ON OPTIMUM DESIGN OF FRAME STRUCTURES

Authors

  • Marek Tyburec Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mechanics, Thákurova 7, 166 29 Prague 6, Czech Republic
  • Jan Zeman Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mechanics, Thákurova 7, 166 29 Prague 6, Czech Republic Czech Academy of Sciences, Institute of Information Theory and Automation, Department of Decision-Making Theory, Pod vodárenskou veží 4, 182 08 Prague 8, Czech Republic
  • Martin Kružík Czech Technical University in Prague, Faculty of Civil Engineering, Departement of Physics, Thákurova 7, 166 29 Prague 6, Czech Republic Czech Academy of Sciences, Institute of Information Theory and Automation, Department of Decision-Making Theory, Pod vodárenskou veží 4, 182 08 Prague 8, Czech Republic
  • Didier Henrion University of Toulouse, LAAS-CNRS, 7 Avenue du Colonel Roche, 31400 Toulouse, France Czech Technical University in Prague, Faculty of Electrical Engineering, Department of Control Engineering, Karlovo námestí 13, 121 35 Prague 2, Czech Republic

DOI:

https://doi.org/10.14311/APP.2020.26.0117

Keywords:

Frame structures, global optimum, polynomial optimization, semidefinite programming, topology optimization.

Abstract

Optimization of frame structures is formulated as a non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii) optimality criteria method, (iii) non-linear semidefinite programming, and (iv) polynomial optimization. We show that polynomial optimization solves the frame structure optimization to global optimality by building the (moment-sums-of-squares) hierarchy of convex linear semidefinite programming problems, and it also provides guaranteed lower and upper bounds on optimal design. Finally, we solve three sample optimization problems and conclude that the local optimization approaches may indeed converge to local optima, without any solution quality measure, or even to infeasible points. These issues are readily overcome by using polynomial optimization, which exhibits a finite convergence, at the prize of higher computational demands.

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Published

2020-03-17

Issue

Vol. 26 (2020): NMM 2019 Nano & Macro Mechanics

Section

Articles

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