Statistical modeling of the assembly of single-layer domes

Moscow State University of Civil Engineering, Yaroslavskoe shosse, 26, Moscow, 129337, Russia

^* Corresponding author: evglebed@mail.ru

Abstract

A special purpose software SBORKA was developed by the author, which is intended for numerical modeling of the assembly process of single-layer lattice domes with respect to random deviations in lengths of individual bars. The dispersion of the inaccuracies in the sizes of bars is consistent with the normal distribution law, and their values are limited by the tolerances corresponding to 3σ. The assembly of a single-layer dome frame is simulated by sequentially calculating the coordinates of its nodes based on the imitation of the connection in these nodes of individual bars. Imperfections in the lengths of the bars lead to the fact that the actual geometric shape of the dome frame will differ from the design shape. Reliable analysis of the nature of the possible errors of the frames of single-layer lattice domes can only be performed by multiple assembly simulations with subsequent statistical processing of the obtained results. For the implementation of numerical statistical simulation of the assembly, the algorithm of the software includes procedures for solving various spatial problems of computational geometry. Computational procedures implemented in the software for modeling the assembly process are described in this paper.