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Q. Li
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1
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.
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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.
Numerical inverse hanging method is a kind of efficient form-finding method which can generate shell structures free of bending moments under certain external loads. This paper proposes an improved numerical inverse hanging method based on the vector form intrinsic finite element (VFIFE), for improving the poor convergence performance of the existing method based on the nonlinear finite element method. By using VFIFE to find the equilibrium form of inverted structures and using the local linearization method to adjust the Young's modulus of cable elements, the form-control problem of inverted structures is solved. Moreover, a step rigidization method is proposed, which can realize the form-control of complex structures with multiple target points. Finally, the accuracy and efficiency of the numerical method is verified by observing one Isler's plaster model and comparing its physical shape with the numerical simulating result.
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Numerical inverse hanging method is a kind of efficient form-finding method which can generate shell structures free of bending moments under certain external loads. This paper proposes an improved numerical inverse hanging method based on the vector form intrinsic finite element (VFIFE), for improving the poor convergence performance of the existing method based on the nonlinear finite element method. By using VFIFE to find the equilibrium form of inverted structures and using the local linearization method to adjust the Young's modulus of cable elements, the form-control problem of inverted structures is solved. Moreover, a step rigidization method is proposed, which can realize the form-control of complex structures with multiple target points. Finally, the accuracy and efficiency of the numerical method is verified by observing one Isler's plaster model and comparing its physical shape with the numerical simulating result.
Form Follows Force
A theoretical framework for Structural Morphology, and Form-Finding research on shell structures
With the springing up of freeform architectures, the key problem to structural engineers is to generate structural forms with high structural efficiency subject to the architectural space constraints during the conceptual design process. In this research, a theoretical framework for Structural Morphology has been proposed, that provides an effective solution to the problem. To enrich the proposed framework, systematic Form-Finding research on shell structures is conducted.
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With the springing up of freeform architectures, the key problem to structural engineers is to generate structural forms with high structural efficiency subject to the architectural space constraints during the conceptual design process. In this research, a theoretical framework for Structural Morphology has been proposed, that provides an effective solution to the problem. To enrich the proposed framework, systematic Form-Finding research on shell structures is conducted.
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 equilibrium form of hanging membranes and thus shell structures. Subsequently, the form-control problem is discussed, which aims to generate a structural form subject to given target height constrains. By introducing the Local Linearization Method to adjust Young’s modulus of the initial structural model, a form-control strategy to generate the equilibrium structural form with a single target height is proposed. By introducing the Inverse Iteration Method to adjust the geometry of the initial model, a form-control strategy to generate the equilibrium structural form with several target heights is proposed. Moreover, to verify the effectiveness of the vector form intrinsic finite element method and form-control strategies, structural analyses and shell behavior assessment of these shells are conducted. These strategies are effective and efficient, which can help architects or engineers to determine structurally efficient geometries in the design process much more easily.
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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 equilibrium form of hanging membranes and thus shell structures. Subsequently, the form-control problem is discussed, which aims to generate a structural form subject to given target height constrains. By introducing the Local Linearization Method to adjust Young’s modulus of the initial structural model, a form-control strategy to generate the equilibrium structural form with a single target height is proposed. By introducing the Inverse Iteration Method to adjust the geometry of the initial model, a form-control strategy to generate the equilibrium structural form with several target heights is proposed. Moreover, to verify the effectiveness of the vector form intrinsic finite element method and form-control strategies, structural analyses and shell behavior assessment of these shells are conducted. These strategies are effective and efficient, which can help architects or engineers to determine structurally efficient geometries in the design process much more easily.
Conference paper
(2017)
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Yue Wu, Xiuming Liu, Qingpeng Li, Boxuan Chen, Peng Luo, Arno Pronk, Elke Mergny
By using inflatable moulds and then spraying cellulose-water mixture, one ice dome and two ice towers were built in Harbin in December 2016. During the whole process, form-finding of the inflatable moulds as well as the construction of these ice composite shell structures are very important for the final results.
