Shape Optimization of free form grid-shells

2010

In this paper an optimization problem related to the tessellation of a free form grid shell is presented. This kind of structures is generally composed by a supporting grid that defines the geometry of a large number of cladding elements always different one from another. ...

2011

In the 21st century, as free-form design grows in popularity, grid shells are becoming a universal structural solution, enabling the conflation of structure and skin (facade) into one single element (Kolarevic 2003). This paper presents some of the results of a comprehensive research project focused on the automated design and optimization of grid structures over some predefined free form shape, with the goal of generating a stable and statically efficient structure. It shows that by combining design and FEM software in an iterative, Genetic Algorithms-based optimization process, stress and deformation in grid shell structures can be significantly reduced, material can be saved and stability enhanced.

2011

In the 21 st century, as free form design gains popularity, free-form grid shells are becoming a universal structural solution, enabling merger of structure and facade into a single layer-a skin [31]. The subject of the presented work is the optimization of grid structures over some predefined free form shape, with the goal of generating a stable and statically efficient structure. It is shown how combining design and FEM software in an iterative, Genetic Algorithms based, optimization process, stress and displacements in grid shell structures can be significantly reduced, whereby material can be saved and stability enhanced. Within this research, design and static analysis software are combined in order to perform a statical optimization of grid shells, generated over a given free form surface. A plug-in for Rhinoceros 3D (software based on NURBS [44] geometry representation) is developed, that uses Genetic Algorithms as an optimization method and implements automated iterative calls to Oasys GSA (commercial FEM static analysis software) in order to generate a statically optimal grid shell. To make this possible, within this research some new types of automatic grid generation are developed. Voronoi diagrams [11] were used together with the adapted Force-Density method [38] to develop a new type of grid structure that we called Voronax. In the presented work it was shown that, using the same free form surface, and using the same number of joints and structural members, we can generate much more efficient grid shells, when compared to the standard (uniform) grid structures, simply by modifying the structural grid, i.e., rearranging the structural members of the grid shell. The work presented offers an explanation of the entire method and how it can be constructed. The results of the experiments are there to prove its efficiency and credibility. Once it is proved that the method works, its application can take various forms and be left to the creativity of the user and the requirements of the specific project. IX Zusammenfassung Motivation Die Produktion von Bauteilen durch CNC (Computer Numerical Control)-gesteuerte Maschinen revolutionierte, gegen Ende des 20. Jahrhunderts, den architektonischen Entwurf. Tragwerke mussten nicht mehr vereinfacht werden, um so viele gleiche Elemente wie möglich zu erhalten. Heutzutage können Gebäude mit Tausenden verschiedener (einzigartiger) Trag-oder Fassadenelemente zu akzeptablen Kosten gebaut werden, indem der ganze Prozess automatisiert wird. Die Automatisierung bezieht sich in diesem Fall auf die Programmierungstechniken, die automatische Zeichnung, statische Berechnung und Herstellung individueller Elemente möglich macht, wo der "manuelle" Prozess (ein Teil nach dem anderen) zu viel Zeit in Anspruch nehmen würde. Diese Revolution im Herstellungsprozess erlaubte eine größere Freiheit im Entwurf. So genannte Freiformen, wie sie hauptsächlich im Industriedesign verwendet werden, konnten nun auch in der Architektur zu erschwinglichen Kosten eingesetzt werden. Die Tatsache, dass die Generierung der Struktur auf Basis freier Formen zu lauter Einzelstücken führt, ist nicht länger ein Hemmnis. Aber mit der Freiheit kommt die Verantwortung und die Frage effizienten Entwerfens freier Formen ist die Grundlage der vorgelegten Forschung. Die Gitterschale ist eine Tragstruktur, bei welcher man versucht, das Verhalten einer Schale mit der Gitterform zu kombinieren. Die Kräfte sollen axial (mit so wenig Biegung wie möglich)über die Oberfläche verteilt werden und gleichzeitig soll dies mit einer Gitterstruktur geschehen, weil diese vorgefertigt und einfach zusammengesetzt werden kann. Dies erweist sich als gute Lösung, da Gitterschalen große Distanzen mit einer leichten einlagigen Konstruktionüberspannen können. Das Gitter, dasüblicherweise aus Stahlelementen besteht, ist oft mit Glas gedeckt, hoch transparent und somit geeignet für Dachkonstruktionen (Freiform-Dachkonstruktionen), wie in Bild 0.1 zu sehen. Gitterschalen werden gegenwärtig meist so entworfen, dass die Stäbe gleichmäßig verteilt werden (wie in den Beispielen in Bild 0.1). Aber schon die Intuition sagt uns, dass für eine unregelmäßige Form die beste und statisch wirksamste Verteilung nicht regelmäßig sein kann. Auch Tragwerkslösungen, die man in der Natur findet, zeigen uns, wie die Dichte in tragenden XI Zusammenfassung

Continuously curved, smooth full glass shells made from double curved glass elements are promising to meet the increasing demand for transparent free-form facades or roofs. As the dimensions of these glass elements are limited by material and manufacturing restrictions, structural joining is necessary to realise large shells. The resulting joint discontinuities weaken the desired membrane-state of the shell; the joint pattern layout thus has an important influence upon the load bearing behaviour and the appearance of the glass construction. Based on spring models of the joints, computational procedures are used to generate and optimise the joining layout of any input NURBS shell geometry. Aiming at the minimisation of particular joint forces, joining patterns beyond straight and regular appearance can thus be created inter-dependently on the global shell geometry, the joint stiffness and the glass element shapes as well as the applied loads.

