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In the stress analysis industries, especially in aerospace, classical hand calculations in structural analysis are pretty much a requirement to analyze even complex geometries. Click Here The stress engineer's ability to perform classical hand calculations in structural analysis is, in my opinion, one of the most important skills highly regarded in the stress engineering circles. You need to be able to do these quick calculations for your own sanity checks, and also for providing quick sizing of simple parts for the benefit of the designer or project engineer or management that comes to you with such requests.

You can see above in the figure, its a simple supported beam. It is a simple case of course, but even in complex cases, good engineering judgement and proper assumptions of conservatism will provide you with a reasonable result that can save you a lot of time in the long run. You do not need to be a stress engineer to do this, design engineers can do this too to avoid potentially costly fixes later in the design release cycle. Free body diagrams are basically diagrams that you draw of the part as a free body by itself with the applied loads and moments balanced with reactive loads and moments, in other words, load and moment equilibrium checks.

This type of analysis is typical for fastener checks, insert checks and section checks of structural joint components. For example, if you have a tie rod assembly, you can determine the allowable load for the tube using simple Euler Buckling analysis, this is the preferred method, period. This is another commonly used method to determine the loads induced in the fasteners of a joint, another type of classical hand calculations in structural analysis.

But I think you get the idea. However, there is no single established method for measuring diversity, and no explicit understanding of how greater optimization output diversity leads to better architectural outcomes. This research project explores different metrics for quantifying diversity and tests how users interact with design processes that employ various diversity measurements. The structural performance of traditional 3D-printed parts is typically limited by nature of the ayer-by-layer construction. Such parts are anisotropic due to decreased adhesion between layers and the internal structure is uniform, not flexible.

This project seeks to overcome these limitations by printing along the edges of a stress-optimized lattice. With this approach, larger-scale, lightweight parts can be printed with an optimal structure that can vary depending on a loading configuration. The results of this project may be promising for diverse fields including concrete rebar design, spaceframe prototyping for buildings, and generative art.

The fabrication component of the project includes designing a custom extruder for a six-axis robotic arm that excels in printing along hard-to-reach toolpaths in free air, with larger nozzle diameters. To complement this technology, a computational tool is in development to generate lattices and toolpaths for any part and its loading configuration.

The layer-based technique of the fused deposition modeling FDM additive manufacturing process creates anisotropy within printed parts, but the full quantitative characterization of this anisotropy is not yet available, making it difficult to predict structural performance of printed parts. This research studies the tensile strength of ABS plastic created by FDM in incrementally rotated orientations, to analytically and experimentally characterize the anisotropy of the material. The known relationship between strength and orientation can then be used to create a predictive model of the local material behavior in any FDM printed object.

In traditional optimization, an algorithm can be applied to a well-defined problem to return a single solution. In architectural design, problems are rarely this simple—building design is a process full of human preferences and interrelated performance tradeoffs.

Introduction to Aircraft Structural Analysis, 3e

Multi-objective optimization MOO is often more appropriate for managing the various design influences and priorities in conceptual design, but it is inherently dependent on human input throughout the process. This research presents a variety of visualization techniques and computational methods that have been developed to facilitate the use of MOO in conceptual architectural design.

This project investigates the use of surrogate modelling algorithms sometimes called machine learning or approximation algorithms for providing rapid performance evaluation in the conceptual design of buildings and large-scale structures. Such algorithms achieve substantially increased speed by substituting computationally expensive performance simulations with low fidelity statistical regression models.

By deploying such techniques, designers are able to explore a design space thoroughly in real-time, run optimization routines, and evaluate many alternatives in a fast and efficient manner. Preliminary work in this project has focused on the development of brick-like voxels, called droxels , that can be transported and assembled into stabile and geometrically complex structures by drones. Ongoing efforts include developing and implementing a parametric software framework that turns architectural geometry into assembly sequences and ultimately drone flight paths.

In particular, structural systems such as long-span trusses contribute a substantial amount to a buildings' total embodied carbon, and are the focus on this work. Two common materials for truss structures are timber and steel. As a result, the choice of the more sustainable material for any given member is dependent on factors such as the truss span or shape. Multi-material structures offer a solution to create structurally efficient structures with lower environmental impact.

