Interactive Design of Shell Structures Using Multi Agent...

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Interactive Design of Shell Structures Using Multi Agent Systems

Design Exploration of Reciprocal Frames Based on Environmental and Structural Performance

David Jason Gerber, Evangelos Pantazis, Alan Wang

University of Southern California {dgerber, epanatazi, alanwang}@usc.edu

Abstract. This paper presents a continuation of research on the prototyping of multi-agent systems for architectural design with a focus on generative design as a means to improve design exploration in the context of multiple objectives and complexity. The interactive design framework focuses on coupling force, environmental constraints and fabrication parameters as design drivers for the form finding of shell structures. The objective of the research is to enable designers to intuitively generate free form shells structures that are conditioned by multiple objectives for architectural exploration in early stages of design. The generated geometries are explored through reciprocal frames, and are evaluated in an automated fashion both on local and global levels in terms of their structural and environmental performance and constructability. The analytical results along with fabrication constraints are fed back into the generative design process in order to more rapidly and expansively design explore across complexly coupled objectives. The paper describes the framework and presents the application of this methodology for the design of fabrication aware shell structures in which environmental and structural trade offs drive the final set of design options.

Keywords: Generative Design, Parametric Design, Multi-Agent Systems, Digital Fabrication, Form Finding, Reciprocal Frames

1 Introduction

Modernisms’ influence in the 20th century pioneered and made pervasive mass-standardization to accommodate the need for rapid and inexpensive erection of buildings and in doing so shifted the attention away from non-uniform nonstandard structures and forms. While shell structures have been used for centuries in architecture and engineering given their capacity to efficiently cover large spans, however the design, modeling and analysis of shells has remained a challenging topic given their complex geometries [1]. The design exploration of these structures are not conceived of in a linear process, requiring extensive iteration as well as close collaboration

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between architects and engineers [2], further making the process less interactive and suited for rapid iterative design exploration. Additionally, the development of new knowledge regarding these types of structures has historically been dependent on extensive physical testing; the establishment of sophisticated building techniques which consequently increased the cost for their realization [3] [4] [5].

However, with the rapid development of computer aided design and modeling tools we have seen a rise in the development of non-standard building forms, including free form shell structures [6]. In parallel a reinvigorated interest in revisiting traditional building techniques through digital craftsmanship and digital technologies is notable [7] [8]. Recently, in concert with a myriad of digital tools that facilitate the handling of complex geometric constraints, a number of computational methods have been appearing, where structural concepts and material constraints are integrated as design drivers for the form finding of complex geometries [9]. Moreover the widespread application of digital fabrication techniques and robotic construction, has made the realization of complex shell structures economically and technically feasible and has broadened our capabilities to include design of material and construction processes [10].

The paper presents an evolution of our research on a Multi Agent Systems (MAS) framework which aims to solve the challenge of bringing into the form finding process a set of complexly coupled and often divergent design objectives, here environmental parameters and materialization constraints. While this may imply less perfected shells in the case of structural objectives, such as minimization of material and load distribution, the work sees integration of multiple analyses as critical for the generation of non-standard architectural forms which necessarily include multiple objectives.

Despite the fact that the increased availability of new tools has enabled designers to design complex and free form geometries, in most cases little feedback relating to the structural or environmental performance of the geometry is provided to the designers interactively in the early design stage [11]. Moreover there is a lack of integrated methods and design systems which combine form finding with manufacturing parameters and environmental aspects like shading and lighting [12]. The use of disparate software for different analyses, fragment the design process among different disciplines and most frequently generated geometries are further rationalized multiple times for environmental, structural and/or construction processes separately and independently [13]. As a result of this lack of integration, the design cycle latency increases creating inefficiencies from concept design to design development and finally construction. Our work focuses on the implementation of a MAS approach, where the formulation of design behaviors for the form finding of shell structures is based on the decomposition of a given problem into different design agencies (i.e. structural agency), and is further based on their coupling with multiple analytical processes early in the conceptual design phase. The objective is to enable designers to design explore much more rapidly and extensively and to form find based on the combination of structural, environmental and material parameters though a bottom up design approach. Through the evaluation of both local and global behavior of the reciprocal frame shell system the designers can define rules which condition the form and result into geometric data representations which can be developed through design automation and non

deterministic methods and finally more easily communicated across different expert disciplines.

