Exploiting the concept of “adaptive growth” found in nature may suggest new methodologies for creating fiber composite structures.
By Christina Doumpioti
A main goal of my research is to propose a biologically inspired computational approach to form generation and design methodologies that are not teleological and linear but parallel and with multiple interdependent hierarchies.
The idea stems from biological entities and the way they develop under load and distribute and organize material by responding to internal factors and environmental conditions. This mechanism allows every load bearing natural construction to “adhere to a uniform stress distribution” and to achieve an optimal design “of high reliability and minimum consumption of material and energy” that will enable them to survive the tough competition of natural selection.1 Therefore, the process of adaptive growth leads to a seamless and gradient differentiation of material distribution, porosity, degrees of transparency and varying mechanical properties generated by the same forces.
Context: Natural and artificial systems
I have thoroughly studied the shape and fiber articulation of shells in natural composites (Figure 4). Fibers form the basic elements of shells, thus affecting their overall performance and shape. The underlying structure of natural systems uses material sparingly in response to a variety of environmental forces, a paradigm to human architecture. To understand and exploit their morphological complexity, we must turn to the field of biomimetics. Even though biomimetics “mimics” biology, the basic concepts that can be extracted from this field are the underlying ideas and principles.
Natural composites are successful not so much because of what they are made of but because of the way in which they are assembled. Nearly all loads of biological structures are carried by fibrous composites. Fibers are extremely good at withstanding tension, but perform poorly in compression. Nature solves this problem with matrices such as cellulose and lignin that glue fibers together and prevent them from buckling.
The same constituents — matrix and fibers — have an identical structure but depending on the conditions in which they grow, as well as their position and performance within the system, they tend to change their shape, topology and organization. The major mechanism involved in this optimization process is called adaptive growth. This intelligent survival strategy enables biological structures, such as trees and bones, to flexibly adapt their original optimum designs to changes in the loading conditions.2
The construction equivalent that gets closest to the biological paradigm is the tow-steering design technique mainly utilized in aerospace engineering and in sailing technology, or 3dl technology. With this technique, each laminate is made by combining layers with various fiber orientations, material properties or thickness. Fibers can be laid up curvilinearly, extending the “tailorability” of the design so they can respond favorably to favorable loading conditions and programmatic requirements.3 By allowing the stiffness to vary from one point to another, this manufacturing technique becomes a step forward of the classical “stacking sequence” method because it avoids the redundancy in spatial organization and opens the possibility for a gradient material distribution where it is needed, leading to an energy- and resource-saving construction analogous to that found in biological systems.
The fiber articulation enabled by the tow-steered method seems an appealing technique to use in an architectural context where programmatic and diverse environmental factors can contribute to the generation of a structure.
I have developed a computational method inspired by “biological self-optimization” — a term cited by the biologist Claus Mattheck for adaptive growth4 — from which the topology of the main surface is first evolved [shape generation] and thereafter the fiber reference-paths [fiber generation]. Both strategies are interlinked following an ontogenetic process of morphogenesis while simultaneously are informed by environmental and structural factors that generate porosity [porosity generation].
Ontogenesis refers to the evolution of individual organisms instead of entire populations and species; this is the way hierarchies of components that make up the individual interact and organize by adaptive response to their environment. Plants and bones are distinctive examples of ontogenetic adaptation, in which stress works as a growth promoting agent; they adapt and respond to variable conditions by material deposition and by changing their form and structure.
My design bridges two existing buildings with a long-span monocoque shell to form a passage and an exhibition space. Typical objectives for a structure like this aim to improve its structural behavior, its strain energy, stress leveling and weight reduction while satisfying directional strength and stiffness. Additionally, its programmatic requirements, movement flow and microclimatic environmental conditions are key to the generation process.
During the shape-generation process, points act as morphogen cells that self-organize and acquire their position and role within the system triggered by stress. During the fiber-generation process, new nodes extracted from the structure act as fibroblast cells that, triggered by stress concentrations, start to release fibers in the direction of the principal stresses.
The environmental setting is simulated and the design domain is defined: the system is composed of a random distribution of points along a cylindrical shape with a diameter of 5m and a span of 10m. A Delaunay algorithm is applied for the tessellation of the structure that connects the neighboring points while maintaining the area free of intersections. Each of these nodes is classified with different loading conditions (load vectors or supports) according to its position within the system.
The resulting structure is evaluated through finite element analysis that, for a given set of materials, density and elasticity, produces a value for the objective function, in this case, stress and strain leveling. The nodes that indicate the lowest values of stress and displacement act as attractors for their neighboring nodes and the system is self-organized in search of equilibrium. (The rate of attraction is analogous to the rate of proximity.) The algorithm reiterates according to values obtained each time by stress analysis until a constant stress state on the surface is achieved, according to the axiom of uniform stress.
