Andrew Borgart

• Delft University of Technology

During his live Heinz Isler built around 1400 shell structures. In July of 2012 Borgart and Eigenraam from Delft University of Technology went to Isler’s office during two days to make 3D scans of his scale models. His scale models were being inventoried so they could be taken to the ETH Zurich to be studied and archived. This paper presents the pr...

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 me...

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 second 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 co...

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 second 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 co...

This paper presents a detailed structural analysis of a bubble shell engineered by Heinz Isler. Through 3D scanning the geometry of this shell structure has become available to the authors. Structural analysis has not been possible before since the geometry of the shell was not available. The bubble shell was Isler’s most built type of shell. In th...

The mechanical performance of grid shells is dependent on their structural geometry and is related to the loads exerted on them. By making use of the close relationship between the design parameters for hanging models and computational form-finding, the shape optimization of grid shells considering their mechanical performance under various loading...

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 s...

This is the abstract for a paper to be presented at IASS 2019 in the session of "CS – Computational Methods I" on Monday, October 7.

During the minor course Bend and Break (CT3270-15) at Delft University of Technology (TU Delft), a workshop is developed by the authors, in which students are asked to manufacture and test a reinforced gypsum shell generated from hanging models. Before the workshop, material tests of the dried gypsum, design and test of the loading system, and othe...

Shell structures generated from hanging models have structurally efficient forms. Form-control of these shells, which aims to obtain structural forms with single- and multiple target heights due to some architectural requirements, is discussed in this article. First, the vector form intrinsic finite element method is applied to generate the equilib...

Firefly Algorithm (FA, for short) is inspired by the social behavior of fireflies and their phenomenon of bioluminescent communication. Based on the fundamentals of FA, two improved strategies are proposed to conduct size and topology optimization for trusses with discrete design variables. Firstly, development of structural topology optimization m...

Vector form intrinsic finite element is a recently developed and promising numerical method for the analysis of complicated structural behavior. Taking the cable-link element as example, the framework of the vector form intrinsic finite element is explained first. Based on this, a constant strain triangle element is introduced, and relevant require...

Based on its structural principle, the form of a hanging model is self-forming and capable of transferring its self-weight and area load solely by means of tension, and when it is turned upside down a pure compression model arises. Isler H. designed many shells by using this kind of models but with relatively limited structural forms. Recently, the...

Due to its wide range of related research contents and diversified research approaches, the term 'Structural Morphology' has not been clearly defined by the Structural Morphology Group (SMG) of the International Association for Shells and Spatial Structures (IASS), founded in 1991, although some scholars have given their own viewpoints. This paper...

Many free form shell structures that have been designed and build in previous decades are fascinating structures. We can learn from these structures by analysing them and studying their structural behaviour. However, in some cases the geometry of these structures is not available; most notably the shapes of shell structures designed and build by He...

Hanging models play an important role in shaping a structure since a very early age, and were favored by A. Gaudi, H. Isler, F. Otto and other architects or engineers. Nowadays, with the development of numerical analysis theory and computer technique, it is more accurate and convenient to simulate these physical models via numerical means. Based on...

Discrete networks is a kind of form-active structural system which actively change its shape under varying load conditions. And for this kind of structural system, form-finding is the initial and essential part in their design process. Before the computer age, people complete the form-finding process using physical models, while with the advances i...

This paper proposes an efficient and reliable topology optimization method that can obtain a black and white solution with a low objective function value within a few tens of iterations. First of all, a transformation of variables technique is adopted to eliminate the constraints on the design variables. After that, the optimization problem is cons...

The International Association for Shell and Spatial Structures (IASS) Working Group 15, Structural Morphology (SMG) held its 7th International Seminar in September of 2011, in London. There were 23 oral presentations and papers and around 100 attendees. Per Dombernowsky and Asbjøm Søndergaard used topology optimization to design a concrete slab str...

The method presented solves statically indeterminate force networks, which are graphical representations of forces (force polygons) of a structure, by using complementary energy. Statically indeterminate force networks, which have nodes where four or more members come together, have for each node multiple possible force polygons that make equilibri...

During the last decade an increasing amount of complex geometry structures have been built. Building these complex structures in an efficient and economic way has posed considerable problems for engineers and construction companies. Computational design tools and form finding / optimization methods can assist in rationalizing the engineering and co...

Air inflated cushions are being used more and more as light roofs for large span structures, such as the Eden Project in Cornwall, UK (fig. 1). Most of the air inflated cushions are made of FTFE foil. Because air inflated cushions are form active structures they are subjected to geometric non-linear behaviour. This is usually dealt with by calculat...

p. 611-617 The purpose of this research is to analyze the structural behaviour of shell structures by studying the way (applied) loads naturally flow through shell structures to their supports and relating this flow off forces to the shell geometry. To unlock this secret will give a fundamental understanding of the behaviour of shell structures and...

In recent years more and more complex buildings have been appearing using more and more free forms. In our research we assume that it is possible to achieve the architectural desired free forms by manipulation of structural membranes. To prove this we have designed a Ski run. The shape of the Ski run is designed by making a physical model of balloo...