This embodied carbon optimization investigates truss structures of various spans using parametric modeling and numerical optimization, and studies how multi-material and single-material designs compare. This research introduces a new approach for multi-material designs for the optimization of embodied carbon and demonstrates the advantages of using structural optimization and multi-material designs for sustainability. Geometric patterns, pioneered centuries ago as a dominant form of ornamentation in Islamic architecture, represent an abundant source of possible topologies and geometries that can be explored in the preliminary design of discrete structures.

This diverse design space motivates the coupling between Islamic patterns and the form finding of funicular grid shells for which structural performance is highly affected by topology and geometry. This thesis examines one such pattern through a parametric, performance-driven framework in the context of conceptual design, when many alternatives are being considered.

Form finding is conducted via the force density method, which is augmented with the addition of a force density optimization loop to enable grid shell height selection. A further modification allows for force densities to be scaled according to the initial member lengths, introducing sensitivity to pattern geometry in the final form-found structures. The results attest to the viable synergy between architectural and structural objectives through grid shells that perform as well as, or better than, quadrilateral grid shells. Historic and cultural patterns therefore present design opportunities that both expand the conventional grid shell design vocabulary and offer designers an alternative means of referencing vernacular traditions in the modern built environment, through a structural engineering lens.

This research aims to explore form finding strategies for deep space exploration habitats on extraplanetary surfaces such as the Moon and Mars. A new sphere packing form finding approach has been studied, trying to optimize the location of different system and subsystems inside a space habitat and respond to the high pressure differentials required in these environments.

Typically the organization of the interior layout follows the functional needs of the crew, such as working, hygiene, preparing and eating food, etc. To respond to relationships between such functional areas, including sizing, adjacencies, and approximate shapes, architects traditionally have used bubble diagrams and adjacency matrices as design aids. This research combines and digitizes these approaches with a sphere packing algorithm powered by dynamic relaxation, which allocates all required activities and respects all analyzed linkages between functions and subsystems. Furthermore, the obtained functional diagram is readily translated in architecture through a transformation into a tension-only pressurized surface using form-finding tools.

The resulting habitat design is evaluated, in terms of its structural performance, through FE analysis tools. In summary, this research presents a new computational design method for space surface habitats that responds to both functional and physical requirements, offering new ways to support future space exploration.

In contemporary design, a high-performing building must minimize energy usage throughout its construction, operation, and end of life. For certain architectural typologies, such as towers, stadiums, or long-span roofs, structural form plays a significant role in determining the lifecycle energy usage of a building.

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The precise nature of the relationship between the embodied energy of the structure and the operational energy of the building changes for different design contexts and climates, but it can be explored through parametric modeling and rapid performance simulations. This research project intends to develop a theoretical framework and practical tools for navigating these tradeoffs, while also uncovering generalizable architectural knowledge that can be applied in the context of integrated design for structural and energy efficiency.

This project explores the potential of folded plate structures to be a structurally optimized architectural typology. A custom Grasshopper script was developed in which the designer can determine the form of a spanning folded plate structures by adjusting the control points of two curves through which the base surface is lofted. The input geometry is then connected to two different optimizers, Goat and Digital Structure's own Stormcloud , to generate different optimized alternatives close to the base shape.

The findings demonstrated that the folded plate typology inherently performed better than a continuous shell of the same shape. Structural optimization was shown to offer a wide design space for the global morphology of folded plate structures. A video overview of the parametric modeling process and a few case studies is presented here. The project presents a new integrated software and hardware process that reconsiders the traditional addive manufacturing AM technique of fused deposition modelling FDM by adding material explicitly along the three-dimensional principal stress trajectories, or stress lines, of 2.

Using a six-axis robotic arm, this project materializes continuous stress fields into discrete structural topologies, rendered computationally as robotic tool paths. The goal of this project is to develop and perfect this new technique, and to explore conditions in which it is favorable to conventional layer-based additive manufacturing. The research is supported by methodologies including computational structural analysis and comparative structural load testing. For more video information, see this YouTube video. Curved structures are characterized by the critical relationship between their geometry and structural behavior, and selecting an appropriate shape in the conceptual design of such structures is important for achieving efficiency.

