This paper analyzes the basic geometric and kinematic characteristics of auxetic structures. The geometric principles are then transferred to a family of new possible forms. We investigate and elaborate auxetic behavior in a purely geometric way which is based on the kinematic movement of different frameworks. We then demonstrate its usefulness by analyzing the involved geometry with computer software but without computer simulations or numerical approximations. Instead, using cut flat material and, depending on the cuts and the material used, we enable the kinematical movement of the structures. We also analyze monostable auxetic structures whose movements can be described as geometrically precise, as well as bistable ones. Based on geometric considerations, we combine rigid materials and composites and select appropriate joint connections to allow the application of this system in an architectural scale in, for example, facades, screens or shading systems.Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.Milena Stavric PhD, is a teacher and researcher at Graz University of Technology. She obtained a PhD (Architecture) with the focus on higher order geometrical curves in architecture from University of Belgrade. She is interested in geometric structures and their application in architecture.Albert Wiltsche PhD, is a teacher and researcher at Graz University of Technology. He obtained a PhD in Geometry with the focus on freeform structures. He has a strong interest in geometric architecture.
In this paper we will do investigations on spatial quadrilateral meshes developed from folding patterns. The simplicity of manual production in combination with the geometrical complexity of paper folding shall lead to an inspiration for designing architectural structures.We propose geometrical methods for designing these quadrilateral structures which follow in their shape geometrical surfaces. Our methods use folding patterns where only four folding lines meet in one node and every quadrangular part stays flat.This enables simpler solutions for architectural realization in a big scale especially for join connections and assembling of the whole spatial and structural system. In order to understand and handle the complexity of paper folding we use CAD tools to model the structures where the entire folding element is reconstructed and its geometric characteristics are controlled.This kind of control reflects on scale models. Models are then adjusted, examined and built to reach certain further geometric conclusions that are once more tested in CAD software.
Folding structures belong to the group of lightweight structural systems, which often consist of polygonal elements like triangles or quadrangles. Folding structures whose construction is made out of cross-laminated timber (CLT) panels represent an innovative step in the timber industry, which has many advantages. CLT panels can be used simultaneously as supporting elements and as finishing building envelopes. There are many prefabrication possibilities, high efficient material consumption, low production and assembly costs, and it has environmental advantages over conventional materials used for folding structure like concrete, metal or glass. CLT folding structures are not sufficiently explored. One of the reasons may lie in the fact of limited design possibilities, which includes the specificity of CLT capacity. Another reason is maybe the inability to use standard wooden connectors to transfer the forces along the thin linear edges where the panels are supported. The aim of this paper is to present design possibilities through parametric modelling using the characteristics of CLT. Using the example of a wooden theatre stage we will present results of our research.
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