from analog to digital: double curved lightweight...

From Analog to Digital: Double Curved LightweightStructures in Architectural Design Education

Georgios Dimopoulos1, Dimitris Kontaxakis2, Ioanna Symeonidou3,Nikos Tsinikas41,2,4School of Architecture, Aristotle University of Thessaloniki 3Department of Ar-chitecture, University of [email protected] 2,4{dkontaxa|tsinikas}@arch.auth.gr [email protected]

The paper describes an architectural design studio for 5th year students at theDepartment of Architecture of the Aristotle University in Thessaloniki, Greece.The educational objective of the studio is the design of double curved lightweightstructures, employing a creative methodology which instrumentalizes the study ofnature as a source of inspiration. The objective of the course is to familiarize thestudents with curves and form-finding (analogue and digital) with the aim todesign forms that display structural stability. The paper will highlight theeducational gains from a hybrid design methodology which employs both analog(physical) form-finding tools and digital modeling for the design of doublecurvature surfaces.

Keywords: Lightweight structures, Form-finding, Dynamic models, Tensilestructures, Architecture education

INTRODUCTIONThe well-established design methodology of form-finding is historically based on the construction of“dynamic” models (Otto & Rasch, 1996). Τhe “dy-namic” model incorporates the forces acting on themodel, therefore simulating itsmechanical and struc-tural behavior, while driving the designer towardsstructurally efficient constructions. The use of “elas-tic”material for thedesignofmembranes contributesto the form-finding of double curvature structuralsurfaces which are anticlastic (tensile), or synclastic(inflatable). Frei Otto referred to these as natural con-structions, notmerely for theirmorphological resem-blance to natural forms but mainly because “these

are constructions which reveal the processes of theircreationwith particular clarity. The form-finding pro-cesses are those which, given a set of conditions andfollowing the prevailing laws of nature give rise tovisible forms and constructions under experimentalconditions. As they take place without human inter-vention they are also termed autonomous formationprocesses” (Barthel, 2005).

Within the studio set-up, the small-scale “dy-namic” model is a useful methodological tool for fu-ture architects to experiment with form-finding, tounderstand forces of tension and to create optimizedsolutions which integrate design and structural de-cisions (Otto, 1988, 1990). This methodology pro-

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vides an experiential learning environment offeringthe opportunity to work hands-on and create lowtech models with high tech logic.

Parallel to the construction of small-scale “dy-namic” models, the students experiment with dy-namic relaxation in Rhino with Grasshopper para-metric design plugin and Kangaroo Physics engine(Piker, 2013). Digital simulation allows designers toinvestigate forms by updating forces, supports andphysical properties. The course focuses on both theanalog/physical and the digital form-finding, not astwo competing design strategies, but as two designmethods which act synergetically giving feedbackto each other, a hybrid design process in a digital-material environment.

A TEACHINGMETHODOLOGYWITH PHYS-ICALMODELS IN THE DIGITAL AGEThe transition from analog to digital architecture is inprogress for some time already. Today we are goingthrough a period, during which artificial intelligence,augmented reality and material intelligence definethe new environment in which the educational dis-course of architectural theory and practice is beingdeveloped. This new reality equips the contempo-rary architect with new tools both in the design pro-cess (novel software) as well as the construction pro-cess (digital fabrication).

At the same time, however, it raises a number ofconcerns and questions about the necessity of em-pirical practice in architectural composition: In theage of 3d printers and robots is it still necessary forstudents to construct physical models? How is theknowledge gain enhanced with the use of hangingchain networks, stretched fabrics, soap films?

According to Aristotle (Barnes, 1982), man cre-ates Art and Science using his mind-based experi-ences. By translating this to the field of architec-ture, the students’ experience of developing physi-cal models, combinedwith intelligence, can lead to adeeper understandingof their compositional choices- an understanding of themain rule that governs andorganizes the elements of their construction. Within

this framework the design studiowill initially follow ahands-on approach. Experiential learing has a seriesof undoubtable benefits, Kolb advocates that activelearning pedagogies are of a very high educationalvalue (Kolb, 1984), he elaborates saying that hands-on processes, followed by critical reflection and ex-perimentation lie in the core of the learning process.In an era, when architecture is dominated by digitaldesign processes, it becomes increasingly importantto engage with analogue design media, and under-stand the correlation between analogue and digitaltools. As the students were setting up the modelsliterally ”with their hands”, they subconsciously ob-tained the tacit knowledge about material behaviorand the way forces translate into geometry.