The paper is structured through a survey of literature for existing form finding methods as well as for identifying the key design parameters and constraints associated with the realization of shell structures using reciprocal frames. It then identifies the gaps, from which we describe how the relationships of form, force and environmental parameters are utilize and validated in simulations via a MAS approach for the generation and evaluation of non-standard geometries with complexly coupled structural, environmental, and fabrications objectives. Finally, a conclusion and discussion is provided regarding the MAS methodology for the design of shell structures through analysis of both global and local geometries and the intended next steps.

2 Background and Precedents

Shell and space frame structures have played a significant role in architectural design given their spatial and geometrical qualities and can be loosely classified into: a) lattice space structures (discrete elements); b) continuous (slabs, shells, membranes); and c) biform space structures (combination of discrete and continuous parts) [14] [15]. Space structures can provide large unified spaces while still being highly efficient in material usage. This is mainly achieved through their complex geometric description, which has proved to be one of the main challenges in their design, modeling and analysis. In order to address the challenges, practitioners and researchers have developed analog and digital apparatuses to empirically form find space structures over the years. Through the systematic study of scaled physical models most notably researchers such as A. Gaudi, H. Isler and F. Otto, have managed to design, analyze and construct fairly complex shell structures [16] [17]. Additionally, F. Candela pushed the boundaries of structural shell design by seeking 1:1 solutions, which by virtue of geometry could limit the amount of necessary calculation for their erection [18] [19].

With the use of digital tools and computation the potential to integrate multiple types of design information as well as fabrication and material constraints into an interactive design and multi objective optimization workflow has now become more productive and interactive [20] [21]. Given the increasing availability of computation, the use of simulation for structural behavior early in the design phase, is considered a viable methodology for architects and engineers to manage engineering constraints in much more interactive, design exploratory, and intuitive fashion [22]. Emanating from the work of these precedents a number of design computing and simulation tools have been developed for aiding designers to understand the relationships between form and force to further the design of free form shell structures. Kilian, using particle spring systems, established an interactive virtual hanging string modelling environment while other researchers have used dynamic relaxation methods which allow for real time exploration of funicular shells [23] [24] [25]. Block, introduced the Thrust Network Analysis (TNA) method, which extends a graphics statics approach for the form finding and calculation of compression only vaults [11]. Of important note, these innovators


between architects and engineers [2], further making the process less interactive and suited for rapid iterative design exploration. Additionally, the development of new knowledge regarding these types of structures has historically been dependent on extensive physical testing; the establishment of sophisticated building techniques which consequently increased the cost for their realization [3] [4] [5].

However, with the rapid development of computer aided design and modeling tools we have seen a rise in the development of non-standard building forms, including free form shell structures [6]. In parallel a reinvigorated interest in revisiting traditional building techniques through digital craftsmanship and digital technologies is notable [7] [8]. Recently, in concert with a myriad of digital tools that facilitate the handling of complex geometric constraints, a number of computational methods have been appearing, where structural concepts and material constraints are integrated as design drivers for the form finding of complex geometries [9]. Moreover the widespread application of digital fabrication techniques and robotic construction, has made the realization of complex shell structures economically and technically feasible and has broadened our capabilities to include design of material and construction processes [10].

The paper presents an evolution of our research on a Multi Agent Systems (MAS) framework which aims to solve the challenge of bringing into the form finding process a set of complexly coupled and often divergent design objectives, here environmental parameters and materialization constraints. While this may imply less perfected shells in the case of structural objectives, such as minimization of material and load distribution, the work sees integration of multiple analyses as critical for the generation of non-standard architectural forms which necessarily include multiple objectives.

