Form-finding Techniques Research Articles

Mesh antenna cable net form finding optimization by an improved NSGA-II

The tension uniformity and surface accuracy of mesh antenna cable net are two well-accepted evaluation criteria for form finding. Traditional form finding techniques often rely on single-objective optimization and weighting factors. Although the Non-dominated Sorting Genetic Algorithm II (NSGA-II) can address the limitation, there are still challenges of wide distribution and insufficient precision of solutions. In the present work, a novel multi-objective optimization method based on an improved NSGA-II is introduced to conduct mesh antenna cable net form finding optimization. Based on the preference region (PR), a self-adaptive penalty function is proposed. The function is designed to steer the optimization process toward the PR, and enhancing the precision of the solutions. The extent of penalization for an individual solution depends on its positioning relative to the PR and is modified by a penalty coefficient that adapts dynamically to the population number within the PR. Additionally, a form finding method considering flexible frames is developed. The initial population for the flexible frame optimization is sourced from results of rigid frames, with the maximum truss node position error as the convergence criterion. Benchmark tests and case studies confirm that the improved NSGA-II enhances distributivity and convergence, while also providing form-finding results with higher surface accuracy and more uniform tension distribution.

Manufacturing sensitivity study of tensegrity structures using Monte Carlo simulations

The successful construction of a tensegrity structure requires not only design techniques but also a means to account for any manufacturing or assembly errors. As a tensegrity is prestressed and is often stabilised by its prestress, it requires a form-finding technique to determine the balanced configuration in the design phase; this property also makes it challenging for engineers to evaluate the effect of manufacturing imperfections on the self-equilibrated configuration. In this paper we investigate the sensitivity of tensegrity structures to manufacturing imperfections, using a stiffness-matrix-based form-finding technique in combination with the Monte Carlo simulation method to introduce manufacturing length errors. The effects at the structural level are captured, and two general relationships between the variance of the input manufacturing error and the output distribution of the member tensions, between the variance and the mean across all groups, are observed. By identifying the most sensitive member group, this work provides a design and analysis strategy when the natural length errors of members are considered for tensegrity structures.

A Toolbox of Analog Form-Finding Techniques: Experiments for the Generation of Bioinspired Forms in Industrial Design

A Toolbox of Analog Form-Finding Techniques: Experiments for the Generation of Bioinspired Forms in Industrial Design

A Toolbox of Analog Form-Finding Techniques: Experiments for the Generation of Bioinspired Forms in Industrial Design

A Toolbox of Analog Form-Finding Techniques: Experiments for the Generation of Bioinspired Forms in Industrial Design

Topology optimization of shell structures in architectural design

Free-form architectural design has gained significant interest in modern architectural practice. Due to their visually appealing nature and inherent structural efficiency, free-form shells have become increasingly popular in architectural applications. Recently, topology optimization has been extended to shell structures, aiming to generate shell designs with ultimate structural efficiency. However, despite the huge potential of topology optimization to facilitate new design for shells, its architectural applications remain limited due to complexity and lack of clear procedures. This paper presents four design strategies for optimizing free-form shells targeting architectural applications. First, we propose a topology-optimized ribbed shell system to generate free-form rib layouts possessing improved structure performance. A reusable and recyclable formwork system is developed for their effective and sustainable fabrication. Second, we demonstrate that topology optimization can be combined with funicular form-finding techniques to generate a rich variety of elegant designs, offering new design possibilities. Third, we offer cost-effective design solutions using modular components for free-form shells by combining surface planarization and periodic constraint. Finally, we integrate topology optimization with user-defined patterns on free-form shells to facilitate aesthetic expression, exemplified by the Voronoi pattern. The presented strategies can facilitate the usage of topology optimization in shell designs to achieve high-performance and innovative solutions for architectural applications.

Experimental Form-finding: A review

This paper deals with the review and categorization of form-finding techniques. Their utilization in architectural design, consisting of realized as well as theoretical concepts, is studied. Employing experiments, parametric and simulation-based designing, or artificial intelligence in the design process provides a platform for novel, architecturally unique, unexpected structures.

