Optimization of steel frames with the choice of materials’ grades with restrictions on general and local stability, strength and stiffness

Abstract

A computational scheme for the optimal design of steel flat frames made of thin-walled rods with closed cross sections has been developed. The structural elements’ total cost is minimized by searching for the materials’ grades and the rods’ cross sections sizes on the variable parameters’ discrete sets. The rods are separately grouped according to the condition of using one steel grade and the criterion for the cross sections’ identity. Active restrictions on the overall structural system’s stability, local stability of the rods’ walls, strength and stiffness are taken into account. The optimization process using a genetic algorithm using a mixed approach to the mutation procedure, a selection option that provides the inoperative design options, and a single-point crossing-over procedure for the simple exclusions from consideration is implemented. The deformable object stress-strain state analysis is carried out on the rod finite element model’s basis. The assessment of ensuring overall stability is carried out by checking the positive definiteness of the tangent stiffness matrix of a finite element system. Local stability using an analytical relationship for rectangular plates, generally subjected to compression-tension and bending in their plane is confirmed. The results of optimization of a three-span frame made of square pipes are presented. Steel grades and profiles were selected for the groups of the structural system’s rods.