of low skilled and skilled worker teams. The teams are trained by an expert mason, in this case James Bellamy (a mason from New Zealand). The tiles are laid with the inner layer resting on a temporary formwork (made of timber and scaffold) that allows the form to take shape. The inner layer of tiles is laid upwards from the perimeter and stays in place through the use of a quick setting gypsum mortar. As the first layer continues, successive layers of tiles are laid in a thin lime and cement mortar inlaid with geogrid. The number of layers is determined by the vault span (in this case up to six layers with a large span of 16m). The tiles are topped with a screed and waterproofed with a torched sheet membrane. On top of this a network of geogrid is laid with a composite granite stone and lime/cement/sand mortar mix.

14-Light Earth Designs Rwanda Cricket Staduim 3
(Light Earth Designs)

The imperfections are celebrated – they are human and beautiful – and when combined with the layering of natural textures the building becomes imbues and celebrates this wonderful place.

Rwanda cricket stadium poster
(Light Earth Designs)
(Light Earth Designs)

All Pictures © Light EarthDesigns unless otherwise noted:

Project Location

  • Gahanga, Kigali, Rwanda


  • Rwanda Cricket Stadium Foundation

Light Earth Designs team

  • Tim Hall -Partner and lead
  • Michael Ramage -Partner and vaulting lead
  • Ana Gatóo -Project lead architectural engineer; on site lead
  • Ben Veyrac -Project architect at tender and architect
  • Wesam Al Asali -formwork design
  • Anton Larsen –architect
  • Marco Groenstege -architectural technician
  • Oliver Hudson -engineering support
  • Killian Doherty -project inception architect


  • Roko Construction, Kigali
  • James Bellamy, Vault Specialist

This post was adapted from a press release kindly provided by Michael Ramage of Light Earth Designs. For more information, please visit:

The thesis: quintessentially Princeton 

the thesis: quintessentially Princeton” features the thesis-writing experiences of Princeton students and their advisers. From research conducted around the world to discoveries made in the library or the lab, students share their joy in doing original, independent work, while relaying some of their mistakes and tips for the next generation of Princetonians. The advisers then explain their side of the thesis journey—from the steps for writing a successful thesis to the close relationships that develop between students and faculty members in a way that is “quintessentially Princeton.”

Below is the account of one of Professor Adriaenssens first thesis advising experiences, when she worked with senior Gregor J. Horstmeyer on his project entitled Structural and Constructional Feasibility of Glass Elements: A Hyperbolic Umbrella.

This post originally appeared at on March 3, 2011


Adviser reflection by Sigrid M. Adriaenssens: A few months into my February appointment as an assistant professor at Princeton University, Gregor Horstmeyer arrived in my office. I had never met him before, but he had learned about me and my research from reading my new website. From this initial conversation, I observed that Gregor had a passion for life. Not surprisingly, I would later find out that the time on his undergraduate thesis was in competition with glassblowing and top-level water polo (he was the 2009 captain of the water polo team!). It struck me that Gregor, a senior in civil and environmental engineering and a glass artist, would be the ideal researcher to investigate and “engineer” a solution for a conundrum that the American glass industry is currently struggling with. In 2006 at the Toledo Museum of Art, the $30 million Glass Pavilion opened as a symbol of America’s “Glass City.” This new structure reflects the legacy of its local glassmakers. One flaw with this image: The curved glass pavilion was completely imported from China, the new world-leading curved glass manufacturer.

Gregor wholeheartedly turned his hobby into his thesis topic and set about investigating the structural and constructional feasibility of a curved glass inverted umbrella shell. Over the summer vacation, prior to the official start of the thesis research, Gregor spent many nights and days in the heat of his hometown glass workshop in Palo Alto, California, making moulds, melting, slumping and fusing glass, and experimentally optimizing his “recipe” to make curved glass panes. My advice for senior thesis students is to start early. Gregor’s investigations confirmed that novel research never develops according to plan A. His physical experiments turned out to be more difficult than they originally seemed. In the fall semester of his senior year, Gregor unconditionally focused on the complex numerical finite element analysis of his shell, which is really a master’s thesis-level topic. His numerical findings confirmed the structural efficiency of the inverted umbrella shell. The shell proved to be extremely thin and could be constructed of minimal amounts of materials, use little resources, and be a showcase of sustainability. Over the winter break, Gregor completed the shell in Palo Alto and shipped the whole model to Princeton for assembly.

And then one day there it was. This extremely thin, strong, stable, and beautiful glass curved object was sitting in my lab. Apart from a single curved glazed dome in a German doctoral study, Gregor was the first to demonstrate the potential these curved glass structures hold. He disseminated the findings of his thesis in a publication in a conference held in fall 2010 in Shanghai, the host of the World Expo. But I am ahead of the story. On Class Day, I got to meet Gregor’s parents and brother. I enjoyed the ceremony in particular because I knew that Gregor was going to win not one but two prizes. He rightly won the George J. Mueller Award for “combining high scholarly achievement in the study of engineering with quality performance in intercollegiate athletics” and the Moles Award for “outstanding promise in construction engineering and management.” I enjoyed the close relationship that I formed with Gregor over my first year in Princeton. I think this friendship will last long past graduation.


Student reflection by Gregor J. Horstmeyer: Engineering students are afforded the luxury of considerable flexibility when choosing their theses. One can do anything from design and build a novel apparatus, undertake seminal research in unexplored areas of study, write a historical perspective on major contributions to a field of study, or anything in between. My thesis involved a physical project in conjunction with a numerical analysis and a written supplement—yes, even though you are an engineer, you do need to show you can form a complete sentence before they’ll hand you a diploma. My project combined three primary interests: engineering, materials science, and art. Ultimately, I designed, fabricated, tested, and analyzed a structural glass canopy.