However, non-structural conditions, such as aesthetics, functionality, and geotechnical issues, often prohibit selection of a structurally ideal funicular shape. This research explores the possible introduction of additional loads that convert a non-funicular shape into a funicular one without changing its base geometry, through the use of external post-tensioning systems. To achieve this, a new generalized methodology based on graphic statics is developed. Principal stress lines, which are pairs of orthogonal curves that indicate trajectories of internal forces and therefore idealized paths of material continuity, naturally encode the optimal topology for any structure for a given set of boundary conditions.

Although stress line analysis has the potential to offer a direct, and geometrically provocative approach to optimization that can synthesize both design and structural objectives, its application in design has generally been limited due to the lack of standardization and parameterization of the process for generating and interpreting stress lines. Addressing these barriers that limit the application of the stress line methods, this project proposes a new implementation framework that will enable designers to take advantage of stress line analysis to inform conceptual structural design.

Trees, when used as structural elements in their natural, round form, are up to five times stronger than the largest piece of dimensioned lumber they could yield. Additionally, these whole-timbers have a lower effective embodied carbon than any other structural material. When combined into efficient structural configurations and joined using specially-engineered connections, whole-timber has the potential to replace entire steel and concrete structural systems in large-scale buildings, bridges, and infrastructure.

Whole-timber may be the most appropriate structural solution for a low-carbon and fully renewable future in both developed temperate regions and the developing Global South. This project proposes new designs for the first and most important element of this kit: a structurally independent column in whole-timber.

New, simple calculation methods are developed for estimating the buckling capacity of tapered timbers. This research studies the potential of fabricating structural connections additive manufacturing, or 3D printing. Unlike typical bolt-and-plate connections that are mass-produced from sheet material, 3D printed connections can have highly variable geometry due to its digital nature.

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This technology not only makes connection design and fabrication more accessible and flexible, but also asks us to reconsider the relationship between the connection, the connected parts, and the forces transferred between them. The ability of 3D printers to produce intricate parts with fine details makes it possible to produce connections that can wrap around connected members and transfer forces through surface texture induced friction.

It also opens up the possibility of integrating snap-fit behavior into connection design to make assembly faster and easier. The research starts with connection geometry exploration, with a goal to parameterize form and link it to structure behavior. Parallel these efforts is connection prototyping using a range of digital fabrication techniques. Analogous to sample-based music, 3D Sampling contributes new frameworks, tools, and compositional strategies for the digital remixing, hacking, and appropriating of material qualities, performances, and behaviours directly from physical samples to produce new designs.

Case studies are presented which demonstrate 3DJ: a prototype 3D modelling tool for synthesizing haptic and optically performing textures from 3D scan-generated source material, which can be applied in the context of other 3D modeling techniques. This research encourages interdisciplinary design exploration through consideration of constructability in conceptual structural design.

Six new metrics are introduced to measure variability in structural components, impose reasonable construction constraints, and encourage standardization of structural characteristics which can improve the ease, efficiency, and costs of construction. This research applies these original constructability metrics to truss facade structures for an objective, quantitative comparison with structural performance metrics. The primary contribution of these new metrics is a computational method that can aid in identifying expressive, high-performing structures in the conceptual design phase, when decisions regarding global structural behavior have the greatest impact on multi-objective project goals.

New additive manufacturing tecniques allow designers to fabricate geometrically complex prototypes with ease, opening up new possibilities for using physical models in the conceptual design process. However, due to the anisotropic mechanical properties inherent in objects fabricated using common 3D printing methods, like fused deposition modeling FDM , it is difficult to use 3D printing for reliable, accurate structural prototyping and comparative load testing.

Specifically, because of the layer-based process used in 3D printing, structures loaded along the axis of filament orientation are about twice as strong in tension than those loaded perpendicular to this axis. This project investigates ways to overcome such anisoptropy limitations by discretizing structural designs, and connecting structural elements that are printed individually in an orientation that aligns filament direction with the main axis of structural force flow. Mechanical and adhesive connections are both explored, implemented, and tested in comparison to structures printed monolithically.

Results indicate that discretized and connected structures can perform better than those printed in a single pass, but more work is needed to design connection strategies that are both performative and easy to assemble. This project developed, fabricated, and tested new designs for braced frame lateral systems for tall buildings. The aim of the project was to test out structureFIT on a relatively complex problem, to explore the design space of lateral systems for tall buildings, and to develop a methodology for connecting digital and physical models through testing.

