Landolf Rhode-Barbarigos | University of Miami (original) (raw)

Papers by Landolf Rhode-Barbarigos

Special Issue on “Structural Engineering” of the American Journal of Engineering and Applied Sciences, 2015

Structural engineering, prompted by advances in mechanics and computing as well as design princip... more Structural engineering, prompted by advances in mechanics and computing as well as design principles such as sustainability and resilience, is evolving towards adaptive structures. Adaptive structures are structures that use active components to change shape and properties in response to their environment and/or to their users’ desires. Form-found structures, such as tensegrity and shell structures, can be designed to accommodate such changes within their structural behavior. Dialectic form finding is an extension of the traditional form-finding process integrating performance-related constraints and criteria in the search of a geometry in static equilibrium. Two examples of dialectic form-found structurally integrated adaptive structures are presented. The first example is a shape-shifting tensegrity-inspired structure, while the second example is a shape-shifting shell structure. Both systems are designed to explore elastic deformations for shape changes reducing actuation requirements and highlighting the potential of the proposed method.

Applied Mathematical Modelling, 2018

Tensegrity structures are frameworks in a stable self-equilibrated prestress state that have been... more Tensegrity structures are frameworks in a stable self-equilibrated prestress state that have been applied in various fields in science and engineering. Research into tensegrity structures has resulted in reliable techniques for their form finding and analysis. However, most techniques address topology and form separately. This paper presents a bio-inspired approach for the combined topology identification and form finding of planar tensegrity structures. Tensegrity structures are generated using tensegrity cells (elementary stable self-stressed units that have been proven to compose any tensegrity structure) according to two multiplication mechanisms: cellular adhesion and fusion. Changes in the dimension of the self-stress space of the structure are found to depend on the number of adhesion and fusion steps conducted as well as on the interaction among the cells composing the system. A methodology for defining a basis of the self-stress space is also provided. Through the definition of the equilibrium shape, the number of nodes and members as well as the number of self-stress states, the cellular multiplication method can integrate design considerations, providing great flexibility and control over the tensegrity structure designed and opening the door to the development of a whole new realm of planar tensegrity systems with controllable characteristics.

Journal of the International Association of Shell and Spatial Structures, 2016

Reciprocal structures are composed of mutually supporting rigid elements that are short with resp... more Reciprocal structures are composed of mutually supporting rigid elements that are short with respect to the span of the entire structure. Although reciprocal structural systems have received significant interest among architects and engineers, they are not yet commonly employed in construction. The main reason for this nonadoption is the complexity of conceiving a structure from a module to the global scale without adapting the structure's final global shape. As a result, two approaches have emerged for the design of reciprocal structures. The first approach takes the module as primary building block and the final global form emerges as a result of the module's properties. The second approach results from adjusting the module's properties throughout the surface of the structure to fit its predefined global shape. This paper presents a complete design-to-construction workflow for reciprocal frames using a cell-based pattern algorithm. The developed parametric model explores geometry and patterning to adapt any module geometry to any free-form surface by adjusting the eccentricities between the modules. The resulting reciprocal structure is then analyzed and sized using finite elements. Finally, manufacturing layouts are generated and construction processes are discussed. The design-to-construction workflow was validated experimentally with the construction of a 5-meter diameter reciprocal hemispherical dome.

Journal of the International Association of Shell and Spatial Structures, 2015

Suspended structures such as cable roofs and bridges are tensile spatial systems. The objective o... more Suspended structures such as cable roofs and bridges are tensile spatial systems. The objective of this paper is to describe an automated robust design methodology that can be used to evaluate suspended structures. Numerical simulations combine dynamic relaxation for the nonlinear structural analysis with a non-dominated sorting genetic algorithm (NSGA-II) for multicriteria optimization. The formulation used is general and adaptable to allow for handling of multiple objectives and constraints concurrently. Robust designs are obtained by including random uncertainties in the methodology. Uncertainties are assigned to model inputs which yields outputs with associated uncertainties. Polynomial chaos expansion (PCE) is utilized to create reduced-order stochastic structural analysis models. These models allow statistical robust measures to be obtained with reasonable computational time. A polyester-rope suspended footbridge case study is analyzed to show how the methodology handles both static and dynamic parameters. Test cases in which Young's Modulus and prestress are taken as random variables are examined. Two objectives (maximization of the lowest in-plane natural frequency and minimization of rope volume) and two static constraints (maximum stress and maximum slope) are considered simultaneously. Best compromise solution sets, also named Pareto fronts, for the deterministic and robust designs are compared and found to be similar for all test cases examined. Thus, for this case study, the deterministic solution is the most robust solution. The design methodology described in this paper can be used to evaluate other suspended systems subject to different constraints, objectives, uncertainties, etc. Consequently, this methodology has the potential to be a powerful computational tool for designing robust suspended structures.