The mould for the ice dome structure was a result of the manipulation of a synclastic membrane with a rope net. The mould for the ice tower structure consisted of some anticlastic surfaces. Form-finding of the inflatable moulds was conducted by the parametric tool “EasyForm” which is a self-programed plug-in in Grasshopper based on Vector Form Intrinsic Finite Element method.
In a low-temperature work environment (-10 ℃ and below), the ice shell structures were constructed on the inflatable moulds. The cellulose-water mixture was sprayed in thin layers continuously and uniformly in order to make the surface of a shell of cellulose-reinforced ice. The construction process is introduced detailedly in this paper.
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By using inflatable moulds and then spraying cellulose-water mixture, one ice dome and two ice towers were built in Harbin in December 2016. During the whole process, form-finding of the inflatable moulds as well as the construction of these ice composite shell structures are very important for the final results.
The mould for the ice dome structure was a result of the manipulation of a synclastic membrane with a rope net. The mould for the ice tower structure consisted of some anticlastic surfaces. Form-finding of the inflatable moulds was conducted by the parametric tool “EasyForm” which is a self-programed plug-in in Grasshopper based on Vector Form Intrinsic Finite Element method.
In a low-temperature work environment (-10 ℃ and below), the ice shell structures were constructed on the inflatable moulds. The cellulose-water mixture was sprayed in thin layers continuously and uniformly in order to make the surface of a shell of cellulose-reinforced ice. The construction process is introduced detailedly in this paper.
Conference paper
(2017)
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Arno Pronk, Peng Luo, Qingpeng Li, Fred Sanders, Marjolein Overtoom, Lancelot Coar
There has been a long tradition in making ice structures, but the development of technical improvements for making ice buildings is a new field with just a handful of researchers. Most of the projects were realized by professors in cooperation with their students as part of their education in architecture and civil engineering. The following professors have realized ice projects in this setting: Heinz Isler realized some experiments since the 1950s; Tsutomu Kokawa created in the past three decades several ice domes in the north of Japan with a span up to 25 meters; Lancelot Coar realized a number of fabric formed ice shell structures including fiberglass bars and hanging fabric as a mould for an ice shell in 2011 and in 2015 he produced an fabric-formed ice origami structure in cooperation with MIT (Caitlin Mueller) and VUB (Lars de Laet)[4]. Arno Pronk realized several ice projects such as the 2004 artificially cooled igloo, in 2014[1] and 2015[2] dome structures with an inflatable mould in Finland and in 2016 one ice dome and two ice towers in Harbin (China) as a cooperation between the Universities of Eindhoven & Leuven (Pronk) and Harbin (Wu and Luo).
In this paper we will present the motivation and learning experiences of students involved in learning-by-doing by realizing one large project in ice. The 2014-2016 projects were evaluated by Sanders and Overtoom[3] using questionnaires among the participants by mixed cultural teams under extreme conditions. By comparing the results in different situations and cultures we have found common rules for the success of those kinds of educational projects. In this paper we suggest that the synergy among students participating in one main project without a clear individual goal can be very large. The paper will present the success factors for projects to be perceived as a good learning experience.
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There has been a long tradition in making ice structures, but the development of technical improvements for making ice buildings is a new field with just a handful of researchers. Most of the projects were realized by professors in cooperation with their students as part of their education in architecture and civil engineering. The following professors have realized ice projects in this setting: Heinz Isler realized some experiments since the 1950s; Tsutomu Kokawa created in the past three decades several ice domes in the north of Japan with a span up to 25 meters; Lancelot Coar realized a number of fabric formed ice shell structures including fiberglass bars and hanging fabric as a mould for an ice shell in 2011 and in 2015 he produced an fabric-formed ice origami structure in cooperation with MIT (Caitlin Mueller) and VUB (Lars de Laet)[4]. Arno Pronk realized several ice projects such as the 2004 artificially cooled igloo, in 2014[1] and 2015[2] dome structures with an inflatable mould in Finland and in 2016 one ice dome and two ice towers in Harbin (China) as a cooperation between the Universities of Eindhoven & Leuven (Pronk) and Harbin (Wu and Luo).
