Integrated Structural and Environmental Form-Finding: A Teaching Experiment.

This paper presents a teaching experiment in which 3D digital computational models are explored as the representational base to integrate formal, structural, and environmental performance criteria in design. By describing the academic experience, the paper reflects on its methodologies and results, as well as on the relation between human and computer factors in the design process. This assessment is important to make the students aware of the increasingly intelligent design systems offered by digital technologies to support architectural design, as well as of their relationship with precedent digital and analog representational mediums.

Form Follows Parameter: Algorithmic-Thinking-Oriented Course for Early-stage Architectural Education.

The digital paradigm requires efficient methods of teaching CAAD tools in architecture schools. With the trend of enhancing the design process with parametric methods, linking architecture with other knowledge areas, such as mathematics, is gaining in importance. Equipping future architects with skills in algorithmic thinking is yet another challenge for education. This paper describes the workflow of an early-stage course addressing this challenge, conducted at the Warsaw University of Technology's Faculty of Architecture. The course focuses on the students' ability to construct complex geometric forms in the digital environment by introducing an extensive analytic phase. The students study the geometric foundations of real-world architectural cases and translate them into parametric models. Later, they explore the potential of the generated solutions space. The results compare the course's teaching efficiency with the outcomes of past courses covering similar subjects.

Novel Technique to Increase the Effective Workspace of a Soft Robot.

This article presents a novel technique for a class 2 tensegrity robot, also classified as a soft robot, to increase workspace by increasing the number of geometric equilibrium configurations of the robot. The proposed modification, unlike the strategies reported in the literature, consists of increasing the number of points where the flexible and rigid elements that make up the robot come into contact without the need to increase the number of actuators, the number of flexible elements, or modify the geometry of the rigid elements. The form-finding methodology combines the basic principles of statics with the direct and inverse kinematic position analysis to determine the number of equilibrium positions of the modified robot. In addition, numerical experiments were carried out using the commercial software ANSYS®, R18.2 based on the finite element theory, to corroborate the results obtained with them. With the proposed modification, an increase of 23.369% in the number of geometric equilibrium configurations is achieved, which integrates the workspace of the modified class 2 tensegrity robot. The novel technique applied to tensegrity robots and the tools developed to increase their workspace apply perfectly to scale the robots presented in this paper.

Dragonfly-Inspired Wing Design Enabled by Machine Learning and Maxwell's Reciprocal Diagrams.

This research is taking the first steps toward applying a 2D dragonfly wing skeleton in the design of an airplane wing using artificial intelligence. The work relates the 2D morphology of the structural network of dragonfly veins to a secondary graph that is topologically dual and geometrically perpendicular to the initial network. This secondary network is referred as the reciprocal diagram proposed by Maxwell that can represent the static equilibrium of forces in the initial graph. Surprisingly, the secondary graph shows a direct relationship between the thickness of the structural members of a dragonfly wing and their in-plane static equilibrium of forces that gives the location of the primary and secondary veins in the network. The initial and the reciprocal graph of the wing are used to train an integrated and comprehensive machine-learning model that can generate similar graphs with both primary and secondary veins for a given boundary geometry. The result shows that the proposed algorithm can generate similar vein networks for an arbitrary boundary geometry with no prior topological information or the primary veins' location. The structural performance of the dragonfly wing in nature also motivated the authors to test this research's real-world application for designing the cellular structures for the core of airplane wings as cantilever porous beams. The boundary geometry of various airplane wings is used as an input for the design proccedure. The internal structure is generated using the training model of the dragonfly veins and their reciprocal graphs. One application of this method is experimentally and numerically examined for designing the cellular core, 3D printed by fused deposition modeling, of the airfoil wing; the results suggest up to 25% improvements in the out-of-plane stiffness. The findings demonstrate that the proposed machine-learning-assisted approach can facilitate the generation of multiscale architectural patterns inspired by nature to form lightweight load-bearable elements with superior structural properties.

Constant stress arches and their design space.