International Journal of Space Structures, Special Issue: Folds and Structures, 2015

Origami, the craft of folding paper, has been a source of inspiration for developable foldable sy... more Origami, the craft of folding paper, has been a source of inspiration for developable foldable systems in various engineering disciplines. Origami-inspired segmented plate systems result in lightweight and stiff structures that change shape by folding. With curved-crease origami, a three-dimensional change in shape can arise from a single fold mechanism. In this paper, the curved-crease mechanism of a single-crease arc is investigated as the driver for the conceptual design of a movable footbridge. The folding mechanism is investigated using particle-spring models and small-scale physical models. The structural feasibility of a 40 m radius curved-crease origami-inspired movable footbridge is investigated using finite element analysis. Static analysis and sizing according to US footbridge design code are presented for the critical configurations of the footbridge. Results show that the footbridge can meet typical civil engineering design criteria and illustrate the potential of curved-crease folding mechanisms to inspire the development of movable structures.

Engineering Structures, 2015

Historically, suspended footbridges have been built from ropes (i.e., cables) constructed of a va... more Historically, suspended footbridges have been built from ropes (i.e., cables) constructed of a variety of materials including iron and natural fibers. However, contemporary suspended footbridges are typically constructed with steel rope. One exception, a 64 m span polyester-rope footbridge completed in 2013, demonstrates the potential for alternative rope materials in contemporary footbridge design and construction. The first goal of this paper is to support the idea that polyester rope has promise in future footbridge applications by comparing minimum rope volume and self-weight results for polyester-rope and steel-rope footbridges with spans ranging from 15 to 64 m in two multi-objective optimization problems. In both problems the competitive objective functions are span which is maximized and rope volume which is minimized. The results are minimum volume systems for spans in the defined range. Minimizing volume reduces rope cost and eases material transport and handling. To provide an alternative measure of rope quantity, volume results are scaled to find the equivalent self-weights. This study focuses on in-plane structural behavior and investigates two-dimensional rope systems with or without prestress and with or without under-deck stays. A combination of static and natural frequency constraints is considered in the optimization problems. The second goal of this paper is to describe the novel methodology developed to evaluate these optimization problems. This methodology combines a non-dominated sorting genetic algorithm for searching the design space with dynamic relaxation and eigenanalysis algorithms for the structural analysis. Results indicate that polyester-rope systems have higher volumes, but lower self-weights than steel-rope systems. This observation supports the premise that polyester-rope footbridges are potential alternatives to steel-rope footbridges. The presented methodology can be adapted to evaluate how other unconventional materials compare to more conventional counterparts that are well established in bridge applications.

Applied Mathematics and Computation, 2015

Inflatable dams are flexible membrane structures inflated by air and/or water. Due to their ease ... more Inflatable dams are flexible membrane structures inflated by air and/or water. Due to their ease of construction, rapid deployability and low cost, these systems have great potential for hazard mitigation applications in the context of global warming. However, designing inflatable dams is a challenging task as the dam’s initial equilibrium shape has to be determined by either experimental or numerical form-finding methods. Furthermore, the dam’s shape and the applied loading are coupled since changes in the form of the structure induce also changes in the loading profile. In this paper, dynamic relaxation, a well-established form-finding and analysis technique, is employed for the cross-sectional analysis of inflatable dams. Using this technique and the proposed extensions, the structural behavior of inflatable dams can be analyzed under constant and varying internal pressure as well as different loading and support conditions. The results are in agreement with published results in literature. Therefore, the presented method provides an alternative computationally advantageous tool for the design of inflatable dams.