Form-finding of tessellated tensegrity structures

Many large-scale tensegrity structures are formed by assembling repeating units; a tensegrity tower formed by stacking tensegrity prisms is one example. Tessellated tensegrity structures tend to feature a repeating topology, but the geometry and self-stress vary across the assembly. In this work we design tensegrity structures by imposing periodic boundary conditions on a single unit cell to enforce repetitive topology, geometry and self-stress. A tessellated tensegrity tower is designed by using a stiffness matrix form-finding technique in combination with nodal position constraints. Since the tessellated tensegrity is not globally in equilibrium, a transition structure is required to balance the tessellated tensegrity tower on one side and to connect to a fixed boundary on the other. The challenge in designing the transition structure is that both coordinates and residual forces are simultaneously predefined at specific nodes. In this paper, we propose an adapted stiffness form-finding method to design the transition structure as an alternative method to the conventional ground structure method.

Form-finding of frame-supported tensile membrane structures using stochastic optimisation

For tensile membrane structures (TMS), form-finding is the first step in design, in which the structure adopts a unique equilibrium shape based on the initial configuration of the structure and the applied initial prestress. However, the choice of a single robust numerical method for form-finding remains debatable, particularly due to the intensive computation involved. The present work proposes a novel form-finding method for TMS using a swarm intelligence algorithm. Particle swarm optimisation (PSO) is used here as the optimiser in the form-finding analysis, formulated as a (area or potential energy) minimisation problem. The computations involve stochastic PSO runs, until the structure converges to an equilibrium configuration. The proposed form-finding method is demonstrated for two study structures with different optimisation objectives.The proposed PSO-based form-finding technique is found to save significant computation cost, when compared to the most commonly used form-finding algorithm of dynamic relaxation. The PSO-based algorithm is also found to lessen arbitrary parameter selections and to be more robust to the selection of an initial TMS configuration.

Comparison of Form-finding Methods to Shape Concrete Shells for Curved Footbridges

Shells are attractive and efficient structures that play a special role for engineers and architects. However, only few bridges supported by concrete shells have been designed and built after the Musmeci’s bridge in Potenza (Italy). Several numerical form-finding methods have been implemented in the last decades to optimize the shape of shells. In the present paper, a comparison of the Thrust Network Analysis (TNA) and Particle-Spring System (PS) is made by searching the optimal shape of a concrete shell supporting the curved cantilevered deck of a pedestrian bridge under the same boundary conditions. Finite Element Analysis was performed to compare the structural behaviour of the footbridges optimized by the two different form-finding techniques. The effectiveness of both form-finding methods in minimizing unfavourable tensile stresses in concrete shells, thus taking advantage of mechanical properties of concrete, is investigated. Furthermore, transverse deflections of the curved cantilevered deck were reduced introducing an external prestressing system applied to the upper flange of the ring box girder. Finally, the obtained results can help architecture and engineering practitioners to develop innovative bridge conceptual design.

Morphing in Form Finding Stage through the Architectural Design Process

Nature has been always a main source of inspiration for human being through different fields, in which, he has always built tools and techniques for development in various life fields inspired in many cases from nature; between these inspiring the rules and phenomena that governed nature, such as rules of form and formation in nature, which is known as metamorphosis. From the Stone Age till the digital era, each era has witnessed a various inspiration from nature to create new innovations throughout our history to retire the old ways and techniques of doing things and ultimately establishing new ways of life. Today, and especially in the architectural field we can find that architecture has inspired a lot of its concepts from nature, as metamorphosis rules that depended on transformation processes, which appeared recently in architecture under the term of morphing, in which the research will concentrate on. These new rules and inspirations not only affected the expressionism and symbolism of the architecture form, but also it influences the architecture design process by many techniques that replace our traditional ways of designing and revolutionize how we conduct the future and how architects live in this digital world with a new methodologies and techniques in the architecture design specially in form finding process. Firstly, the paper will describe the traditional design process and its stages additionally where and when the form stage comes during this stage. Secondly, it attempts to illustrate the techniques that have been added through the design process by the architectural pioneers through the twenty-one century, and how it affects the phases of design process specially the form finding stage. Ending by illustrating the process of morphing and how it can be implemented within the architectural design process, to enhance the qualities of architectural design, aiming to reach a new design process and reaching new form finding techniques that can facilitate the ability of designing new forms, which can express new architectural paradigm.

