The Design-to-Robotic-Assembly project presented in this paper showcases an integrative approach for stacking architectural elements with varied sizes in multiple directions. Several processes of parametrization, structural analysis, and robotic assembly are algorithmically integrated into a Design-to-Robotic-Production method. This method is informed by the systematic control of density, dimensionality, and directionality of the elements while taking environmental, functional, and structural requirements into consideration. It is tested by building a one-to-one prototype, which is presented and discussed in the paper with respect to the development and implementation of the computational design workflow coupled with robotic kinematic simulation that is enabling the materialization of a multidirectional and multidimensional assembly system.@en

Shell structures carry loads with their thin yet curved shapes. Being thin means shells require little material, which is desirable for minimizing embodied carbon footprints. However, the feature of being curved implies shells require immense effort to design and fabricate. To address the challenges, this dissertation consists of three parts: developing a design algorithm based on radial basis functions (RBFs), inventing a fabrication technique based on reconfigurable mechanisms, and producing prototypes based on the new algorithm and mechanism. The first part of this dissertation introduces a new algorithm based on RBFs for designing smooth membrane shells, which is more versatile than existing methods. The algorithm can generate membranes with both tensile and compressive stresses. It can also tweak an initial shape to meet free-edge conditions. It can also incorporate horizontal loads in the form-finding process. The second part of the dissertation presents a new system of flat-to-curved mechanisms, which allows a shell to be fabricated in a flat configuration and deployed into a double-curved state. Such a mechanism consists of panels connected by tilted hinges. The mechanism can contract non-homogeneously and change its Gaussian curvature. The last part of this dissertation demonstrates the integral application of the RBFs form-finding algorithm and the flat-to-curved mechanisms. The prototypes designed and produced deliver form-found shapes that have spans ranging from 0.2 to 4 meters. This dissertation contributes to the development and distribution of shell structures by developing computer algorithms and digital fabrication techniques to minimize the hurdles of designing and fabricating shell structures. @en

This paper investigates the correlations among 3D graphic statics, Maxwell–Rankine stress function, and Pucher's equation (the governing equation of membrane shells). When there is only vertical load, a solution of Pucher's equation can be converted into a Maxwell–Rankine stress function. The resulting stress function can be further discretized into Rankine reciprocal diagrams. The analogous membrane shell will simultaneously be discretized into a gridshell, which has planar polygonal faces and prismatoidal Rankine diagrams. A family of analytical free-edge membrane shells is also presented. Once these membrane shells are discretized, they can have co-apex pyramidal Rankine diagrams. The resulting discretized Rankine diagrams provide an intuitive way for structure designers to perceive the equilibrium of shell structures.@en

In some steep valleys, flood-induced changes in river bed elevation pose significantly greater risks to infrastructure than floodwaters alone. Over the short term, the river may aggrade or degrade by several meters during a single flood. Whereas floodwaters recede after each event, moreover, riverbed changes add up over successive floods. To quantify the resulting geomorphic risk and its evolution over time, we propose in this paper a new stochastic model of river bed elevation change. The bed is assumed to rise and drop according to a random walk, driven by the composition of two gamma processes that respectively pace the hydrologic forcing and the geomorphic response. The model can therefore incorporate various sources of uncertainty, associated with precipitation and debris flow activity within the contributing watershed. To test the model, we apply it to a highly active montane river, the Laonong River in southwestern Taiwan. Model calibration is achieved from a combination of long and short term data, including radiocarbon-dated deposits and modern river records. The modelled distributions fit the data well, including the likelihood of extreme changes. The model also produces a reasonable hindcast of the geomorphic damage suffered over the last ten years by Highway 20, a vulnerable road link sited along the river, and can be used to forecast future geomorphic risk.@en

Advances in architectural geometry make free-form architecture explicitly definable and economically manufacturable. Enhancing the efficiency of fabrication, this research investigates strategies of translating free-form synclastic surfaces to flat pre-programmed reconfigurable mechanisms. The presented bi-stable mechanisms are produced by creating voids on flat materials. In such mechanisms, the generated blocks are outlined by the voids that are connected by the hinges. The position and the orientation of the hinges allow the blocks to rotate around each other, and then reconfigure from flat to synclastic. During the reconfiguration process, the blocks are temporarily deformed. As the elasticity brings the blocks back to the original dimensions, the materials reach the second stable states. Distribution of hinges on the flattened surface needs to be designed according to certain geometric constraints. This paper demonstrates the workflow of identifying the positions of the hinges. The developed methods are validated through prototypes such as a spherical surface and a free-form synclastic surface.@en