In the spring of my junior year, I began to search for both an adviser and a topic. As I sat and spoke with Professor Sigrid Adriaenssens, she learned of my prior work with art glass and insisted that we undertake a project involving that surprisingly complex medium. Looking back on those early meetings, I recall the two of us in a frenzy as we brainstormed potential thesis ideas. After a few meetings, we settled on a topic that excited both of us. That brings me to my first point of advice: Investigate something that really excites you intellectually.


Leaving Princeton that summer, I had a general idea of the tasks I needed to accomplish before the start of the fall semester. My adviser and I drew up an initial timeline of objectives. It was necessary to explore the constructional feasibility of the glass canopy and the fabrication of the individual glass elements. Both of these tasks involved experimentation with glass heating and forming techniques.

It did not take long for me to fall victim to Murphy’s Law: What can go wrong will go wrong. Luckily, my lack of full-time summer employment allowed me ample opportunity to sort through all the problems that cropped up. As I troubleshot for answers, I had a glimpse into the world of experimental research. Starting my thesis work the summer before senior year was invaluable for the successful completion of my project. I returned to campus in the fall with a more refined idea of what I was going to be examining, a better idea of the scope of my project, and a long and clear list of questions I needed to address. Point number two: Start early.

Sifting through books, journals, and research papers in search of the answers to your list of questions can feel like an overwhelming task at the beginning. The research process actually adds questions to your list, and answers you think you arrive at are continually refined and updated. In biweekly meetings with my adviser, we were able to examine my work through my ever-changing list of tantalizing questions. No adviser will be upset with you for showing up at a meeting with questions; if anything, this demonstrates that you are actually doing the work. These regular meetings were great learning experiences for both of us. I would arrive with answers (hopefully) to questions posed the previous week and explain my reasoning. We would then discuss any new questions and possible avenues for answers. Point three: Meet often and regularly with your adviser.


There were always problems that we could not work through or that a paper would raise without sufficient explanation. In these instances, I found it to be incredibly helpful to go directly to the source and contact the author. Most academics will be more than happy to try to answer any specific questions you might have about their work. They are both excited and flattered to find that someone else is genuinely interested in their life’s work. Almost everyone was kind enough to give me an e-mail response to my queries, and in some cases I ended up meeting individuals for coffee. Advice from leaders in your field of research, in addition to the guidance of your adviser, often proves invaluable to your thesis. Number four: Be proactive and ask questions of the experts.

I highly recommend not working on your thesis over intersession. I found it really important to take a break and just let things simmer for a while. That meant no new research, no reading; just relax and think. By the time second semester rolled around, I was refreshed and my thoughts were clear. I was ready to tackle the majority of the writing. I met with my adviser, and we reviewed and updated the biweekly schedule deadlines we had planned for the spring. Every few weeks, I would show my adviser a portion of the thesis. She would review it and suggest changes. This allowed me to work on something new while she reviewed something old. When I received her corrections, I was able to incorporate changes she recommended as well as my own editing changes. Slowly, the project was coming together and taking shape. Section by section, and eventually chapter by chapter, the work began to grow more coherent. In late March, I went in for our biweekly meeting and sat down with my most recent time line of objectives and noticed I was almost completely done.


After that meeting, I went back to my room and looked over the first schedule of objectives we had made a year ago. So many things had changed. Comparing the two, I noticed tasks and objectives that were so different they seemed almost contradictory. It was as if each schedule was for an entirely different thesis. This was concrete proof that the thesis process is very dynamic. Ideas evolve and change as you learn new things and you grow sometimes more, or sometimes less, interested in certain aspects of the project. What seemed insignificant at the beginning of the enterprise now occupies 10 pages of text in my thesis. Don’t be surprised if what you end up working on is not what you initially set out to do. My hunch is that is not unusual. The work is going to follow a circuitous path and you are probably going to end up reading a lot about something you had never known about before. As long as the path tracks with what interests and excites you, you will enjoy the research and, ultimately, the entire thesis experience.

In the end, you’re the person who’s going to be up at night buried in books, running between experiments, and debugging code. If you are enthralled in your work and eager to investigate your topic, the project will be incredibly rewarding and well worth those innumerable cups of midnight coffee.

Paris, City of Bridges, a tour.

In Fall 2017, we experienced how the River Seine is central to the enjoyment of the capital of France, Paris. In an earlier post, we interviewed the French bridge designer Marc Mimram about his design philosophy and he showed us the elegant design of the Passerelle Solférino. However no less than 37 bridges straddle the water of the Seine and provide a link between the left and right bank and the islands such as Ile de la Cité.  These bridges visually show some of the history of bridge design in Western Europe.

Map of the location of the 37 bridges over the river Seine in Paris

Initially the Ile de la Cité island provided an intermediate landing between the two rivers banks and thus reduced the bridge spans needed.  As a result, the Petit Pont was initially built over the smaller branch of Seine and Grand Pont over the largest one.

1550 Map showing the bridges leading to Ile de la Cite and the petit pont is shown to the right of the island

Both bridges were initially built in wood. Although floods and fires destroyed them,  craftsmen rebuilt them again and again and even added houses, shops and even mills on top of them.

La joute de mariniers entre le pont Notre-Dame et le Pont-au-Change, by Nicolas-Jean-Baptiste Raguenet, 1756, shows the houses atop the Pont Notre Dame bridge.

The Pont Neuf even had waterworks Pompe de la Samaritaine installed on its deck.  The Pont Neuf marked the change of an era and was the first bridge built in stone and decorated.

The Pont Neuf, a stone masonry bridge, lit at night.