Six new braced frame geometries of constant volume were designed using structureFIT, and along with a control design, were then digitally fabricated in polycarbonate using a waterjet cutter. The designs were then load tested to failure by applying a linearly varying force simulating wind load. The load testing confirmed that the new designs performed similarly to each other and to the control design, while offering significant variation in aesthetic character. Four of the designs outperformed the control in ultimate load, and all six new designs were initially stiffer than the control. The uniformity in results verified what was found in the design stage of this project: that the design space for braced frame structures is shallow, meaning that large changes in design variables has limited impact on structural performance.

This means that "optimal" designs can't offer significant savings over conventional designs, but it also means that designers have considerable freedom that can be exploited for architectural reasons. Structural engineer Peter Rice has been hailed for his poeticism and daring in structural engineering. Many designers, with whom he collaborated on projects large and small, have lauded his spirit of confidently propelling rather than stifling the design process with his engineering feedback. Fang, D. Cross-Laminated Timber CLT panels are gaining considerable attention in the United States as designers focus on building more ecological and sustainable cities.

These panels can speed up construction on site due to their high degree of prefabrication, and consequently, CLT is deployed for slab systems, walls and composite systems in modern buildings. However, the structural use of the material is inefficient in CLT panels. The core of the material does not contribute to the structural behavior and acts merely as a spacer between the outer layers. This project offers an alternative design of an optimized CLT panel with the goal of reducing material consumption and increasing the efficiency of this building component, which can help it become more ubiquitous in building construction.

In this paper, a theoretical model for the behavior of optimized CLT panels is developed, and this model is compared with scaled physical load tests. The results demonstrate that the theoretical model accurately predicts physical behavior. The reduced material consumption and cost of the proposed optimized CLT panels can help mitigate the ecological impact of the construction industry, while offering a new competitive building product to the market.

Mayencourt, P. This paper presents a fast and flexible method for robotic extrusion or spatial 3D printing of designs made of linear elements that are connected in non-standard, irregular, and complex topologies. Nonstandard topology has considerable potential in design, both for visual effect and material efficiency, but usually presents serious challenges for robotic assembly since repeating motions cannot be used.

Specifically, the assembly sequence, end effector pose, joint configuration, and transition trajectory are all generated automatically using state-of-the-art, open-source planning algorithms developed in the broader robotics community. Three case studies with topologies produced by structural optimization and generative design techniques are presented to demonstrate the potential of this approach.

Huang, Y. Robotic extrusion of architectural structures with nonstandard topology. Innovations in mass timber have ushered in a resurgence of timber construction. Historic timber structures feature joinery connections which geometrically interlock, rarely featuring in modern construction which utilizes steel fasteners for connection details.

Research in the geometric potential and mechanical performance of joinery connections remain disparate. This study seeks to develop a performance-driven design framework for the geometry of joinery connections. Experimental and analytical models for three types of joinery connections are presented and compared. A preliminary parametric study through the analytical model demonstrates how geometric parameters can be varied to achieve desired rotational stiffness. Joinery connections in timber frames: analytical and experimental explorations of structural behavior.

As computation has advanced, more designers are becoming familiar with parametric and performance-based design space exploration, techniques that can provide feedback and guidance even in early-stage design. However, two downsides of such techniques are the time and expertise required for problem setup, and the potential of the large volume of generated data to become overwhelming and difficult to absorb.

Researchers must find ways to organize performance-based information and simplify exploration so that the design process is more manageable, while ensuring that performance feedback leads to better outcomes. This paper proposes two new applications of traditional optimization methods that can help simplify early-stage architectural or structural parametric design. The first involves analyzing the design variables considered in the problem, ranking their importance, and determining which ones should be eliminated or emphasized during exploration.

The second method clusters designs into families and enables designers to cycle through these families during exploration. Two structural design case studies are presented to illustrate the possibilities created by variable analysis and clustering in conceptual, performance-based design. Brown, N. Automated performance-based design space simplification for parametric structural design. Design space catalogs, which present a collection of different options for selection by human designers, have become commonplace in architecture.

