Study Of The Method About The Geodesic Line Generation During The Cutting Design Of A Membrane Structure Based On The Extreme Optimization Of Objective Function Theory

As a new rising large-span spatial structure, membrane structure gets wide attention since inception for its light weight, large span and easy installation. China started late on the field of membrane structure. The research lags far behind the world advanced level both in theory and technology.Improving and deepening the existing theoretical system as well as exploring more optimized techniques, are the starting and footing point of this article.The design process of a membrane structure includes three stages, form analysis, loading analysis and cutting pattern analysis. The analysis of cutting pattern forms a connecting link between form-finding and construction scheme, the importance of which is self-evident. The main achievement of cutting pattern analysis is the cutting- layout scheme, and the most critical part of the cutting- layout scheme is the choose of cutting-line. As the optimal cutting line between two known points on membrane surface, the generation method of the geodesic line is a very important subject which arouse attentions of membrane structure researchers.This article combines several mainstream geodesic line generation method, proposes the extreme optimization of the objective function method creatively. This method is based on classical variation method, it builds the objective function with the total length of geodesic line, determines the initial value of the iteration with the line projection method, expresses the node coordinates of the geodesic line with the node coordinates of the cable net and unknown location parameters to introduce in constraint conditions, calculates the variation of the objective function to find the variational equations of the total length, establishes the Newton-Raphson iterative equations, introduces the boundary conditions of the start and end points with the method of large numbers, solutes the equations with gauss elimination, controls the iterative process with three convergence rules, and comes up with an original method: the second projection method to improve the accuracy.We also crafted a program named GEO with the extreme optimization of the objective function method. Analyzed three typical examples calculated by this program, discussed the source and the affecting factors of error in detail. By this way, we can verify the commonality, efficiency and accuracy of GEO, meanwhile we can prove the correctness of the extreme optimization of the objective function method. Through the above-mentioned approach, a series of conclusions significant are given, which can provide valuable opinions and reference for design.