And although stone remained one of the more noble construction materials until the French Revolution, the sophistication of Parisian bridges came to full expression in the Belle Epoque with the arrival of metal ornate bridges at the beginning of the 19th century.  At that time, Paris was showing the world  its prowess in technology and the arts by holding World Fairs. The most elegant bridges of that period such as the Pont Alexandre III and Pont Mirabeau are all found near the Champs de Mars, which was then the heart of the large-scale international World Fairs.

Pont Alexandre III, ornate metal bridge, built around the time of the World Fairs
View of the structure below the deck of the Pont Alexandre III

The new city rail system and Paris’ expansion demanded a whole new series of bridges which would only carry trains. However, the new construction material, reinforced concrete was deemed to be too unattractive and was rarely used for bridges crossing the Seine.  One exception maybe, the Pont de la Tournelle , built in 1927, was built in reinforced concrete but then clad in stone to harmonize with the Notre Dame Cathedral.

Pont de La Tournelle, a stone clad reinforced concrete bridge, near the Notre Dame.

At the end of the 20th century, the Seine riverbanks became UNESCO World Heritage.  This listing led to the design and (re) construction of a number of  elegant bridges such as the Passerelle des Arts, rebuilt in 1984;

The rebuilt Ponts de Arts.
5 series of metal arches supporting the deck of the Pont des Arts.

the Passerelle Léopold Sédar Senghor (ex-Solférino) which links the Tuileries to the Musée d’Orsay in 1999 designed by Marc Mimram; and, most recently, the daring Passerelle Simone de Beauvoir.

Passerelle Léopold Sédar Senghor, has 2 intertwining pedestrian decks.
Passerelle Léopold Sédar Senghor,

A boat tour on the river Seine really immerses you in the history of bridge design.  You might want to take a virtual tour yourself here . Enjoy!

How can we learn about shells and membranes?

Recently the American Shell Builder Jack Christiansen (1937-2017) passed away. With many other shell builders ( like Luigi Nervi (1891–1979), Eduardo Torroja (1899–1961), Anton Tedesko (1904–1994), Félix Candela (1910–1997) and Heinz Isler (1926–2009)), a
large body of knowledge about the design and analysis of shells has disappeared. Furthermore, a recent study of current US academic curricula showed that few US Civil Engineering Departments offer courses on the subject of “Shells and Plates”. This likely reflects a similar absence to courses worldwide. At the same time, technical know-how about the form finding of non-linear tensile systems can be found in specialized engineering consultancies and academic PhD theses. Recently awarded architectural competitions and realized large span projects (e.g. timber shell elephant house Zurich zoo by Galmarini and Oman Airport prefab concrete shells by Foster and Partners) clearly indicate a revived curiosity in the potential of the structural efficiency and esthetic quality that these complex curved surfaces have to offer.
To bridge the gap in knowledge transfer between academia and practice, I introduced a project-based graduate course “CEE546: Form Finding of Structural Surfaces”, which I have has taught (almost) annually at the Department of Civil and Environmental Engineering at Princeton University since spring 2010.  Table 1 lists a non exhaustive list of courses that have been taught on this topic at different institutions worldwide.This Fall Semester I was on the Princeton Engineering Commendation List for Outstanding Teaching for teaching CEE546: Form Finding of Structural Surfaces.  Therefore, I thought I would share my approach to this course here with you.

Table 1:  List of similar courses on shells and/or membranes offered at Institutions worlwide

All listed courses in table 1 use, in some capacity, a project rather than a problem-based approach. In the project-based approach, the active learning occurs through applying the knowledge of formal lectures to a specific project by sharing informal learning experiences through teamwork. On the other hand, in problem-based learning students lend their own research to solving a problem over a longer time period. For the CEE546 course, the project-based teaching pedagogy was adopted. Annually, the course serves 10 to 15 master students, enrolled in the Graduate Civil Engineering or Graduate Architectural Program, and spans a 12 week term. There are no specific pre-requisites, but it is expected that the engineering students have a bachelor’s degree in civil engineering (courses: Mechanics of Solids, Statics etc. and have basic MATLAB proficiency) and the architecture students are comfortable with computational design. The course is taught by one instructor (me), which limits the maximum enrollment of students. The CEE546 course objectives are for the students to:
1.Develop an in-depth understanding of the basics of surface structures,
2. Cultivate relevant numerical and physical form finding proficiency,
3. Communicate complex technical issues with peers, and
4. Problem scope, brainstorm and generate design alternatives for force-modeled systems.

The approach consists of formal learning through lectures and reading material,
informal learning through lab sessions, and knowledge application in assignments and a design project. The different course components are

  1. Formal lectures: on the history between form and form, membrane and shell structures and form finding techniques (both experimental and numerical) and guest lectures by practitioners such as Knut Stockhusen (Schlaich Bergermann und Partner and David Campbell (Geiger Engineers)
  2. Reading material: on-line slides and videos, book “Shell Structures for Architecture: form finding and optimization”, readings by designers such a Laurent Ney and Sergio Muscmeci, research papers on dynamic relaxation and force density
The course book “Shell Structures for Architecture: Form Finding and Optimization”

3. Lab sessions: To impart students with the necessary form finding skills for tackling the design project, a number of lab sessions are held in a computer lab and in the
structural models lab. During these lab sessions, the students complete tutorials that were designed for the specific purpose of the class or are readily
available. There are two types of lab sessions: experimental and numerical ones.
In the experimental lab sessions, the students make prestressed fabric and hanging plaster models with a focus on archetypal forms of best practice. The
mechanically pre-stressed models include the: 1) saddle, 2) wave and valley, 3) conic membrane and 4) an arch supported membrane.

Students exploring experimental form finding techniques: conoid membrane (left) and shell with opening (right)

For the plaster models, students investigate a shell with a square ground plan to investigate the influence of: 1) a topology pattern, orthogonal to the boundaries on the resulting shell form, 2) the same for a bias warp-weft pattern, 3) an opening on the form generation and 4) the introduction of cross ribs on the form.

