Computer aided curvilinear architectural design

Computing Design Theory, University of New South Wales, July 4, 2003

John Middendorf

Background- Curvilinear Form in Architecture.

Architectural curvilinear form has been around since the dawn of building shelter.

Vernacular architecture, generally of earth construction, is by the nature of the materials

and the construction techniques, curvilinear in form. The practical aspect of the

structural curved arch was discovered by early builders, and 3200 year old mud brick

storage rooms built with arches survive intact in Egypt. As civilizations developed,

preference was given to linear forms, yet curved form continue to develop over the

centuries, initially as structural enhancements, then later as an aesthetic. The 43.2 meter

dome of the Roman Pantheon (c. 118-128), was one of the first uses of concrete (and one

of the last, until 1796, when the technique for making concrete was rediscovered). Sixth

century Byzantine architecture made extensive use of the dome, as is exemplified by the

magnificent Hagia Sophia in Istanbul. In the East, simplicity and form combined to create

functional curvilinear structures. The modular roof design of the Japanese Pagoda, for

example, is highly advanced in its use of materials and resistance to earthquakes.

Incredible advancements in structural engineering and other civil engineering forms were

achieved in the Far East, yet the lack of communication between the East and the West

prevented much of the technology from making its way into the Western architectural

form. Most of the curved form developments in the West of for the next thousand years

were refinements on the arch and the dome, reaching an apex for one of the most

ambitious domes of the Renaissance, the Florence Cathedral, designed and built by

Brunelleschi using innovative stonework techniques from 1420 to 1436. The

construction of the Taj Mahal between 1630 and 1653 could be said to represent the

perfection of the dome form, while perhaps also sealing the use of the dome as an

aesthetic, rather than a practical, building style. Yet the graceful form of the Gothic flying

buttresses, developed by the engineers of the 12

th

century to support the lofty churches

with expansive glazed windows, must have inspired the post-Renaissance explorations

into curvilinear form for the sake of aesthetics. The Baroque period of the 17

th

century,

lavish with curvilinear representing the spirit of the age, as did the later Rococo style.

Yet these forms were likely considered too extravagant even at the time, and styles

generally reverted back to linear forms.

In the 19

th

century, new metallurgical materials sparked new forms: the wrought iron

Eiffel Tower (1887-1889), and Bibliotheque Nationale (1859-1867), by Henri Labrouste,

with a wrought iron domed skeleton which allowed for an glazed center apex, both

emphasize the natural and graceful lines of force which were facilitated by the strong,

lightweight materials (lightweight, that is, relative to stone or concrete). The later part of

the century brought the short lived Art Nouveau movement, with its fluid, curvilinear

lines, and the great Spanish architect, Antonio Gaudi, who wrote,“The straight line

belongs to man, the curve to God”. His buildings in Barcelona, then considered by many

as freakish forms, are now regarded as masterpieces of the era. In the 20

th

century, with

the advent of pre-stressed concrete (1927), architects such as Alvar Aalto and La

Corbusier made use of the latest structural developments and designed magnificent

curvilinear buildings, while Eduardo Torroja, Felix Candela, and Erin Saarinen explored

the limits of minimalist curved forms based on the mathematically precise, optimal load-

bearing hyperbolic paraboloid shapes. The Guggenheim Museum (1956-1959) in New

York City with its circular exhibition space, which Wright refers to as “quiet, unbroken

wave”, is one of Wright’s greatest works. The latter part of the 20

th

century brought

examples of what could be called modern curvilinear form, with the Sydney Opera

House(1957-1973) perhaps being one of the finest examples, as well as being an

excellent study of the interaction (and difficulties) between architects and engineers when

it comes to pioneering new ways to create form on the public building scale. Yet the

predominant architectural form in the 20th century remained linear. Why? The limitations

of hand drawn architectural drawings leads to linear buildings that are easily rendered in

2D form, whereas three dimensional curvilinear form is facilitated by three dimensional

rendering tools, not available until recently.

Computer as Design Tool

Fabric architects were the first to use computers to optimize form and design in

architectural structures. Based on soap bubble research pioneered by Frei Otto in the late

1950’s and resulting in the development of the tension fabric structures, Otto’s funicular

1972 Olympic roofs in Munich were designed with computer program developed by

Klaus Linkwitz at the University of Stuttgart. Later fabric pioneers such as Horst Berger

worked with large engineering firms which developed proprietary (and closely guarded)

computer software to design some of the largest fabric structures in the world, such as the

Haj Terminal in Saudi Arabia (1981).