The equilibrium of a membrane shell is governed by Pucher's equation that is described in terms of the relations among the external load, the shape of the shell, and the Airy stress function. Most of the existing funicular form-finding algorithms take a discretized stress network as the input and find the shape. When the resulting shape does not meet the user's expectation, there is no direct clue on how to revise the input. The paper utilizes the method of radial basis functions, which is typically used to smoothly approximate arbitrary scalar functions, to represent C∞ smooth shapes and stress functions of shells. Thus, the boundary value problem of solving Pucher's equation can be converted into a least-squares regression problem, without the need of discretizing the governing equation. When the provided shape or stress function admits no solution, the algorithm recommends users how to tweak the input in order to find an approximate solution. The external load in this method can easily incorporate vertical and horizontal components. The latter part might not always be negligible, especially for the seismic hazard zones. This paper identifies that the peripheral walls are preferable to allow the membrane shells to carry horizontal loads in various directions without deviating from their original shapes. When there are no sufficient supports, the algorithm can also suggest the potential stress eccentricities, which could inform the design of reinforcing beams.@en

Shell structures achieve stability through double curvature, which brings about construction challenges. This paper presents a strategy to design and assemble a panelized shell with a bi-stable mechanism aiming to make the assembly process more efficient. The developed prototype has two states of flat and three-dimensional stable configuration. This reconfiguration is achieved by reconfiguring the flattened surface of a shell into a three-dimensional structure using embedded bi-stable joints. In order to apply this approach on free-form double curved shells, a workflow to translate a shell into its flattened state is developed. Discrete components are connected using bi-stable joints, where each joint has two stable states. Once the joints are mechanically activated, they guide the adjacent components contracting and rotating into the three-dimensional configuration. Initial explorations indicate that an edge of a shell will turn into an isosceles trapezoid in the flattened configuration while a node of a conical mesh will turn into a cyclic quadrilateral in the flattened configuration. The flattening process is demonstrated using a free-form vault, while scaled physical porotypes are 3D printed with PLA and tested. Future studies require exploration into applications with construction materials at larger scales.@en

This paper extends polyhedral Airy stress functions to incorporate body forces. Stresses of an equilibrium state of a 2D structure can be represented by the sec- ond derivatives of a smooth Airy stress function and the integrals of body forces. In the absence of body forces, a smooth Airy stress function can be discretised into a polyhedron as the corresponding structure is discretised into a truss. The differ- ence in slope across a creases represents the axial force on the bar, while the zero curvatures of the planar faces represent zero stresses voids of the structure. When body forces are present, the zero-stress condition requires the discretised Airy stress function to curve with the integrals of these body forces. Meanwhile, the isotropic angles on the creases still indicate concentrated axial forces. This paper discretises the integrals of body forces into step-wise functions, and discretises the Airy stress function into quadric faces connected by curved creases. The proposed method could provide structural designers (e.g. architects, structural engineers) with a more intuitive way to perceive stress fields.@en

Membrane shells, which have minimized bending moments under certain load conditions, are regarded as ideal structural forms in terms of material efficiency. Most of the existing numerical form-finding methods are based on discretizing membranes into finite panels or funicular networks and focusing on gravitational loading only. In order to obtain smooth shells and to consider horizontal loads, this paper presents a method to find the equilibrium forms of the membrane shells by solving Pucher’s equation. Radial base functions (RBFs) is utilized to represent stresses and shapes of the membranes, and a least square method is applied to find the controlling coefficients which allow the functions to fit the boundary conditions (e.g. zero stresses at the free edges) and the governing equation. When all the parameters are carefully chosen, the stress and shape functions can achieve sufficient accuracy. The presented method has been preliminarily implemented to find shells on a triangle ground plan incorporating horizontal loads. The form-found geometries are then analyzed by finite element models. The result confirms that the form-found shells have the stress distributions similar to the prescribed stresses.@en