In this paper we will present the motivation and learning experiences of students involved in learning-by-doing by realizing one large project in ice. The 2014-2016 projects were evaluated by Sanders and Overtoom[3] using questionnaires among the participants by mixed cultural teams under extreme conditions. By comparing the results in different situations and cultures we have found common rules for the success of those kinds of educational projects. In this paper we suggest that the synergy among students participating in one main project without a clear individual goal can be very large. The paper will present the success factors for projects to be perceived as a good learning experience.
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 method and the basic principle of standard FA are introduced in detail. Then, in order to apply the algorithm to optimization problems with discrete variables, the initial positions of fireflies and the position updating formula are discretized. By embedding the random-weight and enhancing the attractiveness, the performance of this algorithm is improved, and thus an Improved Firefly Algorithm (IFA, for short) is proposed. Furthermore, using size variables which are capable of including topology variables and size and topology optimization for trusses with discrete variables is formulated based on the Ground Structure Approach. The essential techniques of variable elastic modulus technology and geometric construction analysis are applied in the structural analysis process. Subsequently, an optimization method for the size and topological design of trusses based on the IFA is introduced. Finally, two numerical examples are shown to verify the feasibility and efficiency of the proposed method by comparing with different deterministic methods.
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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 method and the basic principle of standard FA are introduced in detail. Then, in order to apply the algorithm to optimization problems with discrete variables, the initial positions of fireflies and the position updating formula are discretized. By embedding the random-weight and enhancing the attractiveness, the performance of this algorithm is improved, and thus an Improved Firefly Algorithm (IFA, for short) is proposed. Furthermore, using size variables which are capable of including topology variables and size and topology optimization for trusses with discrete variables is formulated based on the Ground Structure Approach. The essential techniques of variable elastic modulus technology and geometric construction analysis are applied in the structural analysis process. Subsequently, an optimization method for the size and topological design of trusses based on the IFA is introduced. Finally, two numerical examples are shown to verify the feasibility and efficiency of the proposed method by comparing with different deterministic methods.
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 required equations are deduced. Subsequently, the vector form intrinsic finite element is successfully applied to carry out form-finding of shells generated from physical models, such as hanging models, tension models, and pneumatic models. In addition, the resulting geometries are analyzed with finite element method, thus demonstrating that a dominant membrane stress distribution arises when the shell is subjected to gravitational loading.
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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 required equations are deduced. Subsequently, the vector form intrinsic finite element is successfully applied to carry out form-finding of shells generated from physical models, such as hanging models, tension models, and pneumatic models. In addition, the resulting geometries are analyzed with finite element method, thus demonstrating that a dominant membrane stress distribution arises when the shell is subjected to gravitational loading.
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 presents a different way to understand the meaning of “Structural Morphology” and its connotations. Nowadays, numerical techniques have become the most important means to do research in the field of structural engineering, and they can assist in the design, analysis and optimization of structures by handling a large number of parameters. In this paper, we present a common conceptual scheme for these numerical analysis methods. The scheme classifies the parameters of the initial structural system into five categories and, with the aid of numerical analysis methods, leads to the structural performance of the final structure. Two simple numerical examples are shown to verify the rationality of the scheme. On this basis, a conceptual formula to describe 'Structural Morphology' is proposed, which contains the whole numerical analysis process, shows the goal of structural morphology and also suggests a suitable methodology. Moreover, since numerical form-finding and computational morphogenesis have become two main research foci of structural morphology, a basic introduction, methodology and some achievements related to each research focus are presented in this paper.