A novel shape optimization approach for strained gridshells: Design and construction of a simply supported gridshell

Strained gridshells are reticulated shell structures that are erected from a flat grid of initially straight laths. The structural efficiency of a gridshell is determined by its shape, which is traditionally designed using form-finding techniques. However, these techniques are primarily used to generate structures in pure tension or compression for a single load case only. In cases where classic form-finding techniques are not applicable, such as for cantilevering gridshells or simply supported gridshells, numerical optimization can be used to find a suitable shape. In this paper, an optimization procedure is proposed that optimizes the shape of a strained gridshell for a given grid. The forces applied to erect the gridshell are chosen as the design variables. These erection forces are optimized to minimize the so-called end-compliance, which is defined as the inner product of the external loads and the resulting displacements. The method of moving asymptotes is adopted to solve the optimization problem and implicit dynamic relaxation is used to solve the nonlinear equilibrium equations. Geometric nonlinearity is taken into account by using co-rotational beam elements to model the gridshell laths. To validate the proposed approach, a 6×6 m2 prototype was built. The results show that this approach allows the structure to be optimized considering multiple load cases, while accounting for practical building constraints, and potential designer constraints.

An integrated framework for multi-criteria optimization of thin concrete shells at early design stages

Thin shells are crucially dependent on their shape in order to obtain proper structural performance. In this context, the optimal shape will guarantee performance and safety requirements, while minimizing the use of materials, as well as construction/maintenance costs.Thin shell design is a team-based, multidisciplinary, and iterative process, which requires a high level of interaction between the various parties involved, especially between the Architecture and Engineering teams. As a result of technological development, novel concepts and tools become available to support this process. On the one hand, concepts like Integrated Project Delivery (IPD) show the potential to have a high impact on multidisciplinary environments such as the one in question, supporting the early decision-making process with the availability of as much information as possible. On the other hand, optimization techniques and tools should be highlighted, as they fit the needs and requirements of both the shell shape definition process and the IPD concept. These can be used not only to support advanced design stages, but also to facilitate the initial formulation of shape during the early interactions between architect and structural engineer from an IPD point of view.This paper proposes a methodology aimed at enhancing the interactive and iterative process associated with the early stages of thin shell design, supported by an integrated framework. The latter is based on several tools, namely Rhinoceros 3D, Grasshopper, and Robot Structural Analysis. In order to achieve full integration of the support tools, a custom devised module was developed, so as to allow interoperability between Grasshopper and Robot Structural Analysis. The system resorts to various technologies targeted at improving the shell shape definition process, such as formfinding techniques, parametric and generative models, as well as shape optimization techniques that leverage on multi criteria evolutionary algorithms. The proposed framework is implemented in a set of fictitious scenarios, in which the best thin reinforced concrete shell structures are sought according to given design requirements. Results stemming from this implementation emphasize its interoperability, flexibility, and capability to promote interaction between the elements of the design team, ultimately outputting a set of diverse and creative shell shapes, and thus supporting the pre-design process.

Form Finding Techniques of Branched Construction Developed by Frei Otto

Form Finding Techniques of Branched Construction Developed by Frei Otto

Force density ratios of flexible borders to membrane in tension fabric structures

Architectural fabrics membranes have not only the structural performance but also act as an efficient cladding to cover large areas. Because of the direct relationship between form and force distribution in tension membrane structures, form-finding procedure is an important issue. Ideally, once the optimal form is found, a uniform pre-stressing is applied to the fabric which takes the form of a minimal surface. The force density method is one of the most efficient computational form-finding techniques to solve the initial equilibrium equations. In this method, the force density ratios of the borders to the membrane is the main parameter for shape-finding. In fact, the shape is evolved and improved with the help of the stress state that is combined with the desired boundary conditions. This paper is evaluated the optimum amount of this ratio considering the curvature of the flexible boarders for structural configurations, i.e., hypar and conic membranes. Results of this study can be used (in the absence of the guidelines) for the fast and optimal design of fabric structures.