Energies, 2014

Form finding describes the process of finding a stable equilibrium shape for a system under a spe... more Form finding describes the process of finding a stable equilibrium shape for a system under a specific set of loads, for a set of boundary conditions and starting from an arbitrary initial geometry. However, form finding does not traditionally involve performance constraints such as energy-related criteria. Dialectic form finding is an extension of the process integrating energy-related design aspects. In this paper, dialectic form finding is employed as an approach for designing high performance architectural systems, driven by solar radiation control and structural efficiency. Two applications of dialectic form found shading enclosure structures, a passive and an active one, are presented. The first application example is a site-specific outdoor shading structure. The structure is based on a louver system designed to provide protection from ultraviolet radiation over a pre-defined target only when required, promoting natural lighting and ventilation. The second application example is a shape-shifting modular façade system that adapts its opacity in response to environmental fluctuations. The system can thus improve the environmental performance of a building. Moreover, the system explores elastic deformations for shape changes, reducing actuation requirements. These examples highlight the potential of the dialectic form-finding strategy for the design of high performance architectural integrated structures.

Building and Environment, 2014

Excessive Ultraviolet (UV) radiation exposure results in various health hazards for humans. The U... more Excessive Ultraviolet (UV) radiation exposure results in various health hazards for humans. The United States Environmental Protection Agency maintains that moderate health risk starts at a UV Index of three, where protection such as built shade should be sought. However, commercially available shading structures often fail to take into account varying solar positions at different geographic locations and times of the day. They are typically designed with a “one-design-fits-all” mentality which ignores the site-specificity and time dependency of the position of the sun. This paper proposes and tests a design methodology for a large span louvered shell system that mitigates the harmful effects of UV radiation exposure. The structural beams of the presented grid shell are integrated and optimized as louvers that block out harmful UV radiation only when it poses health risks. The design approach incorporates algorithms that allow for the identification of critical solar positions using a UV Index algorithm, shade analysis, structural form finding and definition of louver orientations and depth. To validate the methodology, a physical prototype is designed, built, equipped with UV sensors and monitored over a period of four months. The presented and tested approach allows for the design of site-specific louvered shells that effectively shade large scale urban spaces (such as public squares, outdoor play and sports grounds and entertainment areas). The resulting novel shades offer an effective strategy for the prevention of UV radiation health risks through the interaction of the built environment.

Applied Physics Letters, 2013

The shape of a dielectric elastomer minimum energy structure (DEMES) depends on the equilibrium b... more The shape of a dielectric elastomer minimum energy structure (DEMES) depends on the equilibrium between a pre-stretched membrane and an inextensible frame. The authors show that an extended dynamic relaxation method, a technique employed for the form-finding and analysis of pre-stressed structures, can be used to simulate DEMES equilibrium shapes. Physical models show excellent agreement with the shape of computed models. Dynamic relaxation, with its low computational cost, is a powerful form-finding technique that efficiently predicts the equilibrium shape as well as the elastic energy of DEMES.

Journal of Structural Engineering-ASCE, 2012

Tensegrity structures are spatial systems composed of tension and compression components in a sel... more Tensegrity structures are spatial systems composed of tension and compression components in a self-equilibrated prestress stable state. Although the concept is over 60 years old, few tensegrity-based structures have been used for engineering purposes. Tensegrity-ring modules are deployable modules composed of a single strut circuit that, when combined, create a hollow rope. The “hollow-rope” concept was shown to be a viable system for a tensegrity footbridge. This paper focuses on the deployment of pentagonal ring modules for a deployable footbridge application. The deployment sequence of a module is controlled by adjusting cable lengths (cable actuation). The geometric study of the deployment for a single module identified the path space allowing deployment without strut contact. Additionally, a deployment path that reduces the number of actuated cables was found. The number of actuated cables is further reduced by employing continuous cables. A first-generation prototype was used to verify both findings experimentally. The structural response during both unfolding and folding is studied numerically using the dynamic relaxation method. The deployment-analysis algorithm applies cable-length changes first to create finite mechanisms allowing deployment and then to find new equilibrium configurations. Therefore, the actuation-step size is identified as the most critical parameter for a successful deployment analysis. Finally, it is shown that the deployability of the footbridge does not affect its element sizing because stresses during deployment are lower than in-service values.