Despite the fact that the increased availability of new tools has enabled designers to design complex and free form geometries, in most cases little feedback relating to the structural or environmental performance of the geometry is provided to the designers interactively in the early design stage [11]. Moreover there is a lack of integrated methods and design systems which combine form finding with manufacturing parameters and environmental aspects like shading and lighting [12]. The use of disparate software for different analyses, fragment the design process among different disciplines and most frequently generated geometries are further rationalized multiple times for environmental, structural and/or construction processes separately and independently [13]. As a result of this lack of integration, the design cycle latency increases creating inefficiencies from concept design to design development and finally construction. Our work focuses on the implementation of a MAS approach, where the formulation of design behaviors for the form finding of shell structures is based on the decomposition of a given problem into different design agencies (i.e. structural agency), and is further based on their coupling with multiple analytical processes early in the conceptual design phase. The objective is to enable designers to design explore much more rapidly and extensively and to form find based on the combination of structural, environmental and material parameters though a bottom up design approach. Through the evaluation of both local and global behavior of the reciprocal frame shell system the designers can define rules which condition the form and result into geometric data representations which can be developed through design automation and non

deterministic methods and finally more easily communicated across different expert disciplines.

The paper is structured through a survey of literature for existing form finding methods as well as for identifying the key design parameters and constraints associated with the realization of shell structures using reciprocal frames. It then identifies the gaps, from which we describe how the relationships of form, force and environmental parameters are utilize and validated in simulations via a MAS approach for the generation and evaluation of non-standard geometries with complexly coupled structural, environmental, and fabrications objectives. Finally, a conclusion and discussion is provided regarding the MAS methodology for the design of shell structures through analysis of both global and local geometries and the intended next steps.

2 Background and Precedents

Shell and space frame structures have played a significant role in architectural design given their spatial and geometrical qualities and can be loosely classified into: a) lattice space structures (discrete elements); b) continuous (slabs, shells, membranes); and c) biform space structures (combination of discrete and continuous parts) [14] [15]. Space structures can provide large unified spaces while still being highly efficient in material usage. This is mainly achieved through their complex geometric description, which has proved to be one of the main challenges in their design, modeling and analysis. In order to address the challenges, practitioners and researchers have developed analog and digital apparatuses to empirically form find space structures over the years. Through the systematic study of scaled physical models most notably researchers such as A. Gaudi, H. Isler and F. Otto, have managed to design, analyze and construct fairly complex shell structures [16] [17]. Additionally, F. Candela pushed the boundaries of structural shell design by seeking 1:1 solutions, which by virtue of geometry could limit the amount of necessary calculation for their erection [18] [19].

With the use of digital tools and computation the potential to integrate multiple types of design information as well as fabrication and material constraints into an interactive design and multi objective optimization workflow has now become more productive and interactive [20] [21]. Given the increasing availability of computation, the use of simulation for structural behavior early in the design phase, is considered a viable methodology for architects and engineers to manage engineering constraints in much more interactive, design exploratory, and intuitive fashion [22]. Emanating from the work of these precedents a number of design computing and simulation tools have been developed for aiding designers to understand the relationships between form and force to further the design of free form shell structures. Kilian, using particle spring systems, established an interactive virtual hanging string modelling environment while other researchers have used dynamic relaxation methods which allow for real time exploration of funicular shells [23] [24] [25]. Block, introduced the Thrust Network Analysis (TNA) method, which extends a graphics statics approach for the form finding and calculation of compression only vaults [11]. Of important note, these innovators


use computational methods and simulations instead of the previous luminaries’ reliance on physical models. In doing so they have laid the ground work for others to shift our research efforts towards computational affordances such as more accuracy, more rapid iteration, and scalability of material testing. It has also enabled a greater ability to integrate often asynchronous and conflicting design domains and objectives.