Form-finding design of cable-mesh reflector antennas with minimal length configuration

Deployable cable-mesh reflector antenna is one popular kind of satellite antennas for space applications. The form-finding design of cable-mesh antennas, which aims to determine the pre-tensioned equilibrium state with a satisfactory reflector surface shape, is vital and indispensable. The tension uniformity of the cables plays an important role in maintaining the stability of the surface shape of on-orbit cable-mesh antennas. A new iterative form-finding technique based on force density method is presented to implement the uniform-tension design of cable-mesh antennas. First, equilibrium equations of the front, the rear and the whole cable nets are derived based on force density method. Then, based on the equilibrium equations, an iterative form-finding strategy is proposed. In the design process, force densities of all the cables are updated simultaneously to achieve the uniform tension of the front and rear nets, and node positions of the front net are iteratively modified to ensure that they are exactly located on the paraboloid. Finally, three typical cable-mesh antennas are employed to illustrate the feasibility and effectiveness of the method. Simulation results show that the front and rear cable nets of the obtained cable-mesh antennas are both minimal length configurations with the tension ties being inclined appropriately.

Comparison of the Performance of Hexagonal Grid and Half-cuboctahedron Grid Tensegrity Systems in Roof Structures

Objective: To study and compare the behaviour of half-cuboctahedron grid and hexagonal grid tensegrity system. Methods/ Statistical Analysis: Ever since the discovery of tensegrity, most works have been concentrated on the classification and form finding techniques but very less on the mechanics of these structures. This study focus on the behaviour of two basic tensegrity modules, the half-cuboctahedron and hexagonal. Findings: Later, the study has been extended to tensegrity grids of spans 2x2, 4x4 and 8x8 of both the configurations (hexagonal modules and half-cuboctahedron modules) which were developed using an FEM based software. The grids were compared on the basis of nodal displacements and member forces, resulting in the half-cuboctahedron grid to be a more feasible configuration for large span roof structures. Applications/ Improvements: The application of the tensegrity structure is to applied in the large span roof structures.

Form-Finding of Tensegrity Structures based on Force Density Method

Background/Objectives: Determining equilibrium configuration of a tensegrity structure is known as form-finding. This paper critically reviews various form-finding techniques based on force density method. Methods/ Statistical Analysis: The most appropriate method out of all the form-finding methods, to ascertain new formation of tensegrity structures is Force density method. The techniques based on Force density method such as Advanced form-finding method, Adaptive force density method, Form-finding via Genetic algorithm and Algebraic tensegrity form-finding are reviewed in detail along with scope, limitation and suitability of each method. Findings: This paper lists out the input and output parameters of each technique and comparing the effectiveness of each. Most of these methods require only type of the member (tension or compression) and topology of the tensegrity structure provided by connectivity matrix as initial parameters. Formfinding of regular shaped structures such as cable domes is best performed by Advanced form-finding method. Adaptive form-finding method is found to be efficient for irregular shaped structures and also to search novel configurations. Form finding by means of genetic algorithm provides solutions for regular shaped tensegrity structures. Algebraic method is found to be highly efficient and automated general method among all the form-finding methods discussed in this paper. A structure’s evolving geometry can be better regulated by this method. Applications/ Improvements: This paper presents the techniques which require minimum initial parameters for form-finding of tensegrity structures which also helps in choice of methods based on known parameters of the structure.

Form-Finding: An Alternative to Structural Optimisation?