This obtained geometry is further analyzed through finite element analysis to get information on the occurring type of stresses, their magnitude and directions. The nodes that indicate the highest stress concentrations along the structure are extracted to act as homeostatic agents, restructuring their environment to regulate tension by releasing fibers along the direction of the quantitatively largest principal stresses (Figure 3).
This optimum arrangement minimizes shear and transverse stresses between the fibers while increasing the maximum load capacity.5 The pattern that emerges out of the arrangement of the fiber courses, in anticipation of the loading conditions, is the force-record of the structure (Figure 2).
Another mechanism is responsible for the generation of porosity as an additional property of the system. Both structural and environmental analyses are conducted to modulate the internal environmental conditions of the structure by reducing its stiffness. This process informs both the global shape and fiber articulation by creating apertures in the shell to allow in light and air. By carefully identifying areas of weakness the important parts of the structure are protected.
Specifying the optimal position of apertures derives from experiments and analyses. Material distribution analysis shows the areas with the least stress concentration, where material can be reduced. Fiber volume fraction analysis shows areas with the least fiber density that would facilitate the creation of voids. Solar exposure analysis displays the distribution and availability of incident solar radiation on the model and prevailing winds analysis defines the best possible position and shape of the openings to accommodate ventilation by avoiding strong currents and water penetration.
Manufacturing and fabrication
The design process is intricately linked with the manufacturing method of steered-fiber lay-up. The splines generated represent the reference paths, which are the curve traversed by the center of the applicator head of the tow-placement machine during the fabrication of a single course. Moreover, fiber paths alter locally in such a way that they do not disrupt the continuity of stress in the fibers when they approach the voids and do not terminate abruptly at the edge of the holes, but follow contours around them.
The whole structure is to be prefabricated, transported to the site and craned into place. First the mold is milled into pieces that can be easily interconnected and dismantled to extract the shell. The shell is a one-piece component constructed by superimposed fiber courses laid up by the tow-steering application head and high-strength adhesives and tape-laying machines are used to attach the shell to the existing buildings that support it. This type of monocoque construction is extremely lightweight, easily transported and low maintenance.
The above research sets a new combination of techniques, concepts and methodologies to come up with a coherent system whose form, materialization and manufacturing logics are integrated and interrelated. A great deal of redundancy and differentiation emerges out of the intricate contextual relationships of repeated components, leading to a structure that is not limited to its load-bearing capacity but to a range of performance criteria. Function and structure are intrinsic to the generation process of the system in search of stress equilibrium; it is an “embodied physiology.”6
This work is to be extended and be applied to varying architectural problems. The main design strategies — shape generation, fiber-path articulation and porosity generation — can be regarded as three separate design processes that are not limited to the domain of fiber composite structures. Each one can be implemented into different design problems, informing different aspects of a project by defining either the overall shape of a shell according to the axiom of uniform stress, tessellating a surface along the force-flow (principal normal stresses), or tuning the microclimatic conditions and generating porosity into a given system without disrupting its structural efficiency.
A long-term goal of the project is the further development of the algorithmic process (already established) with the self-organization of the points. It is a major challenge to set up a computational system that will incorporate various factors to create new design paths through their interrelations. The creation of an open system would allow for a better interaction between the variant inputs of the process and promote the continuous development of the design methodology by introducing new features.
Christina Doumpioti, a recent graduate of the Architectural Association, London, is an architect at Arup Associates, London, where she is responsible for developing parametric, generative and performance-based design solutions.
Editor’s note: This paper was originally presented to the ACADIA conference held 13–19, October, 2008, at the University of Minnesota.
This article is adapted from Ms. Doumpioti’s MArch dissertation for the Architectural Association School of Architecture, London, —EmTech postgraduate course, under the supervision of Michael Weinstock, Michael Hensel and Achim Menges.
Mattheck, C. (2005). Biomechanics and Structural Optimization, Karlsruhe: Forschungszentrum Karlsruhe Institute for Material Research.
www.fzk.de/fzk/idcplg?IdcService=FZK&node=0849&lang=en (accessed July 17, 2008).
Waldhart, C. (1996). Analysis of Tow-Placed, Variable-Stiffness Laminates. Master Thesis, Virginia Polytechnic Institute and State University. Virginia, 1996.
http://scholar.lib.vt.edu/theses/public/etd-520112859651791/etd.pdf (accessed March 5, 2008).
Mattheck, C. (1998). Design in Nature – Learning from Trees. Berlin and Heidelberg: Springer Verlag.
Mattheck, C. (2005), Op. cit.
Turner, S. (2007). The Tinkerer’s Accomplice. Cambridge, Mass.: Harvard University Press.