International Journal of Space Structures, 2012

Tensegrity structures are composed of cables and struts in a prestressed self-equilibrium. Althou... more Tensegrity structures are composed of cables and struts in a prestressed self-equilibrium. Although tensegrity first appeared in the 1950s, it is seldom used in civil engineering. This paper focuses on the design aspects of a deployable tensegrity-hollow-rope footbridge. Deployment is usually not a critical design case for traditional deployable structures. However, for tensegrity systems deployment may be critical due to the actuation required. In this paper, deployment is investigated in a general design framework. The influence of clustered (continuous) cables and spring elements in statics and dynamics is studied. Finally, actuation schemes are explored to identify cases where deployment becomes a critical design case. For this configuration, deployment is a critical design case when the structure has spring elements and continuous cables.

International Journal of Solids and Structures, 2011

Tensegrities are spatial, reticulated and lightweight structures that are increasingly investigat... more Tensegrities are spatial, reticulated and lightweight structures that are increasingly investigated as structural solutions for active and deployable structures. Tensegrity systems are composed only of axially loaded elements and this provides opportunities for actuation and deployment through changing element lengths. In cable-based actuation strategies, the deficiency of having to control too many cable elements can be overcome by connecting several cables. However, clustering active cables significantly changes the mechanics of classical tensegrity structures. Challenges emerge for structural analysis, control and actuation. In this paper, a modified dynamic relaxation (DR) algorithm is presented for static analysis and form-finding. The method is extended to accommodate clustered tensegrity structures. The applicability of the modified DR to this type of structure is demonstrated. Furthermore, the performance of the proposed method is compared with that of a transient stiffness method. Results obtained from two numerical examples show that the values predicted by the DR method are in a good agreement with those generated by the transient stiffness method. Finally it is shown that the DR method scales up to larger structures more efficiently.

Engineering Structures, 2010

Tensegrity structures are spatial structural systems composed of struts and cables with pin-joint... more Tensegrity structures are spatial structural systems composed of struts and cables with pin-jointed connections. Their stability is provided by the self-stress state in tensioned and compressed members. Although much progress has been made in advancing research into the tensegrity concept, a rapid survey of current activities in engineering practice shows that much of its potential has yet to be accomplished. A design optimization study for a tensegrity-based footbridge is presented in order to further advance the tensegrity concept in modern structural engineering. In the absence of specific design guidelines, design requirements for a tensegrity footbridge are stated. A genetic algorithm based optimization scheme is used to find a cost-effective design solution. The dynamic performance of the tensegrity footbridge is studied through parametric studies. Design results illustrate that the proposed tensegrity-based footbridge meets typical static and dynamic design criteria.

Engineering Structures, 2010

Tensegrity systems are spatial structures composed of tensile and compression components in a sel... more Tensegrity systems are spatial structures composed of tensile and compression components in a self-equilibrated state of prestress. The tensegrity concept has already been studied by researchers in various fields over the past decades. A family of tensegrity modules that can offer promising solutions for civil engineering applications such as tensegrity domes, towers and bridges is analyzed. Research into tensegrity systems has resulted in reliable techniques for form finding and structural analysis. However, the tensegrity concept is not yet part of mainstream structural design. This paper presents a design study of a tensegrity-based pedestrian bridge. The structural performance of the bridge using three tensegrity modules is evaluated through parametric studies. Design requirements for pedestrian bridges and results of parametric studies are used to define a design procedure that optimizes section sizes for this type of structure. A structural efficiency indicator is proposed and used to compare proposals for feasible bridge configurations. Design results illustrate that the hollow-rope tensegrity bridge can efficiently meet typical design criteria.

Engineering With Computers, 2010

Tensegrity structures are lightweight structures composed of cables in tension and struts in comp... more Tensegrity structures are lightweight structures composed of cables in tension and struts in compression. Since tensegrity systems exhibit geometrically nonlinear behavior, finding optimal structural designs is difficult. This paper focuses on the use of stochastic search for the design of tensegrity systems. A pedestrian bridge made of square hollow-rope tensegrity ring modules is studied. Two design methods are compared in this paper. Both methods aim to find the minimal cost solution. The first method approximates current practice in design offices. More specifically, parametric analysis that is similar to a gradient-based optimization is used to identify good designs. Parametric studies are executed for each system parameter in order to identify its influence on response. The second method uses a stochastic search strategy called probabilistic global search Lausanne. Both methods provide feasible configurations that meet civil engineering criteria of safety and serviceability. Parametric studies also help in defining search parameters such as appropriate penalty costs to enforce constraints while optimizing using stochastic search. Traditional design methods are useful to gain an understanding of structural behavior. However, due to the many local minima in the solution space, stochastic search strategies find better solutions than parametric studies.