Parametric variations of hanging chain model shells using plaster models

These physical experiences facilitate an intuitive understanding between form and force and highlight the importance of the designer’s choices in the form finding process (such as the nature and location of boundary conditions). For instance, an orthogonal weave topology results in a shell with lower boundary curves whereas a bias weave results boundary curves with a higher rise. The physical models also allow direct testing of the influence of curvature, pre-stress and stiffness.

After being introduced to the theory of the form finding techniques of force-density and dynamic relaxation in a formal lecture context, the students are guided in using these methods through tutorials applied to in-house developed MATLAB coding. To accommodate for varying scientific backgrounds among students, an interactive user-friendly commercial software known as FormFinder (which uses the force-density method for pre-stressed membranes) is introduced. This software allows form generation and analysis, but does not allow the students to fully grasp (and adapt) the form finding algorithms.

4. Assignments and design project:
The students’ learning is evaluated in three assignments and one larger design project. Each assignment receives written feedback from me. The deliverables of design project consists of a hard copy report, a physical model, an oral presentation and critique among peer students.

4.1. Assignment 1: learning from successful precedent curved surfaces
The objective of the first assignment is for students to demonstrate their basic structural and construction understanding of simple realized surfaces geometries (course objective #1). This individual project asks students to identify a surface of their own choice, describe its social-political context, discuss its structural behavior with approximate hand calculations, and investigate the construction methods used. Precedents, that have been successfully studied include :
i) Spherical dome of the Hagia Sophia (showing occurrence of compressive and tensile hoop stresses in a dome (e.g. Fig. 1a.),
ii) Barrel shells of the Kimbell Art Museum (displaying beam behavior and the effect of diaphragms on the stiffening of the shells),
iii) Air inflated beams of the Festo ‘Airtecture’ Exhibition Hall (demonstrating beam behavior),
iv) Conic pre-stressed membranes of the Prophet’s Holy Mosque in Medinah, Saudi-Arabia (illustrating the relationship between tension and curvature), and
v) Hanging roof of the Expo ’98 Portuguese National Pavilion (showing the direct
relationship between sag and the magnitude of the cable forces).
The study of successful precedents allows the student to develop background knowledge to apply to similar or varying situations. The essential lesson is that seemingly complex surfaces have traditionally been understood using analytical approaches, not
complex numerical ones. This realization is important since students might have a tendency to immediately reach out to numerical approaches for the form
generation and shape generation of surfaces, even for simpler geometries. The ability to perform analytical calculations to get a sense of the form/force interaction is crucial before the students start to envision more complex surface geometries. Hence, these formulas provide a good basis for the students to validate and compare more complex forms they generate in subsequent assignments. These formulas further lend themselves to parametric studies, which reveal the direct relationship between form and forces.

Assignment 1: Study of the forces in the dome of the Palazetto dello Sport

4.2. Assignment 2: applying form finding techniques for mechanically pre-stressed
membranes The second and third assignments aim at evaluating course objectives #2 and #3 (the development of form finding proficiency and the communication of complex issues with peers). Assignment 2 is typically completed by pairs of students, usually an engineering student teamed with an architectural student. The need for teamwork is justified by the quantity of the work and the varying skills that may already exist in the Master level students from different backgrounds. That being said, it is found that hypothesis is not necessarily substantiated in the class room setting, and students use the techniques that they are most comfortable with despite their background. Once a collaboration and trust has been established between the students, they tend to stick together in their team for following assignments. Assignment 2 consists of two parts. The
first part requires the solution of the forces in the elements of a specific Geiger Dome under loading, using the in-house developed MATLAB force density code. At this stage, the students have been lectured about force-density and have read Schek’s and
Linkwitz’s papers. This assignment asks them to analyze the algorithms and adapt them slightly to suit their assignment purpose.

Assignment 2: Analysis of the Geiger dome using force-density method

The second part asks for the design and form-finding of a mechanically prestressed system that needs to fulfill a specific function. For example, students have been asked to design and form find a rainwater harvester. For this design project, most students use the commercial software FormFinder. The students are guided in their design by the feedback they receive in two organized desk critiques. By interpreting the preliminary calculations (Learned in assignment 1) and the numerical results (from FormFinder) the students learn about the necessity of anticlastic curvature, feasibility of the forces in the membrane (warp-weft direction, radial versus rectangular net), cables, primary structures and foundations, as well as the other design challenges of ponding, shading and rainwater run-off. Upon critical evaluation and discussion of their work, the students evolve their design so that it fulfills membrane design criteria and best practices. The deliverables are a report as well as a physical form found model. Each group receives written feedback on their handed-in work.


Assignment 2: Physical Model and Shading Analysis of the Rain Water Harvester

4.3 Assignment 3: applying form finding techniques for (grid) shell systems
The third assignment has a similar format to the second assignment. It also involves team work and is composed of two parts. In Part 1, students analyze the same Geiger dome case study as in assignment 2 using the MATLAB Dynamic Relaxation (DR) code. At this point, they have received a lecture about DR and have read the chapter “Dynamic Relaxation: design of a strained timber gridshell”. In part 2, they use this code to design and generate the geometry of a grid shell with a height restriction over a square courtyard. Since the design project is usually well constrained, it leaves little or no room for too extremely complex surfaces. This active learning takes place in a studio format and the deliverables are similar to assignment 2. The desk critiques focus on the approach to the form finding procedure, the choice of the boundary conditions (and its implications in terms of support structures), and the choice (and value) of parameters
that influence the form (which include applied load, stiffness of the members). For example, the students developing the funnel gridshell, shown in Figure below explored how mesh topology (triangles versus diamonds), member stiffness and support conditions influence the form of a gridshell. They chose to evaluate the different design variations according to the architectural program, sculptural appeal and structural performance of the shell. At this stage in the course, having studied precedents and different techniques, the students design ideas are usually no longer unrealistic in terms of complexity of shape, but well informed by the learned skills.