Increasingly, these catalogs are rapidly generated using parametric models and informed by simulations that describe energy usage, structural efficiency, daylight availability, views, acoustic properties, and other aspects of building performance. However, by conceiving of computational methods as a means for fostering interactive, collaborative, guided, expert-dependent design processes, many opportunities remain to improve upon the originally static archetype of the design space catalog.

This paper presents developments in the areas of interaction, automation, simplification, and visualization that seek to improve on the current catalog model, while also describing a vision for effective computer-aided, performance-based design processes in the future. Designing with data: moving beyond the design space catalog.

This paper focuses on optimizing beams made of solid timber sections through a CNC subtractive milling process. A series of these beams are then fabricated and load tested, and their strength is compared to standard timber sections. Mayencourt, P, Giraldo J. A renewed interest in space exploration, mainly proved by the recent funding that NASA received for sending human to Mars by , led to new challenges in architecture and structural engineering. Space architecture is deeply interdisciplinary and connects different fields of research such as aerospace engineering, architecture, design, space science, medicine, psychology and art.

In this paper, a new sphere packing form finding approach has been studied, trying to optimize the location of different system and subsystems inside a space habitat and respond to the high pressure differentials required in these environments. The potential impact of this study relates to the possibility of designing in real-time the final layout of the habitat by simply defining the linkages between functions and subsystems.

This method could be applied to different scales of the habitat, from the urban level down to the architectural one, and to even more complex systems. Therefore the internal pressurization is the main load to consider. Future research could expand this study analyzing also other types of loads, such as the micrometeoroid impact, and the airlock systems.

The aim of this research is to solve an inverse form-finding problem: construct funicular, axial-only structures as close as possible to a target surface defined by the designer. The scope is limited to grid-like, node-and-branch only networks, which can be solved efficiently using the force density method FDM. This problem is formulated as a least-squares nonlinear optimization problem, and is solved using the constrained nonlinear solvers implemented in MATLAB. Two nonlinear constrained solving methods, interior-point and trust-reflective region, are found to be the fastest with a large convergence domain.

The first and second-order derivatives of the objective function are found analytically. Lastly, the problem is shown to have several degeneracies; one in particular cannot be removed with physical arguments and leads to new insights in the numerical form finding of funicular surfaces. Cuvilliers, P. Gradient-based optimization of closest-fit funicular structures. Kawaguchi, M. Takeuchi Eds. Many recent contributions in computational structural design have argued that design quality can be improved when performance feedback and guidance are part of the conceptual design process.

However, the effect of multi-objective feedback and guidance tools has not been studied extensively. This paper presents the results of an educational study that tests the direct relationship between conceptual design tools and the simulated performance of resulting designs. In the study, students were tasked with designing a restaurant canopy roof using a series of increasingly performance-driven computational design tools.

Although there was no consensus on preferred workflows or aesthetic preferences, the average designs chosen using real time feedback or directed optimization performed significantly better in terms of deflection and emissions than those chosen through free exploration.

Overall, this research establishes a link between design tools and performance outcomes, while strengthening the argument for further integration of performance feedback into early stage design processes. The effect of performance feedback and optimization on the conceptual design process. Funicular structures, which follow the idealized shapes of hanging chains under a given loading, are recognized as materially efficient structural solutions because they exhibit no bending under normal loading conditions and minimize the amount of required members, often reducing the amount of material needed.

However, non-structural conditions, such as aesthetics, functionality, and geotechnical issues, often prohibit selection of a structurally ideal funicular shape: bending moments inevitably arise, decreasing the structural efficiency of the design. This paper briefly describes how a new design philosophy consisting in the introduction of additional loads, using external post-tensioning cables, can convert a non-funicular structure into a funicular one without changing its starting geometry. This system is based on the possibility of introducing external forces into the main structure through a system of stressed tension cables and compressive or tension struts resulting in changing internal force distribution.

The theoretical approach, based on graphic statics, has been generalized for any two-dimensional geometry.

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The method has been implemented in a parameterized and interactive environment allowing the fast exploration of different equilibrated solutions. This paper focuses on the physical modeling, testing, and validation of structures implementing this approach. The structures are modelled through reduced-scale non-funicular geometries fabricated through additive manufacturing 3D printing , with the post-tensioning system constructed with thin cable and precise laser-cut struts.

