Geometrie‐Prinzipien für wirtschaftliche und effiziente Schalentragwerke (Teil 1)

Abstract

Es werden anschauliche Bildungsprinzipien für beliebig doppelt gekrümmte, sich aus ebenen Viereckelementen zusammensetzende Schalenflächen vorgestellt.Dadurch wird es möglich, trotz doppelter Flächenkrümmung ebene Verglasungen bzw. ebene Schalelemente einzusetzen, eine wesentliche Voraussetzung für wirtschaftliche verglaste, opak verkleidete oder betonierte Schalentragwerke.Graphic design principles for economic and efficient shell structures. This paper will present graphic design principles for randomly doublecurved shell structures composed of plane quadrangular elements. This procedure allows the use of plane glazing resp. plane formwork elements, a major prerequisite for the economic application of glazed, opaque or concrete spatial structures.

Marionette Meshes: Modelling free-form architecture with planar facets

“…Consider now that the components in x and y are fixed, like in the problem solved by the Marionette technique. We are looking for the height functions f z satisfying equation (3). Adopting the notation f u to denote differentiation of f with respect to u, equation 3is reformulated into…”

“…PQs have been identified by practicians as an important optimisation target for the construction of double curved surfaces, as they avoid using curved panels. 1 Several techniques for generating exact PQ-meshes were proposed, mostly relying on affine transformations, which preserve planarity, a notion illustrated in Pottmann et al 2 For example, Scale-trans surfaces , introduced in Schober, 3 use composition of two affine transformations: translation and homothetic transformations. The designer controls the shape with two curves, making the process highly intuitive.…”

Free-form structures from topologically interlocking masonries

“…The first free-form surfaces covered with planar quadrilaterals were translation surfaces [47]. They are generated by translating a curve along another curve, and are thus covered with planar parallelograms.…”

Fassaden mit komplexer Geometrie – am Beispiel des Enzo Ferrari Museums in Modena

“…Bei der klassischen Panelisierung einer doppelt gekrümmten Fläche erfolgt die Panelisierung in der Regel mithilfe von Translations-oder Streck-Trans-Flächen [2]. Dieser Ansatz wurde beispielsweise bei der Oberflächenabwicklung der Baku Flame Towers in Aserbaidschan (Architektur: HOK Architects) verfolgt [3].…”