Assignment 3: Shell systems and numerical modelling (shown roof for E-Quad whose form relies on varying the grid topology (diamond versus triangulated grid), the member stiffnesses and the support conditions M. Horner, V. Kluytenaar

4.4. Design project:  After gaining basic knowledge about surface structures and developing form finding skills in lectures and lab sessions, the final design project is oriented towards the application of that knowledge and skills (while continuing to deepen the knowledge) in a team project (course objectives #2 and #3). The design
project allows for the development of skills such as problem scoping, brainstorming and generate design alternatives (course objective #4). Each time the
course is taught, the design project brief varies, but often its origin relates to the ongoing research activities in the Form Finding Lab. For example, in the spring of 2012, the students were asked to design a performance stage that would complement the hyperbolic paraboloid shells of the modern Miami Marine Stadium (Miami, USA). At this stage of the course, the students have mastered the form finding skills and gained sufficient knowledge about the structural performance and construction techniques of
complex curved surfaces. The project brief is, hence, formulated much more open ended than any of the previous assignments. The students can now create, taking into account laws of physics and the capabilities of the available techniques. The deliverables of this
project are a poster and a physical prototype. The poster shows which design objective and boundary conditions the students selected, the form finding methodology, a number of parametric variations and an appealing graphic of the final project in its context. The students in each group present their work and respond to critiques in an oral presentation to me and their peers.

Design Project:  Oral presentation and critique

The student evaluations and the outcomes of this course have been the motivation to
share my insights into the success of the course.

In conclusion, I would like to emphasize the following
i) Relevance of studying precedent structural surfaces to gain a first understanding of their structural behavior and construction techniques which differ from more conventional structural systems;
ii) Importance of physical form finding techniques to gain a direct and intuitive understanding between form (curvature, span, sag), forces (prestress or self-weight), stiffness and load bearing capacity;
iii) Necessity of numerical form finding methods for the fast generation of design alternatives, the understanding of the force flow within the system under development and accurate definition of geometry.

Although the course is currently offered at Master level, 3rd and 4th year undergraduate students have successfully participated in the class. On many occasions, the course has sparked further research in the domain of form finding and structural surfaces,
both in the format of graduate (e.g. precast segmented shells, UV shading grid shells, inflatable membranes, DR algorithms and grid shell design methodologies), senior thesis (e.g. on spoke wheel membrane structures, adaptive origami facades) and final Architectural Design Projects.

I would like to take all the students who took the course and all the other instructors who helped me (Ruy, Stefano, Sherif, Knut, Irmgard and Paola), to learn with me how we can best learn about shell and membrane structures.

Structures in the low countries: Cupola over the Dutch Maritime Museum

Last week I had the pleasure of recording a MOOC Lecture with Prof. Garlock on Contemporary Vaults.  This MOOC lecture will be offered in Spring 2018 and I will provide you the details in due time. Much to my excitement we got to spend more than 12 hours underneath the steel/glass cupola of the Dutch Maritime Museum in Amsterdam, the Netherlands.  When I worked for Ney and Partners, I carried out the initial form finding of this gorgeous cupola which won the 2012 Amsterdam Architecture Prize.  Time for some pictures and closer look at the design approach of this slender cupola.

Prof. Garlock and myself recording the MOOC under the cupola of the Dutch Maritime Museum (left), Schoolchildren gazing at the pattern of the grid of the cupola (right).

In the late seventeenth century, the historic building currently housing the museum,  was the headquarters of the admiralship. It was the instrument and symbol of the Dutch maritime power. The development of this sea-faring nation was closely linked to the production of sea charts and the advent of the associated sciences, such as geometry, topography, and astronomy. The historic heavy masonry building also uses geometry as a basis for its design and is arranged around a quasi square courtyard which you can see in the background in the pictures shown above.

The Dutch Maritime Museum  Facade uses geometry as a basis for its design (credit Sigrid Adriaenssens)

In the 20th century, the museum underwent a great restoration and the idea was born to increase the amount of useable floor area by sheltering the inner courtyard with a  roof.  A design competition was held and the cupola roof design of the design consultancy Ney and Partners was chosen to be built. The new roof is a steel gridshell clad with glass. The choice for the initial two-dimensional (2D) grid topology of the shell tells the spectator a story about the building’s history and its close relationship to the history of the sea. At the origin of this 2D topology lies a loxidrome map with 16 wind roses. This geometric drawing is found on sea charts displayed inside the museum.

Example of an old loxidrome map showing windroses

We used this 2D topology diagram as the basis for the structural mesh of the roof. Starting from this geometric 2D mesh pattern, we needed to develop an exact 3D grid shell surface.

2D mesh geometry based on a windrose map pattern found in the museum (credit Sigrid Adriaenssens)

I used a numerical form-finding technique based on a hanging chain model within a Dynamic Relaxation Solver, and converted the 2D mesh into a 3D efficient shallow shell shape.  Due to its efficiency, all the gridshell members can be rather slender and as a result the mesh reads like a line drawing against the sky.  Yet the shell’s shape and its slenderness are exclusively grounded in the rational logic of engineering.

The 3D shape of the cupola is derived from a hanging chain model.

The complexity of obtaining planarity in all of the four and five-sided facets of the gridshell was solved by Dr. Chris Williams in a novel, analytical origami approach based on Maxwell reciprocal diagrams.

