Principle lines of stress created by loading a vault with internal beams and columns
Figures 99-101. Theodor Teichen, Market Hall
Placement of reinforcing along lines of tensile stress. Plan, Detail section of reinforcing.
This thesis is a reconsideration of concepts of openness, integration, and multiplicity within architecture. Recognizing that contemporary algorithmic and morphogenetic architectural projects which seek to critique modernist modularity fail to offer a compelling alternative vision of integration which does not rely on reduction and homogenization to foster coherence, this project seeks to integrate elements which fundamentally differ in kind, exploring such phenomena as the catastrophe and phase shift as mechanisms which bridge between singularities which produce fundamentally different qualities, behaviors, patterns and protocols. The project seeks an alternative both to building systems based on standardized building components and those based on a single building component which is varied to produce a rhetorical parametricism (unable to productively respond to multiple independent environmental variables, and thus ultimately nothing more than an aesthetic of self-similarity). The closed self-consistent organism based either on compulsive repetition of standardized modules, or on a formally driven production of self-similar components is to be countered through the insertion of foreign codes (patterns, logics, protocols which regulate parts-to-whole relations) into an architectural body, building new potentials, competencies, and affiliations with systems outside of its interior.
Flow of principle lines of stress on a surface around two holes, tensile loading.
Interrogating the Singularity of the Monocoque
A new interest in material elegance, achieved via the resolution of multiple performative requirements within a single coherent formal system, as well as an interest in appropriating versioning(108) techniques and technologies used in the automotive industry has made the monocoque an increasing popular focus of architectural research. The monocoque integrates surface and structure, ergonomics and aerodynamics. A closer study of the automotive monocoque, however-- to its joints, material transitions, and pragmatic hybridizations, reveals that the constructed monocoque is never simply a realization of monocoque as pure concept: a singular continuous totalizing system. In practice, the monocoque is composed of various materials with different performative capabilities, each with their own logic of assembly and local densities (fiberglass strands within resin for instance), is often, for ease of production, designed as multiple assembled parts, and often feature non-surface based structural elements which make the monocoque more a hybrid than pure type. Conceptually an absolute or limit condition, a closed body, a singular totality and yet in practice a malleable type-- the monocoque may be used as a vehicle to explore the limits of openness and diversity within a coherent architectural body. By forcing the monocoque to incorporate multiple material and connective logics based on local conditions and requirements, one may test the limits of its coherence and determine the moments when the monocoque dissolves, divides, or multiplies into something beyond itself.
Figure 59. KVA monocoque frame hybrid chassis
Figure 60. The Jaguar XK monocoque
Red: cast aluminum
Blue: extruded aluminum
White: stamped aluminum
Sections joined by welding and blind rivets
To the left is a geometric tesselation which attempts to maximize difference within a continuous field: difference of size and placement of apertures, density, and base geometry. Geometry is a closed system, depending upon its own internal logics for consistency and rigor. To the right are five figures generated by structural analysis and optimization software. A rectangular angle bracket with three holes develops different stresses in each case according to the different applied loads and restraints. The shape of the angle bracket is optimized in each case to minimize stresses, given maximum mass. Unlike geometrical patterns, structural figures and patterns are open bodies, contingent upon external conditions and forces.
Figure 61-76, C. Mattheck.
Column 1 (left): Design space, loads and restraints.
Column 2 (middle): von Mises stress
Column 3 (right) Design proposal
Row 1 (top): Tensile loading
Row 2: Twisting
Row 3: Shear loading
Row 4: Transverse loading
Row 5: Transverse loading, moment connections
Topological optimization algorithms input various environmental contingencies (support/restraint conditions, forces, specific material properties, clearance zones within the design domain which must be free of material, maximum deflection and typically the maximum allowable mass of the part/body to be designed). Goals are typically to minimize stress, or maximize stiffness. These algorithms, therefore allow an interaction between external logics (nature of restraints, position and size of loads, etc) and internal logics (material behaviors due to elasticity, plasticity, isotropic or non-isotropic composition, etc.)
Figure 81,82. Arata Isozaki, Automobile Museum
Above: Increasingly refined iterations (stresses progressively decreased) created through a topological optimization algorithm.
Below: Sections, elevation
Arata Isozaki’s Automobile Museum is one of the few architectural projects which utilizes topology optimization. Its topologically optimized roof and supports are developed as a monolithic body subject to generalized forces. (See Mike Xie’s very similar bridge structures below, which utilize the same ESO algorithm and are based upon a simple design scenario: 4 supports and an equally distributed load.) A structure which is subject to varied local loading conditions, rather than a generic distributed load, would be more highly differentiated. In addition, a field of linked components, rather than a monolithic structure, would create a finer grain of resolution, more clearly registering the effects of local stress gradients. This thesis will explore the creation of pattern, which, like the above geometric tesselation, is a highly differentiated, yet continuous field of modules, and a fusion of different regimes with different rules and behaviors, but unlike the geometric pattern, informed by material and environmental conditions.
Figures 90-95, M.P. Bendsøe.
Objective: Find optimal arrangement of tiles to minimize the weight of the structure while retaining sufficient structural stiffness.
Given: Four tiles of varying material density.
