Cutting patterns of membrane structures

Abstract

Membrane structures are very lightweight and highly optimized structures. Due to the constant stress state, strength of materials is used optimally. In order to prevent the occurrence of large deformations even for small external loads, membrane structures are designed as a double curved surfaces and are stabilized by applying prestress. Minimal surfaces has zero mean curvature and the basic advantage is that the stress at all points and directions is equal and there are no extreme stresses anywhere on the surface. Also have minimal area for the given contour, so the weight and amount of material is reduced to minimum, which make them suitable for application in architecture. Practical realization involve process of cutting pattern generation, which divide surfaces in parts that are developable surfaces. When patterns are assembled and prestressed they provide three-dimensional surface. Ideally, the cutting lines should follow the geodesics lines. We use geodesics as the shortest path between two points on a surface. In the article we give method for finding shortest paths on polygonal representations of surfaces follows continual Dijkstra paradigm which, on some conditions, can give improved accuracy on a computer despite the restriction of available memory and execution time.