Reciprocal frames, also called nexorades, are defined as a structural system of mutually supporting interwoven elements (nexors) [26]. In nature we encounter the principle of reciprocity in structures such as birds’ nests where simple discrete elements are interwoven to form complex geometries but also in micro scale organisms such as cocolithoropes, where calcareous plates, cocoliths are interlocked in a spherical fashion around a central cell. In architecture, reciprocal frames have a long tradition and appear in China and Japan around the 12th century, while in Europe V. Honnecourt introduced the system in the 13th century [5] [27]. Leonardo Da Vinci studied reciprocal frames systematically for different applications including for bridges, ceilings, and roofs; and subsequently a number of architects and practitioners investigated alternatives of the system. S. Serlio and J. Wallis looked into the adaptation of the system for the construction of flat roofs, while others developed and patented a similar system for the construction of timber roofs [14]. The reciprocal frame system requires a minimum of 3 structural elements and is based on the principle that one element supports and gets support from the rest of the elements on the structure. The overall form of a reciprocal frame structure is dictated by the way the elements are interwoven with one another. Recently, reciprocal frames have received the attention of architects and engineers because of the potential that computational methods offer to design, analyze and optimize such structures [27]. The adaptation of reciprocal frames to form shell structures, is made interactive through the use of computational design aids enabling the simulation of the geometrical configuration of the frames. The description of the final geometry is now possible with the use of non-regular frames, characterized by different unit cell shapes and dimensions, or with non-regular topology, and or with variation in the dimensions of bars and position of joints [28] [5]. The generation of reciprocal frames using genetic algorithms and dynamic relaxation methods have been researched as well as methods based on shape grammar rules and tiling theory [29] [30] [31].

While there has been a resurgence of interest and research on reciprocal frames they have not been thoroughly studied, here conjectured to be mainly due to their complexity in terms of number of elements, and therefore number of complex calculations. Although single objective or simple configurations have been studied and successfully realized (with different numbers of elements and materials) complex reciprocal configurations with parametrically varied reciprocal units that respond to more than structural constraints still remain largely unexplored. In most of the previous work the connection between the nexors is considered fully regular or rigid and little work has been focused on the geometry and behavior of the joint or in our case the joints (given purposeful non planarity and overall formal irregularity). While the research on the generation and systemic behavior of regular and planar reciprocal frames on 3D surfaces has progressed this is also where the literature presents a clear gap [32] [5] [14] [31]. Additionally, in surveying the literature of form finding few examples exist

inclusive of integrated workflows which combine structural form finding with environmental parameters such as lighting and shading with fabrication constraints [12]. Despite the maturity of digital design and the field of design computation, there remain but a few examples in the field where combining numerical analysis with a generative design system is explored [33]. The integration of the reciprocal frame into a multi-objective design exploration workflow where irregularity is specifically addressed through a MAS and generative computing is unique.

Fig. 1. Workflow diagram illustrating a Multi Agent System approach including the tools implemented from initial design conditions, to form generation, analysis and materialization.

3 Research Objectives and Hypothesis

Our research objectives include the ability to facilitate the design and construction of geometrically intricate yet efficient, comfortable, and fabricatable shell structures inclusive of combining environmental and structural analysis in the form finding process by coupling them with a modular yet parametrically variable structural system based on the principle of reciprocity. The research hypothesizes that our generative design system can improve the design exploration, generation, and optimization of such structures by providing designers with interactive tools that incorporate structural and environmental feedback with that of constructability. It is further hypothesized that through the use of a MAS for design methodology novel design outcomes will become achievable in terms of previously unattainable levels of geometric and multi objective complexities through the characteristics of the automation and application of a multi agent systems approach. The objective of this stage of the work is to further evaluate the generative design methodology which combines form finding techniques with conceptual environmental and structural analysis tools via a MAS. A goal is to be able to provide practical solutions for the design and construction of free form geometry

CONTEXT GENERATION

Form Finding

Environmental+

ANALYSISIMPROVED

DESIGN OUTCOME

PROGRAM

Input (parameters) Geometry

Feedback

Data

Max HeightFootprint

SITE (BOUNDARY)

STRUCTURAL

ENVIRONMENTAL

DESIGN PARAMETERSReciprocal Frames

ValencyProfileLengthJoint

STRUCTURALSYSTEM

PANELLING Skin

Panel Design

Orientation Support Conditions

ModularityMaterial Efficiency

Global Geometry(shell Structure)

Local Geometry


using reciprocal frames (nexorades), by exploring suitable configurations for their construction. This design exploration and optimization is performed through local and global generation, simulation and analysis of 1) the shape, cross section and joint conditions of the elements (nexors), and 2) structural analysis and environmental analysis of the reciprocal fames. The purpose of the work is to enable designers to generate shell structures that are pareto optimized across multiple objectives rather than purely driven by structural parameters. This is a critical distinction in that the work trades off pure structural efficiency in favor of and to include other efficiencies and hence the need for incorporating generative design, MAS based optimization and design automation.