Maxwell Diagram used to achieve facet planarity in the cupola (credit Chris Williams)

The structurally efficient and constructible shape of the cupola cannot be obtained by producing this form in an exclusively sculptural, esthetic manner. The freedom in generating the efficient form of the cupola lied in the right selection of the material. the loading and boundary conditions, not in the adherence to geometric and nonuniform rational B-spline surfaces. We wrote a great paper about the form finding procedure of this cupola for those who are interested in the finer grain details. Let me know if you would like to read it. The roof also features on the cover of our book “Shells for Architecture: Form Finding and Optimization.”

Shadow of the cupola onto the inner courtyard facade of the museum (credit Sigrid Adriaenssens)

Location: Dutch Maritime Museum, Kattenburgerplein 1, Amsterdam, The Netherlands

Author: Sigrid Adriaenssens

Blow-Up Bulwark

A rendering of the proposed inflatable storm surge barrier if deployed along the coast of the Rockaway Peninsula. Image via the Form Finding Lab

This article was originally published on November 2, 2017 on Urban Omnibus

We associate inflatable structures with ludic landscapes like the bounce castle and hippie hangout. Impractical techno-utopias all. But for engineer Sigrid Adriaenssens and her Form Finding Lab, inflatables could offer a very practical response to the growing threat of storm surge flooding and the uncertainty of climate change. More air bag than pleasure dome, inflatable sea walls could be an affordable and flexible solution to protect coastal cities from rising tides. Adriaenssens and her collaborator Steven Strauss make the case below. Whether building a sea wall or replacing a neighborhood with a swale, soft and hard infrastructures both come with high costs and take a long time to put in place. Ready in three years and deployable in three hours, inflatable rubber barriers present a different direction for life on the water.

At this point, there’s no question: Climate change is real, and it’s happening now. Sixteen of the seventeen warmest years on record have occurred since the turn of the 21st century; 2016 was the warmest year in recorded human history. Manmade greenhouse gas emissions will continue to drive further increases in global average temperatures.

However, the nature of the science is such that while the question of “whether” climate change is under way appears settled, the question of “what” this change will produce has a broader range of potential answers. We may already be experiencing global warming’s effect on polar ice and sea levels. Since 1979, the planet as a whole has lost an average of 13,500 square miles of sea ice per year — an area larger than the state of Maryland. Rising global temperatures will result in the melting of the polar ice caps, which cause a rise in average sea levels worldwide. This poses a particular problem when high winds from tropical storms and hurricanes drive water onto the land, creating “storm surge” tides.

Coastal cities face an increased risk of flooding as sea level rise is exacerbated by a possible increase in storm activity in some regions. But traditional responses to the risk of coastal flooding in dense cities all carry enormous — even prohibitive — financial, social, and environmental costs. At the Form Finding Lab at Princeton University, we are pursuing infrastructural solutions to the advancing risk of coastal flooding that are flexible, adaptable, and economical. Rather than heavy structures with great mass, we focus on coastal defense strategies that use lightweight forms whose most basic design principles account for the uncertainty of the future.

Tidal storm surge in Marblehead, Massachusetts during Superstorm Sandy overwhelmed the man-made barrier. Photo by Brian Birke via Flickr

Vulnerable Cities

Even within an increased risk of coastal flooding due to climate change, there is a range of possible futures — computer simulations generate projections with some variance, and not all locations will suffer the exact same consequences. For instance, one optimistic scenario suggests a global average temperature rise of one degree Celsius between 2046 and 2065, followed by another one degree Celsius increase between 2081 and 2100.[1] Such a global temperature increase could yield minimum sea level rises of 1.7 to 2.4 feet by 2100, and it is expected that high severity flooding events will become more frequent. Many of the world’s leading cities are in coastal areas, and consequently will have significant exposure to climate change (including, for example: Miami, Guangzhou, Calcutta, Shanghai, and Mumbai).[2] But again, each city’s future is likely to look different, and New York City’s challenges are particularly acute. In New York City, recent research suggests that the frequency of a severe hurricane could rise from once in every 400 years, to once in every 23 years.[3] Four out of New York’s five boroughs are on islands, giving the city an unusually long waterfront of 520 miles. This makes it particularly vulnerable both to rising sea levels and to flooding from storms (as was painfully apparent after Superstorm Sandy).

Screen Shot 2017-11-07 at 2.50.01 PM
This map compares the 100-year floodplain with actual levels of flooding during Superstorm Sandy. Map by John Keefe, Stephen Reader, Steven Melendez and Louise Ma. Check out an interactive version at WNYC

Further, some parts of New York are especially vulnerable. The Rockaways, a slender peninsula with the Atlantic Ocean to the South and Jamaica Bay to the North, is home to over 100,000 people. Almost 400,000 New Yorkers live in the 100-year floodplain, at a higher population density than in any other US city facing a similar risk.

Of course, an area’s vulnerability is a consequence of multiple factors, including its initial height above sea level and general physical characteristics, the expected increase in average sea levels, the increase in frequency of severe storms, the increase in maximum expected height of storm surges, and the steps that have already been taken to mitigate the risk. The Rockaway peninsula, surrounded on three sides by water, is likely to be highly vulnerable compared to the Bronx (which is on the mainland and somewhat sheltered by the other boroughs as well as Long Island). Assuming for the moment that, with sufficient notice, significant loss of life can be avoided through evacuation and directing residents to take shelter, the property damage from a storm in a densely populated unprotected area would still be massive. Superstorm Sandy alone was estimated to have wrought $19 billion in damage, largely concentrated in select low-lying areas.