It is generally accepted that an optimal arch has a funicular (moment-less) form and least weight. However, the feature of least weight restricts the design options and raises the question of durability of such structures. This study, building on the analytical form-finding approach presented in Lewis (2016. Proc. R. Soc. A 472, 20160019. (doi:10.1098/rspa.2016.0019)), proposes constant axial stress as a design criterion for smooth, two-pin arches that are moment-less under permanent (statistically prevalent) load. This approach ensures that no part of the structure becomes over-stressed under variable load (wind, snow and/or moving objects), relative to its other parts-a phenomenon observed in natural structures, such as trees, bones, shells. The theory considers a general case of an asymmetric arch, deriving the equation of its centre-line profile, horizontal reactions and varying cross-section area. The analysis of symmetric arches follows, and includes a solution for structures of least weight by supplying an equation for a volume-minimizing, span/rise ratio. The paper proposes a new concept, that of a design space controlled by two non-dimensional input parameters; their theoretical and practical limits define the existence of constant axial stress arches. It is shown that, for stand-alone arches, the design space reduces to a constraint relationship between constant stress and span/rise ratio.

Additive Manufacturing of Sustainable Construction Materials and Form-finding Structures: A Review on Recent Progresses.

Recently, there has been an increasing interest on the sustainability advantage of 3D concrete printing (3DCP), where the original cement-based mixtures used for printing could be replaced or incorporated with environmental-friendly materials. The development in digital modeling and design tools also creates a new realm of form-finding architecture for 3DCP, which is based on topological optimization of volumetric mass and physical performance. This review provides a perspective of using different green cementitious materials, applications of structural optimization, and modularization methods for realizing sustainable construction with additive manufacturing. The fresh and hardened mechanical properties of various sustainable materials for extrusion-based 3D printing are presented, followed by discussions on different topology optimization techniques. The current state of global research and industrial applications in 3DCP, along with the development of sustainable construction materials, is also summarized. Finally, research and practical gaps identified in this review lead to several recommendations on material developments, digital design tool's prospects for 3DCP to achieve the sustainability goal.

Self-organized rod undulations on pre-stretched textiles.

Textile technology is a traditional approach to additive manufacturing based on one-dimensional yarn. Printing solid rods onto pre-stretched textiles creates internal stresses upon relaxation of the pre-stretch, which leads to buckling-induced out-of-plane deformation of the textile. Similar behaviours are well known to occur also in biological systems where differential growth leads to internal stresses that are responsible for the folding or wrinkling of leaves, for example. Our goal was to get a quantitative understanding of this wrinkling by a systematic experimental and numerical investigation of parallel rods printed onto a pre-stretched textile. We vary rod thickness and spacing to obtain wavelength and phase coherence of the wrinkles as a function of these parameters. We also derive a simple analytical description to rationalize these observations. The result is a simple analytical estimate for the phase diagram of behaviours that may be used for design purposes or to describe wrinkling phenomena in biological or bioinspired systems.

Iterated Ritz and conjugate gradient methods as solvers in constrained form-finding: A comparison.

Constrained form-finding results in a nonlinear system of equations unless a linear form-finding method (force density method) is iteratively applied until the given constraints are satisfied. Because the goal of this paper is to contribute to the further development of this method, a brief overview of the method and its existing improvements is provided. Further improvement can be potentially expected by reducing the number of iteration steps in solving systems of linear equations in each application of the force density method. To explore this, a comparison of iterative linear solvers is conducted. The Iterated Ritz method, as a new promising solver (currently under development), was chosen for comparison with typically used conjugate gradients. Form-finding of several truss structures in both tension and compression was performed to compare the number of iteration steps necessary to obtain the solution. The presented form-finding examples indicated a significant reduction in the number of solver iteration steps, showing the potential of the Iterated Ritz method for use as a solver in linear procedures for constrained form-finding.

3D-Printed Biodigital Clay Bricks.