Fig. 2. Diagram illustrating the sequence of the methodology including the feedback of the design, form finding, and analysis steps within the MAS for design.

4 Methodology

In this section the description of the steps in our MAS for design workflow are described in detail (see Fig. 1). The computational design methodology is applied to shell structures and their realization using reciprocal frames. The aim is to develop an approach that shifts away from pure form finding a single objective, towards a more integrative multi objectives design exploration inclusive of environmental parameters and fabrication constraints. This is done in order to influence the geometric exploration of shell configurations where the other pragmatic parameters are given greater weight in the pareto optimization for the architectural design and search of reciprocal frame structures. In order to more efficiently manage divergent objectives for driving the form finding inclusive of environmental parameters a bespoke design and optimization application is developed to generate design alternatives through utilizing open source software and libraries within Processing and IGEO and through the linking of our applet

to commercial software packages through Rhinoceros 3D, Grasshopper, Ladybug, Honeybee, and Karamba [34]. The links and interactive feedback between these different platforms and programs is established by a set of custom interfaces. These interfaces and scripts are written in Python, which provides for establishing communication across the different data representations inclusive of geometric and the analytical properties and drivers. The MAS for design workflow is structured through four main phases (A-D) each with a series of steps (1-10) as can be seen in Fig. 2.

Fig. 3. The diagram illustrates the logic of reciprocity and the parameters of the reciprocal frame element (nexor) and unit (singular nexorade frame). The different eccentricities illustrate a variety of joint conditions and fabrication solutions (ties, pins and 3D printed non-standard couplings).

In phase A steps 1 and 2 a set of global and local design parameters are defined inclusive of footprint area, support conditions, environmental conditions such as location and orientation, and as well as the main parameters of the reciprocal frame topology represented by number (integer), type (discrete nexor geometry option described below) and size (length, width, and depth) of elements. Phase B steps 3 through 5 are the form finding of the shell structure using our MAS modelling and pareto optimizing method. In this phase each point is modelled as an agent which has a weight and tension value when connected to other agents, as well as an environmental sensitivity factor, which defines how much the agent is affected by the environmental objective. The global geometries (nexorades) are design explored generatively and in an automated fashion through different topologies, different support conditions and nexor connectivity options. The form finding process is influenced by solar path positions in order to capture global behavior with respect to an environmental result: how much direct sunlight during the morning hours, or shadow during afternoon hours is provided by the nexorade. In phase C steps 6 through 8 the structural elements are modelled as


geometry agents which interact based on the principle of reciprocity so that each sub system can then be assumed to be statically determinate and in equilibrium. Sequentially structural analysis is performed on all reciprocal frame nexors for their deflection and stress distribution both locally and globally for the nexorade for maximum deflection, and sums of stresses overall. Depending on the global geometry and structural performance of the design alternative a specific configuration at this stage can be selected or rejected by the designer. Fig. 3 illustrates reciprocal element nexor morphology and possible connections between the elements in the nexorade. Internal forces on each planar frame within the freeform polysurface of the global nexorade shell are related through the rules of reciprocity which then are adjusted iteratively by the system to meet these geometric rules and the structural static load capacities. In Phase D steps 9 and 10, an environmental analysis based on solar radiation is performed on each shell’s global surface and below at the ground level. This is done in order to 1) drive the global geometry orientation towards the sun for gathering more light in case the shell is cladded with solar panels, and 2) to change the geometry of the reciprocal frames based on the impact below the surface where the amount of light that penetrates creates too much solar gain. The system cycles through phases B through D repeatedly either for a specified number of iterations or until a geometry is generated and evaluated as performing better both structurally and environmentally in a pareto trade off fashion. At each iteration both the global parameters, such as position of the agents and the local parameters including element size, joint type, and panel type are parametrically varied and a new geometry is generated. Better is defined by the designer who for instance may privilege the configuration to provide maximum shade while using the smallest available element profile for structural stability.