Post-Sandy flooding on Beach 91st Street in the Rockaways, October 31, 2012. Photo by Dakine Kane via Flickr

Existing Solutions

Given the likelihood of increasingly frequent and severe storm surges, in addition to rising temperatures and sea levels, the buildings and residents of low-lying neighborhoods along New York City’s waterfront may soon find themselves regularly under attack by the water that surrounds them. Conventionally, coastal cities have confronted this type of risk by building various types of massive fixed sea walls or barriers. These physical, “hard” barriers could include both coastal armoring structures built along the shoreline, like the seawalls of Sea Bright and Monmouth Beach, New Jersey, or shoreline stabilization structures like breakwaters, such as those in Alamitos, California, which can be off-shore or shore-connected.[4]

But such “armored” barriers carry high initial construction and maintenance costs, and the long project horizons characteristic of many large capital building projects. The US Army Corps of Engineers has estimated that building conventional coastal barriers to protect just the Rockaways would cost $4 billion, and that work, even if approved and funded, would not commence until 2020. A system of traditional surge barriers to protect all five boroughs would cost an estimated $20 to $25 billion and might take 20 to 30 years to design, approve, and build. Beyond the price tag of such projects, their environmental footprint alone could be prohibitive.[5]Hard coastal barriers block the water flow in a floodplain, which can lead to the depletion of plant populations and inhibit animal migration. In New York City, the environmental effects of such infrastructure are unknown but would likely be substantial, and would require extensive review before any project would be approved.

The Galveston, Texas concrete sea-wall under construction in 1902, two years after a devastating hurricane that prompted local officials to build a storm barrier along the city’s coastline. Photo via Wikimedia Commons
The Galveston, Texas sea-wall in 2005, after Hurricane Katrina hit the Gulf Coast. Photo by Bob McMillan via Wikimedia Commons

The difficulties of building traditional coastal barriers have triggered research into “soft and natural” coastal barriers to protect property, economic activity, and human life. Non-infrastructure approaches such as rezoning would depopulate vulnerable areas. Nurturing beach ecosystems like seagrass beds, dunes, mangrove forests, and marshes could then buffer coastal areas by attenuating and dissipating wave surges and wind damage caused by periodic storms.

However, over the last decades, 50 percent of salt marshes, 35 percent of mangroves, 30 percent of coral reefs, and 29 percent of seagrasses worldwide have already been lost or destroyed due to coastal development, population growth, pollution, and other activities.[6] Restoring these environments to the point of effectiveness as a bio-shield against storm surges requires a long-term strategic plan and coordinated population displacement that, in densely populated cities like New York, borders on impractical. While bio-shield strategies could be a component of a total solution, alone they are likely inadequate to the threats posed by climate change.

Finally, changes to the existing built environment by adaptation or accommodation, such as putting all houses on stilts, may also be possible in some areas. But to broadly mandate the elevation of existing buildings in densely populated urban floodplains would again pose significant practical problems.

As coastal cities prepare for global climate change, it appears options are limited: expensive and monumental barriers may mar the horizon and environment out at sea, while ecological or building-level solutions may displace and disrupt residents’ lives on land. Either type of solution seems to imply climate change will radically alter coastal areas. Under the usual paradigms, wherever Rockaways residents were to look, 100 years from now, they would be confronted with the knowledge that climate change had the power to utterly overturn their lives.

A polyester rope suspension bridge in Ait-Bayoud, Morocco, studied at the Form Finding Lab, offers a cost- and weight-effective alternative to a steel cable bridge. Photo by Edward Segal via the Form Finding Lab

Designing for Flexibility

The permanence of hard barriers derives from the tradition of creating strength through material mass — structures that meet nigh-unstoppable forces with more or less immovable objects, like the reinforced concrete seawalls shown above. By contrast, at the Form Finding Lab, we are interested in structures that derive their strength from non-traditional materials and responsive shapes, dictated by the flow of potentially destructive forces. We develop numerical algorithms and design methodologies to identify these shapes, which improve the relationship between form and efficiency in sustainable and resilient urban structures. In this way, we can design innovative force‐modeled structural systems such as lightweight hoop-tensegrity and polyester rope footbridges, flexible adaptive architectural facades, and earthquake-resistant thin shell structures. These forms can be very thin, cost‐effective, and have a low carbon footprint, while maintaining strength and stability. They can also be more beautiful than the ominous, imposing mass of hard structures.

To the challenge of more frequent and more severe storm surges as a result of climate change, our answer is a storable, pressurized, flexible barrier that could be deployed along the coastline should the need arise. Colloquially known as “inflatable seawalls,” these systems are more economical compared to hard coastal structures. The material of the barrier is reinforced rubber, engineered to be durable and to resist the impact of ozone and ultraviolet light — and relatively easy to install and maintain. As a result, the construction and maintenance cost of pneumatic barriers is estimated to be about 75 percent less than that of equivalent rigid traditional seawalls.[7] In addition, the rubber material has a lifetime of 20 to 30 years, which actually constitutes a great advantage over hard, permanent coastal barriers: The inflatable barrier’s design, replacement, and construction can be rethought every so often to accommodate future changes in storm surge behavior. For example, if climate change is more severe compared to what is expected (remember, we are dealing with a range of possibilities) it is easier to modify the inflatable barrier to provide more protection, such as inflating the barriers to higher maximum heights. By contrast, a physical concrete sea wall would probably need to be totally demolished and rebuilt.

An aerial diagram of the proposed inflatable storm surge barrier, which would extend from Breezy Point, at the tip of the peninsula, to Far Rockaway. Image via the Form Finding Lab and Urban Omnibus
A rendering of the proposed inflatable storm surge barrier if deployed along the coast of the Rockaway Peninsula. Image via the Form Finding Lab

While this application of pressurized flexible systems is novel, they have already been successfully used in various engineering applications, from more familiar technologies like parachutes and air bags, to underwater compressed air energy storage, small scale hydraulic dams, and large span roof enclosures such as the pneumatic roof cover over the historic Roman arena in Nîmes, France.[8] But all previous applications (except for air bags) have been designed to bear slowly applied, constant force, rather than the continual battery of ocean waves. What’s more, all other existing applications of this type of pneumatic technology operate at a scale much smaller than that needed for storm surge barriers. So it is important to keep in mind that the proposed inflatable seawalls, while a natural evolution of the existing technologies, also newly applies those technologies to an especially complex situation.

