Optimization of Steel Roof Framing Taking into Account the Random Nature of Design Parameters

Abstract

The main subject of this paper is an optimization of steel roof framing used as a load-bearing structure in commercial pavilions. The authors wanted to draw attention to the necessity to take into account the uncertainty in the description of design parameters during optimization. In the first step, using geometrically nonlinear relationships, a static-strength analysis is performed. The decisive form of loss of stability in this steel roof framing is the jump of the node (snap-through), and not the buckling of the most stressed structure bars. Therefore, when creating the limit function, it was decided to make a condition limiting the permissible displacement. Values of the implicit limit function were calculated with Abaqus software based on the finite element method. Reliability analysis, and robust and deterministic optimization were performed using Numpress Explore software. Numpress Explore software communicates with the Abaqus software to perform analysis. The task ended with the generation of information that contained the failure probability, reliability index and the values of optimized areas of the bars’ cross-sections. The end result of the optimization is not a cost analysis, but an assessment of the safety of the structure.

The comparison of robust and reliability based design optimization

“…Appropriate approximation of the objective function and constraints is crucial for the effectiveness and convergence of the analyzes performed. The work uses the kriging method in its approximation version along with an experimental plan based on the concept of the optimal Latin hypercube and random sampling (Simpson et al, 2001;Liefvendahl and Stocki, 2006;Zabojszcza and Radoń, 2022).…”