Special Issue on “Structural Engineering” of the American Journal of Engineering and Applied Sciences, 2015

Structural engineering, prompted by advances in mechanics and computing as well as design princip... more Structural engineering, prompted by advances in mechanics and computing as well as design principles such as sustainability and resilience, is evolving towards adaptive structures. Adaptive structures are structures that use active components to change shape and properties in response to their environment and/or to their users’ desires. Form-found structures, such as tensegrity and shell structures, can be designed to accommodate such changes within their structural behavior. Dialectic form finding is an extension of the traditional form-finding process integrating performance-related constraints and criteria in the search of a geometry in static equilibrium. Two examples of dialectic form-found structurally integrated adaptive structures are presented. The first example is a shape-shifting tensegrity-inspired structure, while the second example is a shape-shifting shell structure. Both systems are designed to explore elastic deformations for shape changes reducing actuation requirements and highlighting the potential of the proposed method.

Applied Mathematical Modelling, 2018

Tensegrity structures are frameworks in a stable self-equilibrated prestress state that have been... more Tensegrity structures are frameworks in a stable self-equilibrated prestress state that have been applied in various fields in science and engineering. Research into tensegrity structures has resulted in reliable techniques for their form finding and analysis. However, most techniques address topology and form separately. This paper presents a bio-inspired approach for the combined topology identification and form finding of planar tensegrity structures. Tensegrity structures are generated using tensegrity cells (elementary stable self-stressed units that have been proven to compose any tensegrity structure) according to two multiplication mechanisms: cellular adhesion and fusion. Changes in the dimension of the self-stress space of the structure are found to depend on the number of adhesion and fusion steps conducted as well as on the interaction among the cells composing the system. A methodology for defining a basis of the self-stress space is also provided. Through the definition of the equilibrium shape, the number of nodes and members as well as the number of self-stress states, the cellular multiplication method can integrate design considerations, providing great flexibility and control over the tensegrity structure designed and opening the door to the development of a whole new realm of planar tensegrity systems with controllable characteristics.

Journal of the International Association of Shell and Spatial Structures, 2016

Reciprocal structures are composed of mutually supporting rigid elements that are short with resp... more Reciprocal structures are composed of mutually supporting rigid elements that are short with respect to the span of the entire structure. Although reciprocal structural systems have received significant interest among architects and engineers, they are not yet commonly employed in construction. The main reason for this nonadoption is the complexity of conceiving a structure from a module to the global scale without adapting the structure's final global shape. As a result, two approaches have emerged for the design of reciprocal structures. The first approach takes the module as primary building block and the final global form emerges as a result of the module's properties. The second approach results from adjusting the module's properties throughout the surface of the structure to fit its predefined global shape. This paper presents a complete design-to-construction workflow for reciprocal frames using a cell-based pattern algorithm. The developed parametric model explores geometry and patterning to adapt any module geometry to any free-form surface by adjusting the eccentricities between the modules. The resulting reciprocal structure is then analyzed and sized using finite elements. Finally, manufacturing layouts are generated and construction processes are discussed. The design-to-construction workflow was validated experimentally with the construction of a 5-meter diameter reciprocal hemispherical dome.

Journal of the International Association of Shell and Spatial Structures, 2015

Suspended structures such as cable roofs and bridges are tensile spatial systems. The objective o... more Suspended structures such as cable roofs and bridges are tensile spatial systems. The objective of this paper is to describe an automated robust design methodology that can be used to evaluate suspended structures. Numerical simulations combine dynamic relaxation for the nonlinear structural analysis with a non-dominated sorting genetic algorithm (NSGA-II) for multicriteria optimization. The formulation used is general and adaptable to allow for handling of multiple objectives and constraints concurrently. Robust designs are obtained by including random uncertainties in the methodology. Uncertainties are assigned to model inputs which yields outputs with associated uncertainties. Polynomial chaos expansion (PCE) is utilized to create reduced-order stochastic structural analysis models. These models allow statistical robust measures to be obtained with reasonable computational time. A polyester-rope suspended footbridge case study is analyzed to show how the methodology handles both static and dynamic parameters. Test cases in which Young's Modulus and prestress are taken as random variables are examined. Two objectives (maximization of the lowest in-plane natural frequency and minimization of rope volume) and two static constraints (maximum stress and maximum slope) are considered simultaneously. Best compromise solution sets, also named Pareto fronts, for the deterministic and robust designs are compared and found to be similar for all test cases examined. Thus, for this case study, the deterministic solution is the most robust solution. The design methodology described in this paper can be used to evaluate other suspended systems subject to different constraints, objectives, uncertainties, etc. Consequently, this methodology has the potential to be a powerful computational tool for designing robust suspended structures.