Slow motion video captures show how three different non funicular geometries pointed-arch, circular arch and free form curve , made of discrete elements and without bending strength, stand only if the cable is working in the appropriate way, demonstrating the efficacy of the new system. Furthermore, this paper introduces a built example on the scale of real building systems. The paper describes the design and construction process of a post-tensioned pavilion structure. This pavilion, called Funicular Explorations, serves as both a validation and demonstration of this new method, expressing the creative freedom of designers and the structural performance of the results.

The design is an array of eight two-dimensional curves, made from custom-cut corrugated cardboard and nylon webbing. The array begins with a funicular parabolic arch, and progresses toward a visually expressive but structurally arbitrary shape. The external post-tensioning system contributes increasingly from one curve to the next, finally allowing the terminal free-form shape to be achieved with axial forces only.

The use of physical models, independent of their scale, is informative but also didactic, illustrating the possibilities and trade-offs in funicular explorations for architectural design. Furthermore such models demonstrate the structural concept behind the post-tensioning system in an intuitive way.

The aim of this research is to allow architects and structural engineers a way to achieve high-performance, efficient, and safe designs, even when the global geometry departs from classical funicular shapes. Todisco, L. Externally post-tensioned structures: validation through physical models. Proceedings of the 3rd International Conference on Structures and Architecture. In conceptual building design, an architect must simultaneously consider a variety of design objectives, including structural efficiency, total energy usage, and aesthetic expres- sion.

However, conceptual building designers seldom use MOO in practice, and although the use of parametric design tools is widespread, these tools rarely give rapid, multidimensional perfor- mance feedback to guide design exploration. In response, this paper describes relevant MOO methods and discusses how architects and engineers can use them to generate diverse, high- performing designs. It also introduces a number of computational tools that support MOO im- plementation and are embedded in traditional parametric modeling software.

Finally, this paper presents a design case study of a cantilevered stadium roof to show how designers can effective- ly set up and navigate an architectural design space. This paper addresses the potential of multi-objective optimization MOO in conceptual design to help designers generate and select solutions from a geometrically diverse range of high-performing building forms.

With a focus on the long span building typology, this research employs a MOO approach that uses both finite element structural modeling and building energy simulations simultaneously to generate opti- mized building shapes that are not constrained to regular, rectilinear geometric configurations. Through a series of case studies that explore performance tradeoffs of enclosed arches and static overhangs in differ- ent climates, this paper shows how MOO can yield architecturally expressive, high-performing designs, which makes the process more attractive to designers searching for creative forms.

It also provides new insight into specific design responses to various climatic constraints, since optimization that considers both structure and energy can shift best solutions in unexpected ways. Finally, by displaying performance results in terms of embodied and operational energy, this paper presents new data showing how consid- erations of structural material efficiency compare in magnitude to total building energy usage. Together, these three contributions can influence current sustainable design strategies for building typologies that have significant structural requirements.

Design for structural and energy performance of long span buildings using geometric multi-objective optimization. Energy and Buildings , This paper explores the use of data-driven approximation algorithms, often called surrogate modeling, in the early-stage design of structures. The use of surrogate models to rapidly evaluate design performance can lead to a more in-depth exploration of a design space and reduce computational time of optimization algorithms. While this approach has been widely developed and used in related disciplines such as aerospace engineering, there are few examples of its application in civil engineering.

This paper focuses on the general use of surrogate modeling in the design of civil structures and examines six model types that span a wide range of characteristics. Original contributions include novel metrics and visualization techniques for understanding model error and a new robustness framework that accounts for variability in model comparison. These concepts are applied to a multi-objective case study of an airport terminal design that considers both structural material volume and operational energy consumption.

Tseranidis, S. Data-driven approximation algorithms for rapid performance evaluation and optimization of civil structures, Automation in Construction. The presented research uses a 6-axis industrial robot arm and a custom-designed heated extruder to develop a new robotic additive manufacturing AM framework for 2. AM technologies, such as fused deposition modelling FDM , are typically based on processes that lead to anisotropic products with strength behaviour that varies according to filament orientation; this limits its application in both design prototypes and end-use parts and products.