FAMILIARITY WITH DOUBLE CURVATURESURFACE GEOMETRYAmong the initial design exercises to familiarize stu-dents with geometry, is the discretization of doublycurved surfaces. The aim is to constructed a seriesof 3D primitives with flat sheet material, to assemblecurved cylinders, curved cones, saddles and hyper-bolic paraboloids or forms obtained through combi-nations of the above.

A rigid and flat material, such as paper, can onlybend in onedirection and if one tries to bend it in twodirections it will crumple or tear apart. This is due tothe fact that nonelasticmaterial canonly create a sur-face of single curvature such as a cone or a cylinderbut not an ellipsoid or spherical solid, that is to say,surfaces of double curvature.

For the construction of double curvature sur-faces, the rigid material should be cut in discretizedshapes (patterns) that when joined together will ap-proximate a doubly curved surface (M. Kilian et al.,2008; Tachi & Epps, 2011). In this way basic geomet-ric forms are constructed, and through this processthe students are able to experience a hands-on pro-cess of design rationalization, understand how dou-bly curved forms may be discretized to planar or sin-gle curvedparts andhow these canbe synthesized togenerate a taxonomy of several doubly curved forms

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that can be constructed out of cardboard in the de-sign studio (figure 1). For example, through experi-mentationwith the doubly curved cardboardmodelsit appears that the hyperbolic paraboloid is derivedfrom the curved semi cylinder (saddle) which in turnis derived from the curved cylinder (Figure 2).

Figure 1Cardboard model ofa doubly curvedsaddle shapeconstructed fromsingle curvatureelements. Students:Moga Μ., SeferidisΖ. Students: MogaΜ., Seferidis Ζ.

Figure 2The curved cylinderand its subdivisions.From left: curvedcylinder (silo),curved truncatedcone, curvedsemicylinder(saddle) andhyperbolicparaboloid.Students: DrosouniΑ., KonstantinidisΝ., Ibanez F.

In this first introductory exercise, students becomefamiliar with the geometry of basic double curvedsurfaces, mainly with regards to construction log-ics, rationalization and cutting pattern generation.At this initial stage, experimentation with doublycurved surfaces employs rigidmaterial, therefore stu-dents are not yet aware of the forces exerted on thesesurfaces when flexible material is used in physicalform-finding and the repercussion of the forces ontheir shape. This important consideration is to bediscovered during the subsequent exercises in whichstudents will experiment with “dynamic” models.

“DYNAMIC”MODEL AND FORM-FINDINGThe “dynamic” model is more than a three-dimensional object, as opposed to the aforemen-tioned rigid models made of cardboard. The “dy-namic” model responds to the forces acting on themodel, the geometry is the result of the boundaryconditions, the forces, anchorpoints and elasticity ofthe material.

Students experimenting with elastic fabrics andinflatables not only understand from the first mo-ment the forces exerted on the structure, but alsorealize that these forces produce the form of theconstruction. Thus, students are encouraged to en-gage in an experimental design process that com-bines form-finding with the actual understanding ofstructural performance in real time. This experientiallearning approach makes it immediately clear to stu-dents that for lightweight architecture, constructionis not an independent stage, which follows the endof the design process, but is instead, from the out-set, an integral part of architectural design in con-stant feedback with architectural composition. Thus,in the design studio the process of architectural de-sign is linked to issues of construction, stability andmateriality (Figure 3).

STUDENT TASKSThe students experiment with dynamic physicalmodels of lightweight structures, utilizing a variety ofmaterials, as seen in Table 1

Within the category of tensile membranes themodels manufactured are classified according totheir supporting structure (poles, arches, space-frame) and their position in relation to themembrane(outside or inside) (figure 4) (figure 5).

Table 1Models, materials,elements andmechanisms


Figure 3“Dynamic” modeland form finding.Students:Amanatidou Β.,Radou D., SiapkariΚ., Fassa Th.

Figure 4Tensile structurewith poles. Student:Charalambidou M.

The models of self-supporting membrane struc-tures are classified into twocategories. In thefirst cat-egory the membrane is supported by a spaceframeor other primary loadbearing structure, in this casethe membrane simply functions as a secondary ele-ment, it does not participate in the overal structuralperformance of the construction. On the contrary, inthe secondcategory themembraneplays a role in thestructural performance, acting as a tension elementthat stabilizes the rest of the structural elements.