Construction materials and techniques have witnessed major advancements due to the application of digital tools in the design and fabrication processes, leading to a wide array of possibilities, especially in additive digital manufacturing tools and 3D printing techniques, scales, and materials. However, possibilities carry responsibilities with them and raise the question of the sustainability of 3D printing applications in the built environment in terms of material consumption and construction processes: how should one use digital design and 3D printing to achieve minimum material use, minimum production processes, and optimized application in the built environment? In this work, we propose an optimized formal design of "Biodigital Barcelona Clay Bricks" to achieve sustainability in the use of materials. These were achieved by using a bottom-up methodology of biolearning to extract the formal grammar of the bricks that is suitable for their various applications in the built environment as building units, thereby realizing the concept of formal physiology, as well as employing the concept of fractality or pixilation by using 3D printing to create the bricks as building units on an architectural scale. This enables the adoption of this method as an alternative construction procedure instead of conventional clay brick and full-scale 3D printing of architecture on a wider and more democratic scale, avoiding the high costs of 3D printing machines and lengthy processes of the one-step, 3D-printed, full-scale architecture, while also guaranteeing minimum material consumption and maximum forma-function coherency. The "Biodigital Barcelona Clay Bricks" were developed using Rhinoceros 3D and Grasshopper 3D + Plugins (Anemone and Kangaroo) and were 3D printed in clay.

Enumeration-screening method for the design of simple polygonal tensegrities.

Tensegrities, consisting of axially pre-compressed bars and pre-stretched strings, hold broad applications in the design of, for instance, architectures, soft robotics and metamaterials. In this paper, we propose an enumeration-screening method to design planar tensegrities of simple polygonal shapes. In such a polygonal tensegrity, the strings are joined pair-wise to form a simple polygon (a planar shape consisting of straight, non-intersecting line segments) and only one bar is added at each node. The total number of simple polygonal tensegrities designed by this scheme increases exponentially with the number of bars. Moreover, we demonstrate that each of these designed topologies can produce a self-equilibrated and stable tensegrity configuration. This work helps understand the topological features of simple polygonal tensegrities, which can be used as elementary cells to design some novel two- and three-dimensional tensegrity structures.

Curvature, metric and parametrization of origami tessellations: theory and application to the eggbox pattern.

Origami tessellations are particular textured morphing shell structures. Their unique folding and unfolding mechanisms on a local scale aggregate and bring on large changes in shape, curvature and elongation on a global scale. The existence of these global deformation modes allows for origami tessellations to fit non-trivial surfaces thus inspiring applications across a wide range of domains including structural engineering, architectural design and aerospace engineering. The present paper suggests a homogenization-type two-scale asymptotic method which, combined with standard tools from differential geometry of surfaces, yields a macroscopic continuous characterization of the global deformation modes of origami tessellations and other similar periodic pin-jointed trusses. The outcome of the method is a set of nonlinear differential equations governing the parametrization, metric and curvature of surfaces that the initially discrete structure can fit. The theory is presented through a case study of a fairly generic example: the eggbox pattern. The proposed continuous model predicts correctly the existence of various fittings that are subsequently constructed and illustrated.

Affine and non-affine deformations quantified in cytoskeletal networks through three-dimensional form-finding model.

Actin filaments and cross-linkers are main components of cytoskeletal networks in eukaryotic cells, and they support bending moments and axial forces respectively. A three-dimensional form-finding model is proposed in this work to investigate affine and non-affine deformations in cytoskeletal networks. In recent studies, modeling of cytoskeletal networks turns out to be a key piece in the cell mechanics puzzle. We used form-finding analysis to compute and analyze cytoskeletal models. A three-dimensional model is much more flexible and contains more elements than a two-dimensional model, and non-linear finite element analysis is difficult to converge. Thus, vector form intrinsic finite element analysis is employed here for valid results. The three-dimensional model reveals new behaviors beyond earlier two-dimensional models and better aligns with available data. Relative density of actin filaments and height of the form-finding model both play important roles in determining cytoskeletal stiffness, positively and negatively, respectively. Real cytoskeletal networks are quite mixed in terms of affine and non-affine deformations, which are quantified by internal strain energy in actin filaments and cross-linkers. Results are also influenced by actin filament relative density and height of the model. The three-dimensional form-finding model does provide much more room for intensive studies on cytoskeletal networks. In our future study, microtubules, fluidics, viscoelastic-plastic cross-linkers and even the whole cell model may be taken into account gradually to improve the cytoskeletal form-finding model.