Minlp Optimization of Steel Frames

Abstract

ABSTRACT:The paper presents the discrete dimension optimization of unbraced rigid steel plane frames. The optimization of steel frames was carried out by the Mixed-Integer Non-linear Programming (MINLP) approach. The MINLP is a combined discrete-continuous optimization technique. It performs the discrete optimization of discrete decisions simultaneously with the continuous optimization of continuous parameters. The task of the optimization is to minimize the mass of the frame structure and to find the optimal discrete sizes of standard steel sections for frame members. The finite element equations are defined as the equality constraints for the second-order elastic structural analysis. The design constraints for the steel members were formulated according to Eurocode 3. The Modified Outer-Approximation/ Equality-Relaxation algorithm and a two-phase MINLP optimization approach were applied for the optimization. The latter starts with the continuous optimization of the frame, while the standard dimensions are temporarily relaxed into continuous parameters. When the optimal continuous solution is found, standard sizes of cross-sections are re-established and the simultaneous continuous and discrete dimension optimization by MINLP is then continued until the optimal solution is found. A numerical example of the optimization of a steel frame is presented at the end of the paper to show the suitability of the proposed approach.

Mixed-integer Non-linear Programming in Civil Engineering

“…A number of problems in the area of structural optimization were solved with the presented MINLP approach: e.g. hydraulic steel gates for dams and hydro-power plants by Kravanja et al [15,16], steel and aluminum trusses by Šilih et al [18], timber truss structures by Šilih et al [19,20], multi-storey steel frame buildings by Klanšek et al [21], single-storey industrial steel buildings by Kravanja and Žula [22] and Kravanja et al [23], composite I-beam structures from concrete and steel by Kravanja and Šilih [24], Klanšek and Kravanja [25,26], Žula et al [27] and Kravanja et al [28] as well as timber-concrete composite floors by Jelušič and Kravanja [29]. A recent research work is also referred in the field of MINLP optimization of project schedules by Klanšek [30] and Cajzek and Klanšek [31].…”

Mixed-integer Non-linear Programming in Civil Engineering

“…hydraulic steel gates for dams and hydro-power plants by Kravanja et al. [15,16], steel and aluminum trusses by Šilih et al [18], timber truss structures by Šilih et al [19,20], multi-storey steel frame buildings by Klanšek et al [21], single-storey industrial steel buildings by Kravanja and Žula [22] and Kravanja et al [23], composite I-beam structures from concrete and steel by Kravanja and Šilih [24], Klanšek and Kravanja [25,26], Žula et al [27] and Kravanja et al [28] as well as timber-concrete composite floors by Jelušič and Kravanja [29]. A recent research work is also referred in the field of MINLP optimization of project schedules by Klanšek [30] and Cajzek and Klanšek [31].…”