5 Design Experimentations

A series of experimental steps have been performed to date, including testing of the global and local system logics as well as tests to simulate the construction of the shells manually and in anticipation of robotic assembly. The research presents a focus on reciprocal frames, because as a structural system it relies on simple mutually supported structural elements that can be assembled into highly intricate configurations to form large aggregations and spans that have the capacity to create structural shells which can span many times the length of the individual structural elements. Konrad Wachsmann’s research into large span space frames is one exemplar of the capability of the space frame, albeit not a reciprocal frame. The series of tests and experiments move towards proving significant design exploration and generative design and complexity affordances.

Fig. 4. The table illustrates the exploration of increasing nexor count from 3 to 6 elements into the singular nexorade (frame) and their resultant structural analysis in relative terms.

Fig. 5. The table illustrates the structural analysis of singular reciprocal frame units (nexorades) of similar element count (3) for 8 different element (nexor) geometries and joint conditions. The experiment included elements ranging from round to uniform rectilinear to non-uniform flat through to a series of non-standard nexor geometries.

One experiment focused on the design exploration of the topology of the nexorade frame through the change in integer values of nexors (see Fig. 4). Through these experiments the designers could more interactively understand the loading conditions


y adding and subtracting the number of elements. A second step for the experiment on the nexor and singular nexorade was to design explore uniform through to non-uniform nexor designs and their performance. Fig. 5 shows eight nexor designs ranging from simple parametric round and rectangular cross section nexors to that of non-uniform nexors designs. O key question for this stage of the experimentation was whether the system would aid in the finding of nexors design that would be more efficient through non-standard cross sections, twisting and highly intricate geometric designs. Simple resting connections were assumed for these analyses. A third set of experiments was to analyze the performance of nexors in terms of their dimension and engagement lengths or valency with their neighbors (see Fig. 7). The analysis undertaken was to look for more optimal nexors or nexors options within a permissible range and how they accommodate stress, displacement and in which geometric configuration was valency more or less influential in the design decision making.

The next set of experiments moved from the local focus on nexors to that of the form finding of shells and the generation of nexorades influenced by the environmental conditions. Fig. 6 illustrates the structural analysis of a subset of three global configurations which have been form found structurally initially and then re-form found based on the solar radiation influence. From these configurations as illustrated in Fig. 7 the method then adjusts the global configurations to accommodate solar condition preferences set by the designers.

Fig 6. Illustrates 3 shell configurations in plan and perspective with an exaggerated influence and distortion away from the pure form found by virtue of the inclusion of solar path influence. The images below show the structural analysis in terms of stress distribution on their scaled spans.

Through the application of the methodology the designer chooses orientation and support conditions specifies design preference then the system generates the shell structures and discretizes iteratively the surface into panels which are the geometric proxies for the reciprocal frames alternatively explored based on the analytical results of different geometries of the reciprocal element (nexor). The performance of the global geometries are evaluated both structurally (total deflection and stress) as well as environmentally (total radiation on and beneath the structure). The work benchmarks

the single objective of structure against the multi-objective of structure and environmental results. The analysis data is used for the iterative use and optimization of the global geometry then the reciprocal elements.

Fig. 7. The diagram illustrates the global input parameters for the form finding of the shell and then the combination of the environmental analysis and a resultant of three behavioral results.

At the beginning of the process the designer defines the a) support points; b) resolution of the mesh; c) critical solar positions; and d) environmental attraction sensitivity (see Fig. 7). The designer provides an outline of the area either in Rhinoceros or directly in Processing by providing coordinates; then provides input parameter values for material tension between particles and weight, environmental attraction value of each agent and count of iterations an agent/particle based solver can iterate. Once the geometry comes to a state of equilibrium the reciprocal frames are generated and the geometry is exported as NURBS to Rhinoceros 3D. The geometry is analyzed structurally for max displacement and deflection using the Karamba plugin in Grasshopper and


environmentally for total solar radiation using Ladybug and Honeybee plugins. The analytical results are saved into a txt file that is fed back to the Processing applet. Based on the results the reciprocal nexor parameters change one step at a time and the simulation is run again. If the generated geometry does not meet the structural requirements, the global parameters are updated and the process restarts.

Fig. 8. Graphs showing maximum stress in relation to nexor valency, displacement in terms of nexor valency, displacement in relation to nexor lengths and displacement in relation to 8 nexor profile types from circular to irregular.