A pressurized flexible barrier is essentially a flexible closed tube, filled with air or water that creates enough pressure to stand up to assault by storm surge and breaking waves. When deployed, it can change shape extensively while remaining functional. As the wave strikes the pneumatic barrier, the barrier can deform to absorb some of the kinetic energy. It will not break, overflow, or vibrate too much, as it blocks the storm surge, diverting it to the side and back to the ocean.

This schematic representation of an inflated storm surge barrier demonstrates the flexible deformation of the barrier in response to pressure, such as from storm waves. Image via the Form Finding Lab and Urban Omnibus

The barrier would be resistant to ozone and ultraviolet light, and able to withstand debris impact from the storm surge, like boats or flotsam, that might be driven into the barrier at high speeds. It would be relatively easy to install and maintain.

Initially the barrier would be folded, stowed, and clamped to a foundation — beneath a boardwalk, for example. In the event of a reported approaching storm surge, the barrier could be deployed in a matter of two to three hours. Once inflated, it would be monitored, and its pressure adjusted wirelessly, either by an operator or automatically, to adapt to changing conditions. In its inflated state, the clamped barrier would form a watertight seal with the concrete base foundation. Since by design it would be submerged under the boardwalk or surface and would not obstruct animal migration paths, the concrete base would not pose the same ecological problems as a hard sea barrier. 

We have had some success with computer modeling, but a lack of existing research about the effect of real and future projected storm surge and wind on membranes of this sort means that a physical test of the technology, in the form of a pilot project, is necessary. We will carry out physical tests on small scale models of the barriers in 2018. These tests, simulating storm surge conditions in a wave tank, could validate our computer findings and provide data to improve the numerical model.

Following physical testing and improvements to the numerical model, the next stage will be a pilot test under actual coastal conditions. Time is of the essence: Existing, traditional solutions like concrete seawalls have so many inadequacies and drawbacks as to render them unviable in many situations. Absent a radical alternative, citizens of many of the world’s great coastal cities may find themselves forced to abandon waterfront neighborhoods en masse. Funding and technology permitting, we hope to be able to begin construction on a pilot in 2020; we believe that potential disaster, like encroaching tides, can be averted. No monolithic seawall need mar the horizon, and no improbable expanse of grasses and trees need displace the existing ecosystem. New Yorkers could face the ocean and rest easy in the knowledge that, no matter what waves and winds future storms might bring, the protection they need is waiting just beneath the surface.

[1] It is important to note that these are all projections, based on simulations, and that estimates vary considerably (depending on the simulation, as well as whether it represents best case or worst case scenario, assumptions about future amelioration, et cetera).

[2] Hanson, Susan, Robert Nicholls, N. Ranger, S. Hallegatte, J. Corfee-Morlot, C. Herweijer, and J. Chateau. “A Global Ranking of Port Cities with High Exposure to Climate Extremes.” Climatic Change, 104, no. 1 (January 1, 2011): 89–111. doi:10.1007/s10584-010-9977-4.

[3] Lin, Ning, Robert E. Kopp, Benjamin P. Horton, and Jeffrey P. Donnelly. “Hurricane Sandy’s Flood Frequency Increasing from Year 1800 to 2100.” Proceedings of the National Academy of Sciences of the United States of America 113, no. 43 (October 25, 2016): 12071–75. doi:10.1073/pnas.1604386113).

[4] K.  Harada and F. Imamure, “Experimental Study on the Effect in Reducing Tsunami by Coastal Permeable Structures,” in The Twelfth International Offshore and Polar Engineering Conference, Kitahyusha, 2002. ; E. Barbier “Marine Ecosystem Services,” Current Biology, vol. 27, no. 11, pp. 507-510, 2017.

[5] See for example Dugan, J. E., Hubbard, D. M., Rodil, I. F., Revell, D. L. and Schroeter, S. (2008), Ecological effects of coastal armoring on sandy beaches. Marine Ecology, 29: 160–170. doi:10.1111/j.1439-0485.2008.00231.x or Kraus, Nicholas C., and William G. McDougal. “The Effects of Seawalls on the Beach: Part I, An Updated Literature Review.” Journal of Coastal Research, vol. 12, no. 3, 1996, pp. 691–701. JSTOR, JSTOR,

[6] E. Barbier, “Marine ecosystem services,” Current Biology, vol. 27, no. 11, pp. 507-510, 2017.

[7] M. Van Breukelen, “MSc. These Improvement and scale enlargement of the inflatable rubber barrier concpet,” TU Delft, Delft, 2013.

[8] 2014. Snyder, J. Sitter and J. Chung, “Design and Testing of an Airbag System for High-Mass, High-Velocity Deceleration,” Journal of Dynamic Systems, Measurement and Control, vol. 119, pp. 631-637, 1997; A. Pimm, S. Garvey and M. de Jong, “Design and Testing of Energy Bags for underwater compressed air storage,” Energy, vol. 66, pp. 496-508, 2014.

Sigrid Adriaenssens is an Associate Professor in the Department of Civil and Environmental Engineering at Princeton University. Her research goal is to transform the engineering approach to design through structural form for a sustainable and resilient built environment.

Steven Strauss is one of the John L. Weinberg/Goldman Sachs Visiting Professors of Public Policy at the Princeton University Woodrow Wilson School of Public and International Affairs, where he teaches courses on management in the public sector, smart cities, and urban economic development.