Of course, in the realm of engineering since the dawn of the space age, engineers have

been pushing the boundaries of computers for analysis, and were used on larger building

projects by the building engineers in the early days of computing, but generally only after

the architect had completed the design. Finite element programs, originally developed

for the aerospace industry (NASA), have recently become available to smaller design

firms, narrowing the traditional expansive gap between architects and engineers. In a

sense, the practice of building structures is coming full circle, with the concept of the

Renaissance Master Builder, who oversaw all the (inseparable) aspects of design and

construction, becoming once more a plausible role for designers, as computers become

more accessible.

In the past few years, computers have gained status as a standard tool for architectural

design. As history has shown, as new materials and tools become available, their use is

eventually fully incorporated to the absolute limit resulting in entirely new genres. The

nature of architectural design itself is currently in an evolutionary phase. Yet the

transition is still in its infancy, and could potentially lead to realms only hinted at by the

most recent computer aided architecture. In the early days of CAD, in the 1980’s, the

computer was primarily used for drafting. Yet many architects and institutions continued

to rely on traditional hand drawn architectural drawings, and some universities even

prohibited the use of computer aided drawings for final submissions, in the thought that it

limited the creative process (which perhaps the early computer tools did). By the 1990’s,

the computer in architecture became mainstream, and soon thereafter, the limits of the

existing technology were pushed. The concept of the architectural “blob”, for example,

of 3D curvilinear form, became popular in architectural literature in the early and mid

1990’s, and many firms specialized in the application of the blob in practice. Blob design

was generally based on the use of the newly available B-spline technology, and allowed

previously unworkable designs (in terms of construction drawings and artifact

production) become fashionable during this period. As the use of the computer has

matured, the prevalence of the random blob has (thankfully) decreased, as the novelty

wore off and the technology to create blob designs became commonplace.

Current state of the art of computer aided architecture could perhaps be represented by

Frank Gehry’s Guggenheim Museum in Bilbao (1993-1997), digitally rendered and

refined, after the shape was physically formed sculpturally using massing foam blocks,

with the use of Catia, a popular aerospace CAD tool, although it must be noted that the

Bilbao Guggenheim, often touted as the coming of age of computer aided architecture,

uses a very linear interior structure, and the curved outer façade (and inner skin) are

bolted onto the interior structure, similar to the methodology the French architect and

engineer team Frederic Bartholdi and Gustave Eiffel used to design and construct the

Statue of Liberty in 1884. In other fronts, Renzo Piano’s Tjibaou Cultural centre in New

Caledonia (1991-1998) was designed from bottom to top with computers, as well as his

Kanzai airport (1988), which was pioneering in its attempt to use computational fluid

dynamics software to optimize the shape with the thermal performance of the building.

Current Development Overview

Developments in the methodology of applying computational resources to the creative

process of architectural design have been accelerating in the past years. The advanced

state of digital visualization tools, for example, allow for ultra-realistic portrayal of a

given design. Such programs, however, generally are only useful after the concept (and

details) have been decided prior to the use of the computer as an aid. The nature of the

creative process itself has been explored and advancements been made to recreate the

traditional conceptual creative venues of architecture, such as digital sketching and

massing tools, with the use of the computer. Shape grammars can be programmed to fit a

certain ideal set of shape requirements. Digitally stored libraries of information,

accessible by systems such as case base reasoning, as well as knowledge based systems,

offer the potential to help guide the design process in a more efficient manner. Computer

collaboration tools, which accelerate the transfer of information between parties, offer the

promise of synchronizing and converging the often diverse intent of a building project.

Other programs, such as genetic algorithms and intelligent agents, can aid in the

optimization process. All of these tools have potential to be of great use to the architect,

but none in and of themselves offer the promise of the recreating the concept of the

master builder, the designer or single design team, that can combine and optimize the

architectural design and engineering requirements that a modern building demands.