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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 presents a different way to understand the meaning of “Structural Morphology” and its connotations. Nowadays, numerical techniques have become the most important means to do research in the field of structural engineering, and they can assist in the design, analysis and optimization of structures by handling a large number of parameters. In this paper, we present a common conceptual scheme for these numerical analysis methods. The scheme classifies the parameters of the initial structural system into five categories and, with the aid of numerical analysis methods, leads to the structural performance of the final structure. Two simple numerical examples are shown to verify the rationality of the scheme. On this basis, a conceptual formula to describe 'Structural Morphology' is proposed, which contains the whole numerical analysis process, shows the goal of structural morphology and also suggests a suitable methodology. Moreover, since numerical form-finding and computational morphogenesis have become two main research foci of structural morphology, a basic introduction, methodology and some achievements related to each research focus are presented in this paper.
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 in computational techniques, the research has focused on the numerical form-finding methods since the 1960s. A brief discussion on several numerical formfinding methods is presented in this paper. Firstly, two relatively mature numerical method, Dynamic Relaxation method and Force Density method, are introduced conceptually. And then, a newly developed numerical method, the Vector Form Intrinsic Finite Element method, is presented in more detail. At last, with a replacement of the calculation of the internal force of the element which obeys the Hooke's Law by the product of the force density and the length of the element, two derived methods based on the above three methods are proposed in this paper. Moreover, several numerical examples of hanging networks are shown to illustrate the validity and characteristic of the VFIFE method and the two newly proposed derived methods.
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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 in computational techniques, the research has focused on the numerical form-finding methods since the 1960s. A brief discussion on several numerical formfinding methods is presented in this paper. Firstly, two relatively mature numerical method, Dynamic Relaxation method and Force Density method, are introduced conceptually. And then, a newly developed numerical method, the Vector Form Intrinsic Finite Element method, is presented in more detail. At last, with a replacement of the calculation of the internal force of the element which obeys the Hooke's Law by the product of the force density and the length of the element, two derived methods based on the above three methods are proposed in this paper. Moreover, several numerical examples of hanging networks are shown to illustrate the validity and characteristic of the VFIFE method and the two newly proposed derived methods.
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 the background, this paper presents a numerical form-finding method of gridshell structures generated from hanging-chain models by using Dynamic Relaxation method and the NURBS technique, which aims to obtain more complex structural forms with multiple control points.
This method uses global NURBS surface interpolation to describe the initial cable-net model passing through the given target points, which serve as the fitting points of the NURBS surface. The cable elements of the cable-net are not allowed to elongate after form-finding, and clearly, this kind of cable-nets belongs to geometrically unstable system, whose form-finding process of it has a very strong nonlinearity. To solve this problem, it uses the Dynamic Relaxation method, which can complete the form-finding of geometrically unstable systems but with some special sets, to get the equilibrium form of the hanging cable-net under the gravity. However, this structural form may no longer pass through the given target points, and then it introduces the inverse iteration method to adjust the coordinates of the fitting points of the NURBS, which actually means to find the initial structural form which after form-finding can just right meet the target requirements. At last, some numerical examples are presented to demonstrate the validity of the proposed method in this paper.
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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 the background, this paper presents a numerical form-finding method of gridshell structures generated from hanging-chain models by using Dynamic Relaxation method and the NURBS technique, which aims to obtain more complex structural forms with multiple control points.
This method uses global NURBS surface interpolation to describe the initial cable-net model passing through the given target points, which serve as the fitting points of the NURBS surface. The cable elements of the cable-net are not allowed to elongate after form-finding, and clearly, this kind of cable-nets belongs to geometrically unstable system, whose form-finding process of it has a very strong nonlinearity. To solve this problem, it uses the Dynamic Relaxation method, which can complete the form-finding of geometrically unstable systems but with some special sets, to get the equilibrium form of the hanging cable-net under the gravity. However, this structural form may no longer pass through the given target points, and then it introduces the inverse iteration method to adjust the coordinates of the fitting points of the NURBS, which actually means to find the initial structural form which after form-finding can just right meet the target requirements. At last, some numerical examples are presented to demonstrate the validity of the proposed method in this paper.