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.
The fabrication and construction of curved beams along freeform skins pose many challenges related to their individual and complex geometry. One strategy to simplify the fabrication process uses elastic deformation to construct curved beams from flat elements. Controlling the curvature of the design surface and beams has the additional potential to create repetitive building parts with beneficial beam orientation. We aim for strained gridshells built entirely from straight or circular lamellas of the same radius and with orthogonal nodes. The lamellas are aligned normal to a reference surface enabling an elastic assembly via their weak axis and a local transfer of loads via their strong axis. We show that the corresponding reference surfaces are of constant mean curvature and that the network of beams bisects principal curvature directions. We introduce a new discretization of these networks as quadrilateral meshes with spherical vertex stars and present a computational workflow for the design of such structures. The geometric advantages of these networks were key for the fabrication and assembly of a prototype structure, the Asymptotic Gridshell. We describe the complete process from design to construction, presenting further insights on the symbiosis of geometry, fabrication and load-bearing behavior.
Constant mean curvature surfaces (CMCs) have many interesting properties for use as a form for doubly curved structural envelopes. The discretization of these surfaces has been a focus of research amongst the discrete differential geometry community. Many of the proposed discretizations have remarkable properties for envelope rationalization purposes. However, little attention has been paid to generation methods intended for designers. This paper proposes an extension to CMCs of the method developed by Bobenko, Hoffmann and Springborn (2006) to generate minimal S-isothermic nets. The method takes as input a CMC (smooth or finely triangulated), remeshes its Gauss map with quadrangular faces, and rebuilds a CMC mesh via a parallel transformation. The resulting mesh is S-CMC, a geometric structure discovered by Hoffmann (2010). This type of mesh have planar quads and offset properties, which are of particular interest in the fabrication of gridshells.
Designing freeform architectural surfaces with due regard to economic and feasibility factors is a challenging task. Rationalizing such surfaces by means of quadrilateral meshes following principal curvature lines has proven to be beneficial for manufacturing reasons, such as planar cladding panels and simplified substructure connections. On the other hand, for structural efficiency, it is convenient to ensure static equilibrium in the load bearing structure through axial forces only. It turns out that both of these goals can be reached for surfaces in membrane equilibrium where principal stress and curvature directions coincide. In this paper, we present a method for the optimization of a given shape towards stress and curvature alignment, within a workflow for the design of principal meshes in equilibrium. Our method can be applied to shapes without any geometric or topological limitation.
The aim of this paper is to discuss the form-finding of an innovative structural system through the design and construction of a full-scale timber pavilion. Nexorades, or multi-reciprocal grids, are structures where members support each other along their spans. This structural principle allows simple assembly and connection details, but leads in counterpart to poor structural performance. Introducing planar plates as bracing components solves this issue, but result in a complex and intricate geometry of the envelope and supporting structure. This paper discusses the different challenges for the designers of shell-nexora-de hybrids and algorithmic framework to efficiently handle them in a project workflow.
This paper presents a strategy for topological exploration of structural patterns, such as beam grids for gridshells or voussoir tessellations for masonry vaults. The authors define topology finding, by analogy and in complement to form finding, as the design of the connectivity of patterns in relation to architectural and structural requirements. The method focuses on the design of the singularities in the pattern through the automated generation and subsequent rule-based editing of a coarse quad mesh that encodes the properties of the singularities and their relationships before mesh densification, pattern mapping, geometrical exploration and performance assessment.
The use of the virtual work theorem enables one to derive the equations of static equilibrium of fabric, shell and gridshell structures from the compatibility equations linking the rate of deformation of a surface to variations in its velocity. If the structure is treated as a continuum there is no need to consider its micro-structure provided that the grid is fine compared to the overall geometry. Thus we can include fabrics, ribbed shells, corrugated shells and gridshells with a fine grid, such as the Mannheim Multihalle. The equilibrium equations are almost identical to those obtained by assuming that a shell is thin and of uniform thickness, but are more general in their application. Our formulation introduces the concept of geodesic bending moments which are relevant to gridshell structures with continuous laths. The virtual work theorem is more general than the energy theorems, which it in- cludes as a special case. Hence it can be applied to surfaces which admit some form of potential, including minimal surfaces and hanging fabrics. We can then use the calculus of variations for the minimization of a surface integral to define the form of a structure. Many existing formfinding techniques can be rewritten in this way, but we concen- trate on surfaces which minimize the surface integral of the mean curvature subject to a constraint on the enclosed volume, producing a surface of constant Gaussian curvature. This naturally leads to the more general study of conjugate stress and curvature directions, and hence to quadrilateral mesh gridshells with flat cladding panels and no bending moments in the structural members under own weight.
Facing a growing world population and a general economic model which focuses on growth on the one hand and on respectively decreasing limited natural resources on the other, the issue of resource efficient construction becomes more and more important in architecture and building industry. It is well known that double curved structures represent one of the most efficient principles of natural design, as shell structures are able to fulfil different requirements with a minimal consumption of material. Implementing large scale spatial curvature in a world full of the linear and flat products inherent to mass-production is one of the most discussed structural topics of the last two decades in architecture and civil engineering. This paper presents a new, structural approach to implementing resource efficient double curved structures using flat panels. The basic idea is to utilize a quasi-double-layer system by folding rhombic quadrangular panels and connecting them with a simple plug-connection which is stiffened by the different spatial orientation of neighboring elements. As a result it is possible to create a wide range of semi-permeable structures which are adaptable double curved surfaces.