International Journal of Space Structures, Special Issue: Folds and Structures, 2015

Origami, the craft of folding paper, has been a source of inspiration for developable foldable sy... more Origami, the craft of folding paper, has been a source of inspiration for developable foldable systems in various engineering disciplines. Origami-inspired segmented plate systems result in lightweight and stiff structures that change shape by folding. With curved-crease origami, a three-dimensional change in shape can arise from a single fold mechanism. In this paper, the curved-crease mechanism of a single-crease arc is investigated as the driver for the conceptual design of a movable footbridge. The folding mechanism is investigated using particle-spring models and small-scale physical models. The structural feasibility of a 40 m radius curved-crease origami-inspired movable footbridge is investigated using finite element analysis. Static analysis and sizing according to US footbridge design code are presented for the critical configurations of the footbridge. Results show that the footbridge can meet typical civil engineering design criteria and illustrate the potential of curved-crease folding mechanisms to inspire the development of movable structures.

Engineering Structures, 2015

Historically, suspended footbridges have been built from ropes (i.e., cables) constructed of a va... more Historically, suspended footbridges have been built from ropes (i.e., cables) constructed of a variety of materials including iron and natural fibers. However, contemporary suspended footbridges are typically constructed with steel rope. One exception, a 64 m span polyester-rope footbridge completed in 2013, demonstrates the potential for alternative rope materials in contemporary footbridge design and construction. The first goal of this paper is to support the idea that polyester rope has promise in future footbridge applications by comparing minimum rope volume and self-weight results for polyester-rope and steel-rope footbridges with spans ranging from 15 to 64 m in two multi-objective optimization problems. In both problems the competitive objective functions are span which is maximized and rope volume which is minimized. The results are minimum volume systems for spans in the defined range. Minimizing volume reduces rope cost and eases material transport and handling. To provide an alternative measure of rope quantity, volume results are scaled to find the equivalent self-weights. This study focuses on in-plane structural behavior and investigates two-dimensional rope systems with or without prestress and with or without under-deck stays. A combination of static and natural frequency constraints is considered in the optimization problems. The second goal of this paper is to describe the novel methodology developed to evaluate these optimization problems. This methodology combines a non-dominated sorting genetic algorithm for searching the design space with dynamic relaxation and eigenanalysis algorithms for the structural analysis. Results indicate that polyester-rope systems have higher volumes, but lower self-weights than steel-rope systems. This observation supports the premise that polyester-rope footbridges are potential alternatives to steel-rope footbridges. The presented methodology can be adapted to evaluate how other unconventional materials compare to more conventional counterparts that are well established in bridge applications.

Applied Mathematics and Computation, 2015

Inflatable dams are flexible membrane structures inflated by air and/or water. Due to their ease ... more Inflatable dams are flexible membrane structures inflated by air and/or water. Due to their ease of construction, rapid deployability and low cost, these systems have great potential for hazard mitigation applications in the context of global warming. However, designing inflatable dams is a challenging task as the dam’s initial equilibrium shape has to be determined by either experimental or numerical form-finding methods. Furthermore, the dam’s shape and the applied loading are coupled since changes in the form of the structure induce also changes in the loading profile. In this paper, dynamic relaxation, a well-established form-finding and analysis technique, is employed for the cross-sectional analysis of inflatable dams. Using this technique and the proposed extensions, the structural behavior of inflatable dams can be analyzed under constant and varying internal pressure as well as different loading and support conditions. The results are in agreement with published results in literature. Therefore, the presented method provides an alternative computationally advantageous tool for the design of inflatable dams.