The concept of form-finding is well established in the field of tension structures, but is not explored sufficiently outside that field, with structural optimisation being the main contender to providing robust, functional and durable designs. Form-finding can be defined as an iterative process of shaping structures according to prescribed boundary configurations and forces acting on them. It is a process that may, or may not, involve the elastic response of the structure. This paper presents a review of form-finding techniques, including a variety of computational approaches (preferred by engineers), and physical modelling (preferred by architects). Amongst the computational approaches, the best known are: dynamic relaxation, force density, stiffness matrix, and the updated reference strategy. The main characteristics of each method will be outlined in the context of their suitability to a given application. The role of soap-film analogy in form-finding of fabric structures will be discussed from the theoretical and practical perspectives, and contrasted with the idea of differentially stressed forms. This will be followed by a discussion of common misconceptions related to the design of fabric structures. Form-finding, if properly implemented, has the potential to deliver 'minimal' structures, or minimum energy forms, characterised by maximum stability and strength with minimum weight. This minimal principle operates in the formation of highly optimised objects we find in nature. It will, therefore, be postulated that formfinding techniques should be used not only to model shapes of flexible fabric structures, but also rigid structural forms. Examples of applications to rigid structural forms will include biomedical and aerospace structures, modelled through computational form-finding using the soap-film analogy. The biomedical application will concern a bone replacement scaffold - a minimal structure of appropriate surface curvatures to promote rapid growth of bone-forming cells, porosity to transport nutrients and waste, and stiffness for load sharing with the host bone. The aerospace application will concern a family of compressor blades subjected to aerodynamic loading. Comparisons between the form-found, and aerodynamically optimized structures, will be given. Structural optimisation is an established approach to finding optimal shapes of rigid structural forms with methods such as evolutionary structural optimisation having the potential for delivering natural, minimum energy objects. However, there are distinct differences between structural optimisation and form-finding, and while optimisation criteria are, in general, well understood, form-finding presents a challenge in knowing what set of forces should be used to model an optimal shape of a structure.

Foreword

There is a close link between the action of folding and the design of structures. Folding is a fabrication process; folding generates new shapes; folding gives structural thickness to a surface. This link was identified for a while by architects, designers and engineers. However, recent advances in folding simulations and digital fabrication process offer new perspective for designing structures. The present special issue on folds and structures contains 10 articles providing a rather broad picture of latest advances from several research teams. The first article is a review of form-finding techniques with origami and applications to structures which shows that there are many unexplored geometries for designing structures. It is thus not surprising that several contributions investigates new patterns which presents kinematic or static interest. For instance, the egg-box pattern and Miura-ori are generalized in several ways and corresponding parametrization are provided in in articles 3, 4 and 7. Considering folded strips allows more freedom and simpler fabrication process. A review of these possibilities is provided in the last article (10). Applications which are presented investigate folded structures from the scale of the fold itself to the challenging scale of a bridge. The medium scale applications presented in article 5 and 6 make use of wood panels and would not have been possible without digital cutting. This motivates the closer look at the mechanical assembling of these panels in three contributions from two different teams (articles 6, 8 and 9). Finally, a movable footbridge is investigated in article 2, showing that larger scale may be reached with folding concepts. The rather wide range of emerging applications shows the versatility of folds and allows great expectations in this domain. The support from the editors of International Journal of Space Structures who encouraged this special issue on folded structures is kindly acknowledged. Arthur Lebee

Modeling dielectric-elastomer minimum-energy structures using dynamic relaxation with appropriate material behavior

ABSTRACTForm-finding describes the process of finding a stable equilibrium shape for a structure under a specific set of loading for a set of boundary conditions. Both physical (experimental) and numerical (computational) form-finding methods have been employed by structural engineers and architects for the design of shape-resistant structures: structures whose behavior depends mostly on their global spatial configuration and less on the properties of their individual components. The shape of dielectric elastomer minimum energy structures (DEMES) depends on the equilibrium between the pre-stressed elastomeric membrane and its inextensible frame. Therefore, DEMES can be modeled and analyzed using structural form-finding techniques. We applied dynamic relaxation (DR), a well-established explicit and efficient numerical form-finding and analysis method, to simulate DEMES equilibrium shapes and predict the elastic energy of DEMES. The DR-DEMES model shows generally good agreement with its physical implementation counterpart, as it captures the equilibrium shape and also the elastic energy in function of shape. However, we found that the numerical and the physical models differ in the pre-stress that is required to obtain a specific equilibrium shape. Therefore, in this study we introduce hyper-elasticity in the DR-DEMES model. With this refinement in physical parameters the DR-DEMES model approaches the pre-stress state of the physical DEMES implementation more closely, while it maintains the computational efficiency of the form-finding approach. We conclude that dynamic relaxation, with its low computational cost, is a powerful tool for the design of novel DEMES applications.