Top left to bottom right:
1. Four tiles available to build structure
2. Design space, loads and restraints
3. Topology optimization result
4. Magnification of result
Bendsøe, Diaz, and Chellappa have worked on the problem of introducing multi-scale modularity into a topological optimization algorithm.(109) They introduce a finite number of modules which vary in density/mass into an optimization algorithm. Predetermining the arrangement of mass within the module and limiting the number of different variables creates a compromise between optimization and standardization. It creates a microscale weave which anticipates fabrication to a greater extent than monolithic optimization solutions, breaking it into assemblable components, but does not allow optimization to inform/deform this microstructure. This thesis will seek to design an architecture that achieves optimization at both the scale of the global and at the scale of the component/microweave.
Figures 86-89, M.P. Bendsøe.
Objective: To find optimal arrangement of perforated modules to minimize the weight of the structure while retaining sufficient structural stiffness.
Given: A finite collection of modules with varying perforation radii
Top light to bottom right:
1. Design space, loads and restraints
2. Conventional topology optimization result.
3, 4. Results using perforated modules, varying allowable radii range.
Seeding a field with multiple logics
This thesis will develop multiple unique localities which will together constitute an environment for the development of structure. These may include ground conditions allowing edge support and those requiring point supports, a locality required to channel water for drainage purposes, localities in which a structural interruption/discontinuity is required, a locality characterized by the necessity for cantilevering structure, a locality requiring minimal shell curvature, and thus evolving a structure which carries loads primarily in bending, a locality in which structure is required to bifurcate to partition space, a locality in which a space which is shaded, yet open to the air is desirable, necessitating the use of tension structures, localities subject to high levels of torque and areas subject to large shear stress. Unique components and connective protocols will be developed for each locality. Research will also be directed towards the margins between and overlap of localities and the special conditions created in these areas.
Figures 51-54, C. Mattheck.
Right to left: Growth a of tree around a railing
Finite element mesh, loads and restraints
Initial von Mises stress plot
Optimized design with stress plot
Figures 47-50, C. Mattheck.
Left to right: Growth a of tree constricted by a rope.
Initial von Mises stress plot
Optimized design with von Mises stress plot
Exploration of mechanisms of phase shift/catastrophe
Taking example from the grid shell/diatom research of Frei Otto detailed above, this thesis will explore the convergence of conditions which precipitates phase shifts and catastrophes. The transition between localities, each governed by different singularity, will likely be the location of a phase shifting between patterns. These phase shifts may be seamless; however they may also contain unique morphologies which are not simply a blend between patterns (what Otto terms “net defects.”)
Konrad Wachsmann, Aircraft hanger
This thesis will develop several interdependent, behaviorally distinct material systems in order to create a structure which is highly responsive to local edge conditions, lines of stress, and local methods of load transmission (i.e. via membrane stresses). Material systems will at a minimum include a system of components developed to carry tensile forces (steel or fiber-based components), a system which carries compressive forces and glazing components.
Figure 102. BX-58 Grid, 3-way Tetrahedron
Integrated tensile and compressive systems
Reinforcement meshes are typically placed along principle lines of stress. A net system of tension components must be capable of local densification, shifts in weave direction, and local unstitching and reorientation to accommodate apertures. Principle lines of compression run at right angles to principle lines of tension. Weaving together tension and compression meshes requires a contingent connective system at right angle intersections.
Figure 97,98. George Wimberly, Howard Cook Windward City Shopping Center, Elevation, roof plan, reinforcing plan
Above: Tension and compression component couple, with principle directionality perpendicular to one another
Middle: Partial mesh oriented to principle lines of tensile stress (middle). Partial mesh oriented to principle lines of compressive stress (right).
Below: Principle lines of stress on a vault. Component based meshes following lines of principle tension (right) and compression (middle).
108 see Architectural Design: Versioning, vol.72, n.5, (2002 ), particularly Ingeborg Rocker, Versioning: evolving architectures, dissolving identities - ‘nothing is as persistent as change’, p.-17 for a discussion of versioning.
109 M.P. Bendsøe, Department of Mathematics, Technical University of Denmark and A. R. Diaz S. Chellappa, Department of Mechanical Engineering, Michigan State University, Design Optimization in a Multiscale Setting.
Figures 77-80. Top left to bottom right:
1, 2. E. Saarinnen, MIT Kresge auditorium
3. E. Lamm, structurally optimized shell
4. Deformation plotted against self-weight, original and optimized design
Saarinnen’s Kresge auditorium is a dome that is trimmed such that it rests on point supports rather than continuous edges. As Martin
Bechthold explains in Innovative surface structures: technologies and applications, this trimming created engineering difficulties that required undesirable design compromises. Removing segments of the dome created interruptions in the path of hoop forces, inducing bending moments that necessitated large edge beams. In plane shearing stresses developed at the junction between these edge beams and shell edges. These issues lead Saarinnen to add vertical supports in the glazed facades. E. Ramm later digitally modeled and analyzed the auditorium’s shell, optimizing its shape through FEA (finite element analysis) such that neither edge beams nor the added vertical support would be necessary. In this case, departing from primitive geometry by adding local curvature, it may be argued, rationalizes the structure.
Bechthold, Martin. Innovative surface structures: technologies and applications. New York Taylor & Francis, 2008.Figures 83-85, E. Ramm.
Topology optimization of point loaded dome
Objective: Maximum stiffness
Constraint: Given mass
Top left to bottom right:
1. Loads and restraints
2-4. Optimized structure, reducing mass at each step
Figures 55-58, M. Xie.
Initial design domain with loads and restraints
Revised design domain (gap inserted in domain)
Revised optimized structure