Creation of mathematical model optimization of Freeform Double-Layer Grids for use in the software package

Abstract

It is known that metal spatial coatings can be made in shape of spatial structures, folded dual-slope structures, double mesh grid shells, double-layer braced barrel vaults, double-layer braced domes, free-form spatial structures, etc. In this paper we consider constructions on a rectangular base. The shape of the structure and distribution of material inside it are defined by solving the parametric optimization task. In the task, it has been assumed that the geometric shape of the structure can take the shape of a free-form spatial structures. A mathematical model of parametric optimization task has been presented. The task may be formulated as the discrete optimization task. The quality criterion is the minimum mass of the structure. The objective function is written through the task parameters. The analysis of permissible geometric forms of structures was made. Based on this analysis, the functions of restrictions are recorded through the parameters of the task. The restrictions are compressed by including them into objective function. As a result, a mathematical description of the objective function for the task of parametric optimization in an unconditional formulation was proposed.