Combining form and structure

Structural optimization codes which can both analyze and optimize a design based on

parameters set by the designer have been accessible for quite some time, yet these tools

are generally not employed by the architectural profession. The form and structure of a

building project have been treated as separate processes. The elegance of combining

these two facets of design is often lost. Although several noted architect/engineers, such

as Santiago Calatrava, have been successful at unveiling the beauty possible with

structural form, it is only through their sheer genius that their works of art and

engineering have come to pass. Is it possible to create a computing tool that will allow

the more typical creative designer to extend the realm of the design that combines form

and structure? Two paths of the puzzle are presented here, first by their engineering

definition, then by their application to the building trade, and finally with some thoughts

as to how these can be integrated into the creative design process in the future.

Optimization in Engineering

Structural optimization is a numerical technique for the determination of an optimum

material distribution in a given design space. The numerical technique in its current

common form involves formulating a design with a given set of parameters, specifying

which parameters can be adjusted, setting the constraint conditions, and running the

program to find the optimal solution based on the input. The process is analogous to

being on a hilly surface with the goal of finding the maxima or minima. The contours of

the hill represent the parameters, and the constraints can be considered fences which

cannot be crossed. Because the computer is essentially blind as it searches for the

maxima/minima, it will initially determine its path by discovering the local gradient

around the starting point (by a design sensitivity analysis), proceed until it hits a fence (a

constraint), the follow the fence until it finds a maxima/minima, which will generally be a

junction of two or more constraints. Approximation concepts are used along the path to

the maxima/minima, which couples parameters and constraints into sub-sets of variables

in a process known as design variable linking. The process distinguishes the design

variables from the analysis variables and utilizes the linking to determine the path to the

optima. Approximation allows for speedier path to the optima, as performing a full

analysis at each step along the way would be highly computationally expensive. Modern

programs generally use the Kuhn-Tucker conditions to determine the maxima/minima,

which involves calculating the sum of the gradient vectors of the objective and constraint

functions, which will be zero at the optimum. A popular finite element program set

Patran/Nastran (the pre- and post-processor) allows for hundreds of design variables and

hundred of constraints to be simultaneously solved. A common baseline is the study of a

basic beam/truss structure, such as the Michell truss, which also has an analytical

solution.

Topological optimization, which allow topological changes to the general shape for a

given load, are considered here, as these are most applicable to the combination of

engineering and architecture that we seek to incorporate into the design of a structure.

The default methodology seeks the smallest volume of material for a given load, by

seeking maximum stiffness for a minimum of stored elastic energy. Generally, a starting

solution is given, and the computer removes material in its search for the optima.

Genetic and other evolutionary methods have been used with some success. Querin et.

al. (1999 and 2000) outline an additive method in several papers using evolutionary

algorithm which allows for the thickness of the design to vary as well. Steven et. al.

(2002), have worked on methods that optimizes maximum stiffness and minimum stress

simultaneously using both additive and subtractive methods. Extending the process to

laminate structures (but only in 2D), Hansel et.al (2002) have combined a heuristic

algorithm which removes single layers of material at locations where it is not needed,

with a genetic algorithm which adds local reinforcement to areas to meet the specified

structural needs. In this manner, complex patterning of laminate layup can be determined

by the computer. Such developments could be applied to the “Gehry problem” of

engineering a structure of a given shape to optimal dimensions, eg. a structure that is

single layer of varying thickness material that complies with an architect’s design,

avoiding the current problem in such buildings as the Bilbao Guggenheim, where the

dead space in between the outer and inner structure can be as much as 5 meters.

The normal optimization methods generally have fixed given loads. In a paper by Chen

and Kikuchi (2001), a system for creating a topologically optimized linear elastic

structure to design dependent loads is outlined. This points a way for the creation of a

system which can take in more general parameters in order to determine a given optimal

shape. In Chen and Kikuchi’s paper, problems with hydrostatic pressure loading are used

as a means to study the creation of structures which can resist loads optimally. Nature

seems to work in a similar manner, for example, a tree will grow differently in regions of

high wind compared to a sheltered tree of the same species.

There are still considerable hurdles to overcome before the realization of creating 3D

structural volumes based on optimal material usage, yet strides are progressing rapidly.

Golay and Seppecher (2001) have proposed a system based on a fictitious material (i.e.

with a theoretical stress strain curve) in order to work out the mathematics of finding a

optimal topology with only the forces and material characteristics as parameters. Their

work points to possibilities of discovering entirely new shapes, much as nature

continually surprises us with intricate shapes, because, as Leonardo pointed out in the

15

th

century, “Every action in nature takes place in the shortest possible way”. As the

growing body of research shows, optimizing architectural structures in which the

topology is determined by the load and spatial characteristics required, is becoming a

more realistic proposition every day.