Since stress lines are curves that indicate the optimal paths of material continuity for a given design boundary, the proposed stress-line based oriented material deposition opens new possibilities for structurally-performative and geometrically-complex AM, which is supported here by fabrication and structural load testing results. Called stress line additive manufacturing SLAM , the proposed method achieves an integrated workflow that synthesizes parametric design, structural optimization, robotic computation, and fabrication.

Tam, K. Robotics-enabled stress line additive manufacturing. Saunders Eds. Cham, CH: Springer. Funicular structures, which follow the shapes of hanging chains, work in pure tension cables or pure compression arches , and offer a materially efficient solution compared to structures that work through bending action.

However, the set of geometries that are funicular under common loading conditions is limited. Non-structural design criteria, such as function, program, and aesthetics, often prohibit the selection of purely funicular shapes, resulting in large bending moments and excess material usage. In response to this issue, this paper explores the use of a new design approach that converts non-funicular planar curves into funicular shapes without changing the geometry; instead, funicularity is achieved through the introduction of new loads using external post-tensioning. The methodology is based on graphic statics, and is generalized for any two-dimensional shape.

The problem is indeterminate, meaning that a large range of allowable solutions is possible for one initial geometry. Each solution within this range results in different internal force distributions and horizontal reactions. The method has been implemented in an interactive parametric design environment, empowering fast exploration of diverse axial-only solutions.

In addition to presenting the approach and tool, this paper provides a series of case studies and numerical comparisons between new post-tensioned structures and classical bending solutions, demonstrating that significant material can be saved without compromising on geometrical requirements. Design and exploration of externally post-tensioned structures using graphic statics. Journal of the IASS , 56 4 , Addressing these barriers that limit the application of the stress line methods, this paper proposes a new implementation framework that will enable designers to take advantage of stress line analysis to inform conceptual structural design.

Central to the premise of this research is a new conception of structurally inspired design exploration that does not impose a singular solution, but instead allows for the exploration of a diverse high-performancedesign space in order to balance the combination of structural and architectural design objectives.

Stress line generation for structurally performative architectural design.

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Perry Eds. Funicular geometries, which follow the idealized shapes of hanging chains under a given loading, are recognized as materially efficient structural solutions because they exhibit no bending under design loading, usually self-weight. However, there are circumstances in which non-structural conditions make a funicular geometry difficult or impossible. This paper presents a new design philosophy, based on graphic statics, that shows how bending moments in a non-funicular two-dimensional curved geometry can be eliminated by adding forces through an external post-tensioning system.

An interactive parametric tool is introduced for finding the layout of a post-tensioning tendon for any structural geometry. The effectiveness of this approach is shown with several new design proposals. Funicularity through external post-tensioning: design philosophy and computational tool Journal of Structural Engineering ASCE , 2.

Most architectural modelling software provides the user with geometric freedom in absence of performance, while most engineering software mandates pre-determined forms before it can perform any numerical analysis. This trial-and-error process is not only time intensive, but it also hinders free exploration beyond standard designs. This paper proposes a new structural design methodology that integrates the generative architectural and the analytical engineering procedures into a simultaneous design process, by combining shape grammars and graphic statics.

Design tests presented will demonstrate the applicability of this new methodology to various engineering design problems, and demonstrate how the user can explore diverse and unexpected structural alternatives to conventional solutions. Lee, J. Grammar-based generation of equilibrium structures through graphic statics. Case studies are presented which demonstrate 3DJ: a prototype 3D modelling tool for synthesizing haptic and optically performing textures from 3D scan-generated source material, which can be applied in the context of other 3D modelling techniques.

Patel, S. In the field of digital fabrication, additive manufacturing AM, sometimes called 3D printing has enabled the fabrication of increasingly complex geometries, though the potential of this technology to convey both geometry and structural performance remains unmet. Typical AM processes produce anisotropic products with strength behavior that varies according to filament orientation, thereby limiting its applications in both structural prototypes and end-use parts and products. The paper presents a new integrated software and hardware process that reconsiders the traditional AM technique of fused deposition modelling FDM by adding material explicitly along the threedimensional principal stress trajectories, or stress lines, of 2.