Energies, 2014

Form finding describes the process of finding a stable equilibrium shape for a system under a spe... more Form finding describes the process of finding a stable equilibrium shape for a system under a specific set of loads, for a set of boundary conditions and starting from an arbitrary initial geometry. However, form finding does not traditionally involve performance constraints such as energy-related criteria. Dialectic form finding is an extension of the process integrating energy-related design aspects. In this paper, dialectic form finding is employed as an approach for designing high performance architectural systems, driven by solar radiation control and structural efficiency. Two applications of dialectic form found shading enclosure structures, a passive and an active one, are presented. The first application example is a site-specific outdoor shading structure. The structure is based on a louver system designed to provide protection from ultraviolet radiation over a pre-defined target only when required, promoting natural lighting and ventilation. The second application example is a shape-shifting modular façade system that adapts its opacity in response to environmental fluctuations. The system can thus improve the environmental performance of a building. Moreover, the system explores elastic deformations for shape changes, reducing actuation requirements. These examples highlight the potential of the dialectic form-finding strategy for the design of high performance architectural integrated structures.

Building and Environment, 2014

Excessive Ultraviolet (UV) radiation exposure results in various health hazards for humans. The U... more Excessive Ultraviolet (UV) radiation exposure results in various health hazards for humans. The United States Environmental Protection Agency maintains that moderate health risk starts at a UV Index of three, where protection such as built shade should be sought. However, commercially available shading structures often fail to take into account varying solar positions at different geographic locations and times of the day. They are typically designed with a “one-design-fits-all” mentality which ignores the site-specificity and time dependency of the position of the sun. This paper proposes and tests a design methodology for a large span louvered shell system that mitigates the harmful effects of UV radiation exposure. The structural beams of the presented grid shell are integrated and optimized as louvers that block out harmful UV radiation only when it poses health risks. The design approach incorporates algorithms that allow for the identification of critical solar positions using a UV Index algorithm, shade analysis, structural form finding and definition of louver orientations and depth. To validate the methodology, a physical prototype is designed, built, equipped with UV sensors and monitored over a period of four months. The presented and tested approach allows for the design of site-specific louvered shells that effectively shade large scale urban spaces (such as public squares, outdoor play and sports grounds and entertainment areas). The resulting novel shades offer an effective strategy for the prevention of UV radiation health risks through the interaction of the built environment.

Applied Physics Letters, 2013

The shape of a dielectric elastomer minimum energy structure (DEMES) depends on the equilibrium b... more The shape of a dielectric elastomer minimum energy structure (DEMES) depends on the equilibrium between a pre-stretched membrane and an inextensible frame. The authors show that an extended dynamic relaxation method, a technique employed for the form-finding and analysis of pre-stressed structures, can be used to simulate DEMES equilibrium shapes. Physical models show excellent agreement with the shape of computed models. Dynamic relaxation, with its low computational cost, is a powerful form-finding technique that efficiently predicts the equilibrium shape as well as the elastic energy of DEMES.

Journal of Structural Engineering-ASCE, 2012

Tensegrity structures are spatial systems composed of tension and compression components in a sel... more Tensegrity structures are spatial systems composed of tension and compression components in a self-equilibrated prestress stable state. Although the concept is over 60 years old, few tensegrity-based structures have been used for engineering purposes. Tensegrity-ring modules are deployable modules composed of a single strut circuit that, when combined, create a hollow rope. The “hollow-rope” concept was shown to be a viable system for a tensegrity footbridge. This paper focuses on the deployment of pentagonal ring modules for a deployable footbridge application. The deployment sequence of a module is controlled by adjusting cable lengths (cable actuation). The geometric study of the deployment for a single module identified the path space allowing deployment without strut contact. Additionally, a deployment path that reduces the number of actuated cables was found. The number of actuated cables is further reduced by employing continuous cables. A first-generation prototype was used to verify both findings experimentally. The structural response during both unfolding and folding is studied numerically using the dynamic relaxation method. The deployment-analysis algorithm applies cable-length changes first to create finite mechanisms allowing deployment and then to find new equilibrium configurations. Therefore, the actuation-step size is identified as the most critical parameter for a successful deployment analysis. Finally, it is shown that the deployability of the footbridge does not affect its element sizing because stresses during deployment are lower than in-service values.

International Journal of Space Structures, 2012

Tensegrity structures are composed of cables and struts in a prestressed self-equilibrium. Althou... more Tensegrity structures are composed of cables and struts in a prestressed self-equilibrium. Although tensegrity first appeared in the 1950s, it is seldom used in civil engineering. This paper focuses on the design aspects of a deployable tensegrity-hollow-rope footbridge. Deployment is usually not a critical design case for traditional deployable structures. However, for tensegrity systems deployment may be critical due to the actuation required. In this paper, deployment is investigated in a general design framework. The influence of clustered (continuous) cables and spring elements in statics and dynamics is studied. Finally, actuation schemes are explored to identify cases where deployment becomes a critical design case. For this configuration, deployment is a critical design case when the structure has spring elements and continuous cables.