Computational Fluid Dynamics

The currently separate research into applying computational fluid dynamics to buildings

in order to predict thermal performance and comfort is also developing by leaps and

bounds in the past years. Current limitations generally derive from the lack of computing

power, rather than the application of theory, which is fairly developed and based on basic

theories of physics: mass conservation (equations of continuity), momentum in the x,y, z

directions (Navier Stokes equations), and the principle that energy is conserved (energy

equation). These five equations are not possible to solve analytically, so the partial

differential equations are discretized and calculated by the finite volume method. The

complicating factor of modeling turbulence creation and dissipation requires

simplifications to be made in the modeling of fluid motion, resulting in results that

generally must be verified empirically to be useful. Furthermore, limitations in

computational resources (i.e. solutions that can solve by modern computers in less than a

few days), requires analyst to generally consider only a two-dimensional model. As the

technology of computing power increases, “purer” equations to model turbulence will

become reasonable to use, and the process of analyzing thermal characteristics of a

general given three dimensional volume will be a more likely proposition.

There are two methods currently utilized to measure the thermal performance of a

building: the simpler, more assumptive method used is the Energy Simulation method

(ES) which is a networked nodal based system which breaks up the regions according to

the room layout of a building, and averages room and wall temperatures and balances

mass and thermal transfers throughout the entire building. Although utilized for well-

validated computer models such as TRNSYS, BLAST, ESP-r, Energy Plus, and DOE-2,

the nodal approach is limited as it assumes room air is completely mixed and uses

empirical models (based on standard rectangular dimensional layouts) to model

convective heat transfer (some using a pressure based method) between each room.

Thermal comfort within each room is not predicted, as well as indoor air quality (air

changes) is not considered with the ES model. To implement a method which includes

intra-room air movement, a CFD approach, which includes momentum effects, must be

used. Furthermore, the nodal approach because of its empirical inclusions cannot be

adapted to new topologies that have not been previously experimentally measured..

Beginning with Negrao (1998), several papers outline methods for coupling ES with CFD

(Bartak et. al, 2002, Zhai et. al, 2002, and Zhai and Chen, 2003). Because wall

temperatures only need to be updated on a hourly scale, whereas air movement and

temperatures require updating on a micro-second time scale, the advantage of combining

the two methods allow for each method to perform the calculations which are most

appropriate to the method. For example, CFD performs poorly (because of round off

errors) in modes where changes occur slowly over time, such as thermal transfer through

walls, and is more suited for rapidly changing turbulent air flow as is found in buildings.

In such models, CFD algorithms use the surface temperatures calculated by the ES data,

and ES algorithms use the CFD data to calculate the convective heat transfer coefficients

and air transfer between each room. This combinational approach offers great potential

to thermally model a given three-dimensional volume. CFD applications are also

required to study innovative technologies such as passive downdraught cooling

(Bowman, 1996), solar chimneys (Gan, 1998) which can be integrated into the building

envelope to decrease heating and cooling requirements.

A review of the available research reveals only a few studies of shape and its influences

thermal and ventilation characteristics of the volume inside. A paper by Kindagen et. al

(1996) studied the effect of roof shapes on airflow in buildings. Using CFD, the authors

discovered that the exterior shape had significant effect on the ventilation inside, yet the

paper only researched a few simple shapes and concludes by recommending further

research with more varied parameters. Another paper by Landon and Campo (1999)

looked at the process of optimizing shape to improve natural convection. Although the

authors only looked at laminar 2D flow for a small object, the research gives an idea of

the challenges that will be faced to combine structural and thermal optimization

simultaneously.

Conclusion

As nature demonstrates, a structure which is optimal both structurally and thermally will

be curvilinear in form. The idea of creating an architectural volume based on structural

and thermal optimization is within grasp of reality using computers, yet it is clear that a

great deal of research of the specific components of the system still needs to be

developed prior to the deployment of full-scale, three dimensional integrative approach.

The material and energy requirements could offer advantages for our resourceful

consumptive methods currently employed. The aesthetics of such optimal structures will

likely have a beauty of their own, yet retaining the flexibility of modifications based on

external parameters, including the desired aesthetic, will be paramount to the acceptance

of an integrated solutions approach.

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