Design and Fabrication of Grid-shells Mockups

Engineering Structures, 2016

Grid-shells are lightweight structures used to cover long spans with few load-bearing material, as they excel for lightness, elegance and transparency. In this paper we analyze the stability of hex-dominant free-form grid-shells, generated with the Statics Aware Voronoi Remeshing scheme introduced in Pietroni et al. (2015). This is a novel hex-dominant, organic-like and non uniform remeshing pattern that manages to take into account the statics of the underlying surface. We show how this pattern is particularly suitable for free-form grid-shells, providing good performance in terms of both aesthetics and structural behavior. To reach this goal, we select a set of four contemporary architectural surfaces and we establish a systematic comparative analysis between Statics Aware Voronoi Grid-Shells and equivalent state of the art triangular and quadrilateral grid-shells. For each dataset and for each grid-shell topology, imperfection sensitivity analyses are carried out and the worst response diagrams compared. It turns out that, in spite of the intrinsic weakness of the hexagonal topology, free-form Statics Aware Voronoi Grid-Shells are much more effective than their state-of-the-art quadrilateral counterparts.

Figure 1: We perform a FEM static analysis of the input surface to obtain a stress tensor field, which is decomposed into a double orthogonal line field (a), an anisotropy scalar field (b) and a density scalar field (c). Then we build an Anisotropic Centroidal Voronoi Tessellation having its elements sized and aligned according to the stress tensor field; this tessellation is optimized for symmetry and regularity of faces. The resulting grid-shell is hex-dominant and it is designed to fulfill the required static properties.

Grid shells supporting transparent or opaque panels are largely used to cover long-spanned spaces because of their lightness, the easy setup, and economy. This paper presents the results of experimental static and dynamic investigations carried out on a large-scale free-form grid shell mock-up, whose geometry descended from an innovative Voronoi polygonal pattern. Accompanying finite-element method (FEM) simulations followed. To these purposes, a four-step procedure was adopted: (1) a perfect FEM model was analyzed; (2) using the modal shapes scaled by measuring the mock-up, a deformed unloaded geometry was built, which took into account the defects caused by the assembly phase; (3) experimental static tests were executed by affixing weights to the mock-up, and a simplified representative FEM model was calibrated , choosing the nodes stiffness and the material properties as parameters; and (4) modal identification was performed through operational modal analysis and impulsive tests, and then, a simplified FEM dynamical model was calibrated. Due to the high deformability of the mock-up, only a symmetric load case configuration was adopted.

Designs

The present paper investigates the mechanical behavior of a biomimetic Voronoi structure, inspired by the microstructure of the shell of the sea urchin Paracentrotus lividus, with its characteristic topological attributes constituting the technical evaluation stage of a novel biomimetic design strategy. A parametric design algorithm was used as a basis to generate design permutations with gradually increasing rod thickness, node count, and model smoothness, geometric parameters that define a Voronoi structure and increase its relative density as they are enhanced. Physical PLA specimens were manufactured with a fused filament fabrication (FFF) printer and subjected to quasi-static loading. Finite element analysis (FEA) was conducted in order to verify the experimental results. A minor discrepancy between the relative density of the designed and printed models was calculated. The tests revealed that the compressive behavior of the structure consists of an elastic region followed by a...

Shaping original rod structures goes less and less frequently according the traditional methods of design, whereas optimization processes rise in significance. Bionic explorations impact the development in contemporary architecture trends that inspire architects to create more tectonically fascinating solutions. The logic behind forming such structures is effectiveness in the use of materials and energy. The dynamic development of digital technology provides new tools for authors to design increasingly complex spatial forms, often arising as a result of multi-criteria optimization processes. In the times of universal computerization, generative design methods are modern, creative tools of the architects that allow them to create diverse, multi-variant structures based on similar assumptions about the common boundary in the search of synergistic solutions for a new generation in architecture and design. The search for optimal solutions was adopted to study the bionic trends in regular and irregular flat rod structures on the Voronoi-based divisions.

Architectural Intelligence, 2023

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.

In this paper we present two different optimization procedures, developed and implemented to deal with economic and constructive problems of free form grid shells. This kind of structures is generally composed by a supporting grid that defines the geometry of a large number of cladding glass elements always different one from another. From the constructive point of view it means that every single piece needs to be designed and produced “ad hoc”, then marked and laid with the aid of an assembling table. Moreover if the grid is defined by four or more sides elements the realization of curve glass slabs turns out to be very expensive because of the carving process, forcing very often designers to try to avoid it by triangulating the grid where the shape results more complex. In order to reduce the cost of complex glass grid shells by limiting the number of element typologies and, if we have quadrilateral elements, defining at the same time a plane panels configuration, two optimization...

2019

Quadrangular Grid shells have generated interest in recent years for their application in rationalizing free form geometry in the built environment. Shell structure are efficient because their form is governed by flow of internal forces. But while discretizing shells into grid shells, instead of using flow of forces, current method follows patterns and tessellation techniques. Quadrangular grids are easier to manufacture but they are not stiff inherently compared to triangulated meshed grid, which doesn’t allow them to be used as frequently. There is a scope to improve stiffness by discretization informed by flow of forces. A workflow was developed for designing quadrangular static-responsive grid shells which are structurally efficient, homogenous and has near planar cladding, including preferences of the designer. The workflow is set up in a parametric environment in grasshopper, a plugin for Rhino 3d modelling software. It uses particle spring method for form finding a shell whic...

The International Journal of Advanced Manufacturing Technology, 2019

Additive manufacturing (AM) enables the direct manufacture of complex geometries with unique engineering properties. In particular, AM is compatible with topology optimisation (TO) and provides a unique opportunity for optimal structural design. Despite the commercial opportunities enabled by AM, technical requirements must be satisfied in order to achieve robust production outcomes. In particular, AM requires support structures to fabricate overhanging geometry and avoid overheating. Support generation tools exist; however, these are generally not directly compatible with the voxel-based representation typical of TO geometries, without additional computational steps. This research proposes the use of voxel-based Cellular automata (CA) as a fundamentally novel method for the generation of AM support structures. A number of CA rules are proposed and applied with the objective of generating robust support structures for an arbitrary TO geometry. Relevant CA parameters are assessed in terms of structure manufacturability, including sequential and random CA, rotation of the cellular array, and alternate CA boundary rules, including permutations not previously reported. From this research, CA with complex cell arrangements that provide robust AM support for TO geometries are identified and demonstrated by manufacture with selective laser melting (SLM) and fused deposition modelling (FDM). These CA may be automatically applied to enable TO geometries to be directly fabricated by AM, thereby providing a unique, and commercially significant, design for AM (DFAM) capability.

Journal of the International Association for Shell and Spatial Structures, 2019

Modern architectural design has seen a shift towards iconic doubly-curved envelopes enclosing large column-free spaces. Gridshells have long been considered an efficient solution to such designs, but their actual use in practice has not spread worldwide. For elastic gridshells, their advantages in terms of substantial material savings can often be overshadowed by the significant challenges associated with their construction. Similarly, for rigid gridshells, the manufacture of a large number of different members and nodal connections is often a barrier to their implementation. This paper proposes an effective way of designing, fabricating and erecting gridshells. The "Patchwork Gridshell" consists of a number of efficient elastic gridshell patches assembled using rigid gridshell frames. It can easily generate a number of different configurations, use a wide range of materials, and allows more architectural expression of practical long-span forms. The benefits of combining t...