Application of Gradient Projection Method to Parametric Optimization of Steel Lattice Portal Frame

Abstract

The paper has proposed a mathematical model for parametric optimization problem of the steel lattice portal frame. The design variable vector includes geometrical parameters of the structure (node coordinates), as well as cross-sectional dimensions of the structural members. The system of constraints covers load-carrying capacities constraints formulated for all design sections of structural members of the steel structure subjected to all ultimate load case combinations. The displacements constraints formulated for the specifiednodes of the steel structure subjected to all serviceability load case combinations have been also included into the system of constraints. Additional requirements in the form of constraints on lower and upper values of the design variables, constraints on permissible minimal thicknesses, constraints on permissible maximum diameter-to-thickness ratio for the structural members with circle hollow sections, as well as the conditions for designing gusset-less welded joints between structural members with circle hollow sections have been also considered in the scope of the mathematical model. The method of the objective function gradient projection onto the active constraints surface with simultaneous correction of the constraints violations has been used to solve the formulated parametric optimization problem. New optimal layouts of the steel lattice portal frame by the criterion of the minimum weight, as well as minimum costs on manufacturing and erection have been presented.

Optimization of cross-section dimensions of structural members made of cold-formed profiles using compromise search

“…Thus, in paper [1], the problem of finding the optimal length of a single edge fold for C-shaped cold-formed profiles operating under axial compression conditions is considered. The objective function and constraints of the mathematical model are presented by the author as continuously differentiated functions, which made it possible to solve the problem of parametric optimization by a nonlinear method of gradient projection [11,12]. A similar optimization problem was also considered in [13], where the authors applied a genetic algorithm to solve it.…”