A Spoked Wheel Structure for the World’s largest Convertible Roof – The New Commerzbank Arena in Frankfurt, Germany

Göppert, Knut; Stein, Michael

doi:10.2749/101686607782359155

Cited by 9 publications

(7 citation statements)

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“…Input model with constraints and Resulting constrained model in equilibrium external loads branch with force density bounds compression force, line weight proportional to the square root of the force branch without force density bounds tension force, line weight proportional to the square root of the force external force external force support node support node unsupported node constrained to position geometry of the input model unsupported node constrained to plane constraining plane structure. Inspired by an article by Göppert and Stein [30], describing the principle of pre-stressed "spoked wheel" roof structures for sports stadiums, the aim in this example is to design a pre-stressed wheel structure based on a given freeform surface. This is not an obvious goal as the geometry of both rings depend on each other.…”

Section: A Pre-stressed Cable-stayed Roofmentioning

confidence: 99%

Interactive Equilibrium Modelling

Lachauer

Block

2014

International Journal of Space Structures

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This paper presents a novel method for computer-aided equilibrium modelling of structures in early design stages. Based on the force density method, an iterative procedure is developed that enables the generation of spatial kinematic pin-jointed structures that are in equilibrium close to a given input geometry, while satisfying additional constraints on both geometry and forces. This method forms the core of an interactive form-finding process that consists of alternating steps of modelling and computational optimization. In each modelling step, the user is able to modify geometry, topology, external forces and constraints of the structure. In each optimization step, equilibrium is re-established while respecting the user-defined constraints. A prototype has been implemented within an existing CAD software package, and three examples illustrate the use of the presented method, ranging from a playful exploration of surprising shapes to the rationalization of structural geometry. The method allows to intuitively explore the formal freedom of spatial equilibrium shapes with mixed compression and tension forces, within hard, user-defined constraints. In conclusion, it is claimed that by providing interactive equilibrium modelling methods, the design of new, surprising spatial forms with efficient structural behaviour is facilitated.

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Section: A Pre-stressed Cable-stayed Roofmentioning

confidence: 99%

Interactive Equilibrium Modelling

Lachauer

Block

2014

International Journal of Space Structures

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“…Here, the individual geometric configurations vary significantly. Examples are retractable roofs of stadiums (e.g., the Commerzbank‐Arena in Frankfurt, Germany 10 ) or closing and opening of facade elements (e.g., the biomimetic facade element Flectofin 11 ), which contribute to energy efficiency of a building. But also in aviation, shape changes by morphing wings to improve efficiency of airplanes are investigated 12‐16 .…”

Section: Introductionmentioning

confidence: 99%

Constrained motion design with distinct actuators and motion stabilization

Sachse

Geiger

Bischoff

2021

Numerical Meth Engineering

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The design of adaptive structures is one method to improve sustainability of buildings. Adaptive structures are able to adapt to different loading and environmental conditions or to changing requirements by either small or large shape changes. In the latter case, also the mechanics and properties of the deformation process play a role for the structure's energy efficiency. The method of variational motion design, previously developed in the group of the authors, allows to identify deformation paths between two given geometrical configurations that are optimal with respect to a defined quality function. In a preliminary, academic setting this method assumes that every single degree of freedom is accessible to arbitrary external actuation forces that realize the optimized motion. These (nodal) forces can be recovered a posteriori. The present contribution deals with an extension of the method of motion design by the constraint that the motion is to be realized by a predefined set of actuation forces. These can be either external forces or prescribed length chances of discrete, internal actuator elements. As an additional constraint, static stability of each intermediate configuration during the motion is taken into account. It can be accomplished by enforcing a positive determinant of the stiffness matrix.

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“…This is, for example, the case for deployable and retractable structures. Prominent examples are the opening and closing of roofs, especially of stadiums (e.g., the Commerzbank‐Arena in Frankfurt, Germany 13 ) or adaptive folding bridges (e.g., the Kiel Hörn Footbridge in Kiel, Germany 14 ). But also adaptive façade elements, beyond conventional sun‐blinds, which can be opened and closed depending on the position of the sun and the control of interior daylight, belong to this kind of adaptive structures and may significantly contribute to the energy efficiency of a building 15 .…”

Section: Introductionmentioning

confidence: 99%

A variational formulation for motion design of adaptive compliant structures

Sachse

Bischoff

2020

Numerical Meth Engineering

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Adaptive structures are characterized by their ability to adjust their geometrical and other properties to changing loads or requirements during service. This contribution deals with a method for the design of quasi-static motions of structures between two prescribed geometrical configurations that are optimal with regard to a specified quality function while taking large deformations into account. It is based on a variational formulation and the solution by two finite element discretizations, the spatial discretization (the standard finite element mesh) and an additional discretization of the deformation path or trajectory. For the investigations, an exemplary objective function, the minimization of the internal energy, integrated along the deformation path, is used. The method for motion design presented herein uses the Newton-Raphson method as a second-order optimization algorithm and allows for analytical sensitivity analysis. The proposed method is verified and its properties are investigated by benchmark examples including rigid body motions, instability phenomena, and determination of inextensible deformations of shells.

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A Spoked Wheel Structure for the World’s largest Convertible Roof – The New Commerzbank Arena in Frankfurt, Germany

Cited by 9 publications

References 0 publications

Interactive Equilibrium Modelling

Interactive Equilibrium Modelling

Constrained motion design with distinct actuators and motion stabilization

A variational formulation for motion design of adaptive compliant structures

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