As curves that indicate paths of desired material continuity within a structure, stress lines encode the optimal topology of a structure for a given set of design boundary conditions. The use of a 6-axis industrial robot arm and a heated extruder, designed specifically for this research, provides an alternative to traditional layered manufacturing by allowing for oriented material deposition.

The presented research opens new possibilities for structurally performative fabrication.

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Stress line additive manufacturing SLAM for 2. For most traditional applications of structural optimization and form finding for conceptual design, it is possible to pursue a single objective to arrive at an efficient, expressive form. However, when developing a modern building, the design team must consider many other aspects of performance, such as energy usage, architectural quality, and constructability in addition to structural efficiency. In response to this potential, this paper presents a new MOO process that can be integrated into the typical workflow for conceptual building designs.

This MOO process is original in how it allows for interaction with performance feedback across separate design disciplines while generating diverse, sometimes unexpected results. This paper applies the MOO process to a long-span roof design example while focusing on two quantitative optimization objectives—structural efficiency and operational energy efficiency—in a variety of climate contexts. The results generated in this case study include a diverse range of designs that exhibit clear trade-offs between objectives.

Overall, this paper illustrates new potentials of the MOO approach in conceptual design for producing context-responsive, high-performing, geometrically diverse design solutions. Multi-objective optimization for diversity and performance in conceptual structural design. This paper proposes a grammar-based structural design methodology using graphic statics. By combining shape grammars with graphic statics, this method enables the designer to: 1 rapidly generate unique, yet functional structures that fall outside of the expected solution space, 2 explore various design spaces unbiasedly, and 3 customize the combination of grammar rules or design objectives for unique formulation of the problem.

Design tests presented in this paper will show the powerful new potential of combining computational graphic statics with shape grammars, and demonstrate the possibility for exploring richer and broader design spaces with much more trial, and less error. In architectural and structural design, current modeling and analysis tools are extremely powerful and allow one to generate and analyze virtually any structural shape. However, most of them do not allow designers to integrate structural performance as an objective during conceptual design. As structural performance is highly linked to architectural geometry, there is a need for computational strategies allowing for performance-oriented structural design in architecture.

In order to address these issues, the research presented in this paper combines interactive evolutionary optimization and parametric modeling to develop a new computational strategy for creative and high-performance conceptual structural design. Parametric modeling allows for quick exploration of complex geometries and can be combined with analysis and optimization algorithms for performance-driven design. On the other hand, interactive evolutionary optimization empowers the user by acknowledging his or her input as fundamental and includes it in the evolutionary optimization process.

This approach aims at improving the structural performance of a concept without limiting the creative freedom of designers. Taking advantage of the two frameworks, this research implements an interactive evolutionary structural optimization framework in the widely used parametric modeling environment constituted by Rhinoceros and Grasshopper. The tool can accommodate a wide range of structural typologies and geometrical forms in an integrated environment. The paper includes a description of the tool and demonstrates its applications and benefits through several conceptual design case studies.

Danhaive, R. Combining parametric modeling and interactive optimization for high-performance and creative structural design. The paper will emphasize on the results of the first part of the project, related to the construction of structures made of geometrically modified blocks bonded together, called dricks and droxels.

Latteur et al. Drone-based additive manufacturing of architectural structures. This paper presents original research on two historical developments in the field of thin-shell concrete structures in the United States, both at the Massachusetts Institute of Technology MIT in Cambridge, Massachusetts in the s. The second topic is a seminal conference on the architecture, engineering, and construction of thin concrete shells hosted by MIT in , which included presentations by architect-engineer Felix Candela , engineer Anton Tedesko , architect Philip Johnson , among many important designers and scholars.

Both the building and the conference are historically significant, and together, they mark the peak of a design era optimistic about the enduring value of thin-shell concrete structures. However, they also reflect the underlying tensions and contradictions of thin-shell concrete technology that contributed to its limited use in subsequent decades. The project therefore serves as an early example illustrating the limitations of thin-shell concrete applied to arbitrary formal ideas.

The concurrent conference often related directly to the design and construction of Kresge Auditorium: both its structural engineer Charles Whitney, Ammann and Whitney and contractor Douglas Bates, George A. This paper gives a critical review of the influential conference, based on conference proceedings and supporting historical documents.