The models of the folding-retractable mem-branes are classified, according to the way they aredeployed or collapsed, into the following categories:folding, rotating, extending-shrinking, nesting, slid-ing, etc. Themodels incorporatemovement, which isachieved with the use of different mechanisms suchas: knot - joint (hinge), telescopic mechanism, scis-sors mechanism, umbrella mechanism among oth-ers.

In the case of a collapsible membrane, therefore,the concept of adaptability comes into play. The de-sign must facilitate quick changes from one condi-tion to another, enhance the ability of the model tomodify its morphological and functional characteris-tics, in order to adapt it to a number of variable fac-tors such as the changing weather conditions.

Finally, students experiment with inflatablemodels which are classified into four distinctive cat-egories:

• Inflatablemodels that take their form fromagridstructure or spaceframe that surrounds them

• Inflatable models in the form of air tubes orairbags (combining positive and negative pres-sure)

• 3D printing of a non-elastic structure on an elas-tic inflatable membrane (Figure 6)

• Inflatable structures with internal pressure fluc-tuation. That is, structures that can changeshape and function by controlling the internalpressure of the tubes from which they are com-posed (Figure 7)

INSTRUCTIONS FOR MAKING “DYNAMIC”MODELSThe instructions given to students for the construc-tion of the aforementioned “dynamic” models maybe summarize in the following guildlines. The stu-dents were promted to:

• avoid flat sections of membranes, for both aes-thetic and functional reasons, as double curva-ture surfaces contribute to the resistanceagainstwindload

• use pin joints instead fixed ones. An exampleof the above is the use of pillars that are an-chored by cables to the ground. If the posts arefixed (embedded) in the ground, then the lateralforces bent them, while if they are not fixed, theforces penetrate vertically along the pillars, re-sulting in better buckling


Figure 5Multiple peaktensile structuresuspended fromfloor and ceiling.The inverted peaksmutually supportthe tension of eachside. The doublycurved parabolicsurfaces form a“spiky” installationfor walk and play.Students: Yagou A.,Kasviki V.

• make the connection between the elements ofthe structure visible and clear

• ensure easy and fast installation and uninstalla-tion of the structure

• emphasize the sense of lightness that governslightweight constructions

Finally, in addition to the above technical and mor-phological criteria, students establish their own de-sign decisions which may relate to different criteriaand design parameters. To this end, each group ofstudents creates their own scenario while taking intoaccount not only technical and technological factorsbut also environmental, social and economic factorsinvolved in the planning process.

Figure 6First step: 3Dprinting of anon-elasticstructure on anelastic inflatablemembrane. Secondstep: deflate themembrane tocreate hollowsurfaces. Students:Mokka A., MousafiriE..


Figure 7Dynamic inflatablestructure at highpressure (above)and low pressure(below). Students:Goumenaki P.,Beltou P.

WAYS TO SOLVE A DESIGN PROBLEMObserving the key cognitive manipulations withwhich students attempt to solve a design problem, itis found that the majority of students follow a mixedapproach. There are several iterations of “trial and er-ror”, inspiration and rationalism, with a clear prefer-ence for exploratory approaches for the early stagesof design. The hands-on approach proves to be ofhigh educational value. Although unaware of thematerial properties and behaviour, students developa variety of “accidental” reactions, by reflecting inaction (Schon, 1984) in an exploratory environmentwhere design solutions emerge through experimen-tation, knowledge, intuition and refinement. The stu-dents obtain tacit knowledgeandunderstand thedy-namic physical model as a vehicle for understand-ing the design characteristics of lightweight struc-tures, the role of forces acting upon the model, andthe emergence of form, the potential shapes thatmay respond to a design problem. Through suchdesign experiments, “we can know more than wecan tell” (Polanyi, 1966) and thus the students areable to design structurally efficient structures with-out the need for extensive and complex calculations.The great majority of students affirmed that hands-on-experimentation improved their understandingof structural behaviorof the structures aswell as com-putational thinking and that they were able to con-textualize the empirical learning.

