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.
A Study on Cutting Pattern Generation of Membrane Structures Using Spline Curves