Another set of experiments has focused on developing the automated fabrication and erection of the reciprocally framed shells. This has been performed in two ways, one being a manual simulation and the second being through simulation of the MAS which generates frames for cementitious deposition. The simulation has included the constraints that industrial robotic arms have in terms of reach, clash and singularity as well as patterns for efficient use of multiple robots working in collaboration. Through these experiments the research has both begun to anticipate the tectonic and fabrication constraints and parameters for future full scale automation.

Fig. 9. An illustration of design exploring the erection sequence study performed manually (top); a set of simulated frames illustrating the cementitious deposition and resultant shading analysis (middle); and a set of 3 global configurations illustrating a variety of agent driven porosities (bottom).


6 Discussion and Future Steps

This paper presents the further development of a “Design Agency” research, specifically a MAS for design methodology that is based upon a multi objective optimization where multiple agencies interact to negotiate towards a more informed design. The research furthermore illustrates the complexity of reciprocal frames and the need for a bespoke design computing method to enable the designer to interact and design explore where the project is cognitively too complex with out the aid of computing in two primary ways: that of the complexity of the trade off in the analysis an that of the constructability of the shell in terms of elements, unique connections and overall non-standard form.

The contribution of the work enriches structural form finding with additional objectives, including environmental impact and those of the tectonic system. Of note is the conflicting nature of these objectives and yet how critical they are for architectural design from concept through to fabrication. The paper presents a demonstration of our methodology where the system successfully modifies the generation of shells inclusive of an environmental target by assigning different environmental behaviors to our agents. We utilize structural analysis of reciprocal frames locally in order to calibrate the agents’ behavior for their application globally so that we can avoid the generation of bad performing geometries. This is achieved by generating and analyzing different structural element (nexor) designs and by analytically observing how different geometries affect the structural behavior of the element then frame then shell. The results so far indicate that the increase in the number of elements in a reciprocal unit significantly decreases maximum stresses and displacement, while the increase of the individual elements’ length increase the displacement almost linearly. These results are encoded into the geometric agent behavior in order to steer design generations towards more optimal solutions.

The implementation of our tool to date is in progress and the data passing between the analytical and generative components of our methodology needs to be further automated. A current step is being taken to extend our methodology so that it includes the generation of perforated panels directly connected to reciprocal frames. The vision is to simulate the robotic construction of the shells both in terms of the nexor placements but as well as the nexorade in-fill for more optimal shading and light filtration. Another extension of the work, is to develop an intuitive web based user interface (UI) for generating and visualizing a gallery of design alternatives which contains analytical (i.e. stresses, displacement, environmental performance) as well as the possible range of formal geometric alternatives.

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Stair Design Using Quantified Smoothness

Abel Groenewolt

[email protected]

Abstract. This paper introduces metrics to evaluate stair geometry and shows how these metrics can be used to develop versatile computational stair design tools for the design of smooth stairs. The proposed stair smoothness metrics are based on the angles between tread lines, the angles between the walk line and tread lines, and the dimensions of tread sides. Using these metrics in combination with evolutionary algorithms results in computational methods that are highly flexible: as opposed to common software tools that generate particular classes of stairs (such as helical stairs or u-shaped stairs), this approach could be used for any stair design. The proposed methods produce results that match or surpass the smoothness of manually designed stairs and enable the implementation of features that are not available in other design tools, such as obstacle avoidance. Applications of the proposed method are shown for both freestanding stairs and stairs with a predefined footprint.

Keywords: Stairs, Stair Design, Evolutionary Algorithms, Computational Design

1 Introduction

1.1 Stair Balancing

A major design consideration in stair design is how to deal with turns in direction. For walking comfort and safety as well as for aesthetic reasons, gradual transitions are typically desired [1], [2]. Stairs in which treads are locally adjusted to create smoother transitions are called balanced stairs or dancing stairs [3].

The process of balancing stairs involves rotating treads horizontally around the point where they intersect the walk line. Various geometric methods to execute this process manually exist [2], [4-6], of which the unrolled projection method is the most widely applicable, as it can deal with any angle between straight series of treads. This method (illustrated in Fig. 1) has been known for over 200 years [7] and can be found in various sources [6], including recent publications [4], [8].

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