Investigating improving of the geometric regularity of the Ati Center Mashhad Space Structure

The definition of regularity is different as it has different goals. Most engineers agree that a space structure is regular if a high percentage of its elements (sides) are equal or almost equal. There are several ways for improving regularity of the space structures, In this regard, Professor Nooshin et al used methods such as Traviation Process, Stepping Projection, Recursive techniques and etc to create a special category of structures (domes and flats) and they presented grid shells that were designed in a multimodal way. They defined regularity indicators quantitatively which are known as degrees of regularity or geometric parameters or regularity measuring meters. The regularity in this research is related to the increase of elements with equal or almost equal length, reduction the number of elements with different lengths, and the reduction of the number of length intervals while maintaining the geometry of the form. The freeform space structure of Ati Center were designed by the engineers of the Ofogh Noor Space Structures Company by using a single layer grid in Rhino software. This study aims to investigate the previous regularity indicators and improving regularity of this structure with triangulation techniques and proposed algorithm which is the optimization of Delaunay triangulation obtained from 176 random points with the help of circle packing algorithm and octopus optimization to reach a suitable pattern. Also we have presented algorithms to calculate the regularity indices and we have calculated them for each structure, investigated the improving regularity and we have suggested the general definition of regularity index and we have shown that the definitions of regularity indices alone are not the basis for evaluating the regularity of two structures. So a unique definition is needed. The result of this research is effective in solving problems related to form selection, improving regularity.