International Journal of Solids and Structures, 2011

Tensegrities are spatial, reticulated and lightweight structures that are increasingly investigat... more Tensegrities are spatial, reticulated and lightweight structures that are increasingly investigated as structural solutions for active and deployable structures. Tensegrity systems are composed only of axially loaded elements and this provides opportunities for actuation and deployment through changing element lengths. In cable-based actuation strategies, the deficiency of having to control too many cable elements can be overcome by connecting several cables. However, clustering active cables significantly changes the mechanics of classical tensegrity structures. Challenges emerge for structural analysis, control and actuation. In this paper, a modified dynamic relaxation (DR) algorithm is presented for static analysis and form-finding. The method is extended to accommodate clustered tensegrity structures. The applicability of the modified DR to this type of structure is demonstrated. Furthermore, the performance of the proposed method is compared with that of a transient stiffness method. Results obtained from two numerical examples show that the values predicted by the DR method are in a good agreement with those generated by the transient stiffness method. Finally it is shown that the DR method scales up to larger structures more efficiently.

Engineering Structures, 2010

Tensegrity structures are spatial structural systems composed of struts and cables with pin-joint... more Tensegrity structures are spatial structural systems composed of struts and cables with pin-jointed connections. Their stability is provided by the self-stress state in tensioned and compressed members. Although much progress has been made in advancing research into the tensegrity concept, a rapid survey of current activities in engineering practice shows that much of its potential has yet to be accomplished. A design optimization study for a tensegrity-based footbridge is presented in order to further advance the tensegrity concept in modern structural engineering. In the absence of specific design guidelines, design requirements for a tensegrity footbridge are stated. A genetic algorithm based optimization scheme is used to find a cost-effective design solution. The dynamic performance of the tensegrity footbridge is studied through parametric studies. Design results illustrate that the proposed tensegrity-based footbridge meets typical static and dynamic design criteria.

Engineering Structures, 2010

Tensegrity systems are spatial structures composed of tensile and compression components in a sel... more Tensegrity systems are spatial structures composed of tensile and compression components in a self-equilibrated state of prestress. The tensegrity concept has already been studied by researchers in various fields over the past decades. A family of tensegrity modules that can offer promising solutions for civil engineering applications such as tensegrity domes, towers and bridges is analyzed. Research into tensegrity systems has resulted in reliable techniques for form finding and structural analysis. However, the tensegrity concept is not yet part of mainstream structural design. This paper presents a design study of a tensegrity-based pedestrian bridge. The structural performance of the bridge using three tensegrity modules is evaluated through parametric studies. Design requirements for pedestrian bridges and results of parametric studies are used to define a design procedure that optimizes section sizes for this type of structure. A structural efficiency indicator is proposed and used to compare proposals for feasible bridge configurations. Design results illustrate that the hollow-rope tensegrity bridge can efficiently meet typical design criteria.

Engineering With Computers, 2010

Tensegrity structures are lightweight structures composed of cables in tension and struts in comp... more Tensegrity structures are lightweight structures composed of cables in tension and struts in compression. Since tensegrity systems exhibit geometrically nonlinear behavior, finding optimal structural designs is difficult. This paper focuses on the use of stochastic search for the design of tensegrity systems. A pedestrian bridge made of square hollow-rope tensegrity ring modules is studied. Two design methods are compared in this paper. Both methods aim to find the minimal cost solution. The first method approximates current practice in design offices. More specifically, parametric analysis that is similar to a gradient-based optimization is used to identify good designs. Parametric studies are executed for each system parameter in order to identify its influence on response. The second method uses a stochastic search strategy called probabilistic global search Lausanne. Both methods provide feasible configurations that meet civil engineering criteria of safety and serviceability. Parametric studies also help in defining search parameters such as appropriate penalty costs to enforce constraints while optimizing using stochastic search. Traditional design methods are useful to gain an understanding of structural behavior. However, due to the many local minima in the solution space, stochastic search strategies find better solutions than parametric studies.