FROM “DYNAMIC”MODEL TO DIGITALThe “dynamic” model plays a crucial role not only infinding the form but also in understanding the in-terplay of underlying forces. The “dynamic” physi-cal model is itself an example of computational de-sign, we may refer to such models as analog com-putation, as they compute physical forces to reacha state of equilibrium. Having understood that,it was now easier and more intuitive for the stu-dents to engage in computational and algorithmicexperimentations where physical forces are simu-lated and representedby a spring-particlemodel (Kil-ian & Ochsendorf, 2005). Therefore, students haveonly to transpose the internal logic of the dynamicmodel, a logic that can lead to a multitude of finalforms by changing some parameters in the paramet-ric definition. A membrane is described by a net-work of springs in Kangaroo (Figure 8), parameterssuch as stiffness, rest length, anchorpoints, etc aredefined in the parametricmodel. The physics simula-tionwill take place and an optimized and stable formwill emerge as a result of the forces in play. This hy-brid analogue and digital practice helps the studentsto understand the essence of computational design,the logic through which the form emerges, or rathera multitude of forms that are linked by a set of rules.There aremanybenefits of structural form-findingus-ing particle-spring systems. A design exploration inthis environment embeds criteria of structural opti-mization already from the early stages of the designprocess, while it assists architects to increase theirintuitive understanding of the structural behaviourof geometrically complex forms. While traditionalarchitecture and engineering aims at the structuraloptimization of an existing form, a dynamic form-finding system can lead to a “real time” discovery ofstructural form encouraging the morphogenesis ofoptimized structures rather than a post-design opti-mization. This justifies the methodological choice ofthe course to start with low tech models in an era ofdigital dominance.


Figure 8Analogue anddigital models ofmembranes bystudents:Mitropoulou N.,Podara A.

Figure 9Construction ofdouble curvaturesurface withnon-elasticcomponents. Thecutting pattern isderived from digitalprocessing of thedynamic model.Students:Dimitriadis A.,Zygoulis N., SakkasK.

DESIGN AND CONSTRUCTION OF DOUBLYCURVED SURFACESWITH DIGITALMEDIAOneof themost challenging issues for thedesign andconstruction of double curvature surfaces is the de-sign of the membrane pattern (Figure 9). In the earlydays, designers used to apply glue to the fabric of themodel in order to neutralize the elasticity so it couldbe cut into small pieces to form the cutting patternson scale. From small (model) to large (real scale), theyscratched the patterns with the use of a pantograph.This was the process before the emergence of com-puters (Tsinikas et al., 2019).

The advantage of digital design is therefore notonly that it reduces the time it would take to developand optimize the model compared to traditional de-

sign tools, but also because with the use of softwarea designer can generate construction drawings anddetailing.

CONCLUSIONThe teachingmethodology and the results of the de-sign studio highlight the importance of a hybrid ana-log and digital design process, the reciprocal rela-tionship between hands-on learning through phys-ical models and the digital / algorithmic design pro-cesses. The main knowledge gain was the ability tounderstand the emergence of structural form as a re-sult of forces anddesigndecisions, through analogueor digital computation. As Wassim Jabi explains “As-sociative and parametric geometry, in essence, de-scribe the logic and intent of design proposals, ratherthan the formof the proposal itself” (Jabi et al., 2013).

This exploratory teaching approach of the de-sign studio confirms that the hands-on experiencenot only helps in finding the form andunderstandingof the logic behind the “dynamic” and digital model,but it also instigates students for further design re-search as they “play” with building materials, foster-ing teamwork and collaboration. Students acquiredan intuitive understanding of what works and whatnot, and they were able to further conceptualize andunderstand the reasons of certain behaviour, theywere able to developwhat Albers referred to as “feel-ing for materials” (Albers, 2013).

From an educator’s point of view, the idea of ac-tively engaging in a hands-on exploratory process,both with analogue and digital media is extremelyvaluable for students for a variety of reasons relat-ing to perception, cognitive psychology and learningtheories. During the last decades there is a growingacceptance of learning-by-making, it is broadly rec-ognized that knowledge is a consequence of experi-ence and that the role of technology is significant inthe construction of knowledge (Stager, 2014).

During the design studio “Nature and spacestructures” at the Department of Architecture of theAristotle University in Thessaloniki, Greece, explo-rationswere taking place in parallel in both analogue


and digitalmedia driving the design to solutions thatwere both aesthetically pleasing and structurally sta-ble, so that design schemes canbe further developedinto an architectural artefact.

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