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.

The sensitivity analysis could be defined as a study of how the variability of the output parameter of the considered model can be distributed to its sources, actually, on the variability of the various input model parameters. It helps to identify the most important design parameters of a particular structure and to focus on them during the design and optimization process. This paper is focused on the application of stochastic sensitivity analysis of maximum equivalent stress and maximum mid-span deflection of timber-concrete composite beam. All input parameters were considered to be random variables. Latin Hypercube Sampling numerical simulation method was employed. The estimation of the sensitivity was derived from Spearman rank-order correlation coefficient.