International Journal of Electrical and Computer Engineering (IJECE), 2023

Gridshells are commonly known as structures with the shape and rigidity of a double curvature shell consisting of a grid, not a continuous surface. In recent decades, these structures have attracted significant attention. The impact of various geometric patterns on free form gridshell structures is investigated here to demonstrate the necessity of collaboration between structural and architectural characteristics in enhancing structure efficiency. To that goal, a framework is proposed where three shells are first designed, and then six geometric patterns are formed on them. The main factors for evaluation of gridshells are decreasing the steel weight as an economic index and decreasing the displacement as a structural index, also, finite element method is used for structurally analyzing the gridshells, and the generated gridshells are compared to each other based on the mentioned indices. For the optimization process, an approach is suggested to find the most optimum gridshell, then numerical results show the efficiency of the proposed alternative approach.

IOP Conference Series: Earth and Environmental Science, 2019

While it is of primary importance to deliver high performance architecture within constraints of time and money, the integration between structural and energy-based aspects presents significant challenges for the organisation of the design process, especially in the early stages. In the case of complex envelopes, such as glazed gridshells, these engineering-related aspects should be considered from multiple points of view from the very beginning of the concept development, exploiting the potential conflicts between architects and engineers to let creative solutions emerge, and thus avoiding expensive and time-consuming design modifications downstream. This paper aims to define the framework required to integrate a multi-objective optimisation capable of combining such aspects into an integrated flow of information. Such an integrated analysis presents difficulties because, in the early design phases, conceptual changes happen faster than computational capacity; so, to overcome this obstacle it is necessary to define an iterative flow of information between structural and energy-based procedures, while at the same time taking into account the aesthetic requirements. This particular flow not only guarantees a correct passage of technical data among different software tools, but it also allows for a better communication and comprehension of information between diverse actors, such as architects and engineers. Based on this specific plan, a conceptual framework for optimising gridshells under structural, geometrical and energy-based criteria is developed and presented. The final goal of such a procedure is not, clearly, to replace the designer, but to give guidance to transform potential conflict into creative discussion and improve the efficiency of the later phases of the design process.

Automation in Construction, 2004

The design and construction of free-form glass roofing structures is generally accomplished through the use of either planar triangular glass facets or curved (formed) glass panes. This paper describes ongoing research on the constructability of such structures using planar quadrilateral glass facets for the Jerusalem Museum of Tolerance project by Gehry Partners, in collaboration with Schlaich Bergermann & Partners, engineers. The challenge here lies not only in the development of a geometric strategy for generating quadrilateral planar facet solutions, but also in the fact that said solutions must closely match the designs created initially in physical model form by the architects.

Engineering Structures, 2013

This paper demonstrates a novel two-phase approach to the preliminary structural design of grid shell structures, with the objective of material minimization and improved structural performance. The two-phase approach consists of: (i) a form-finding technique that uses dynamic relaxation with kinetic damping to determine the global grid shell form, (ii) a genetic algorithm optimization procedure acting on the grid topology and nodal positions (together called the 'grid configuration' in this paper). The methodology is demonstrated on a case study minimizing the mass of three 24 Â 24 m grid shells with different boundary conditions. Analysis of the three case studies clearly indicates the benefits of the coupled form-finding and grid configuration optimization approach: material mass reduction of up to 50% is achieved.

Continuously curved, full glass shells have a large potential for application in freeform façades or roofs. Glass elements needed for such a construction can be fabricated either by heat bending or cold lamination bending. But as the curvature and size of glass laminates are limited by manufacturing restrictions, structural joining is necessary for assembling large shells. Unfortunately, such joint discontinuities conflict with the desired membrane state of the shell. The joint pattern layout has a large influence on the load bearing behaviour, stability and appearance of glass shells. Hence, computational procedures have been used to optimise the joint geometry layout by targeting either at minimising particular joint forces or by following the principal membrane force trajectories of the shell.

Meccanica, 1979

Questa metodologia deriva dal concerto per cui inverte41do la forma di una rete sospesa si ottiene pet" il guscio grigliato corrispondente la forma ottimale. La nota vuol porte attenzione sul fatto che ci6 non viene verificato quando le condizioni di carico che il guscio deve sostenere siano pili d'una. Attraverso una proeedura di calcolo automatizzata si arriva, con un suecedersi di perturbazioni della forma iniziale della rete sospesa, a trovare la geometria che porta all'effettivo minimo di materiale per la struttura del guscio progettato. Questo aw,iene sotto alcuni vincoli di tipo costruttivo,, per esempio lunghezza costante delle aste hlterne e sezioni trasversali delle aste del guscio scelte entro un ¢¢sagomario)) prestabilito.