Mathematical optimization and engineering applications

Kulcsár T., Timár I.
PDF icon 2016_3_1_059_078.pdf852.22 KB
New challenges raised almost in all segments of the global economy in the last two decades. The energy-, finance-, environmental crises, as well as the intensive use of natural resources require new design methods in the engineering activity, for both the product design and the manufacturing process planning. An effecting tool to be competitive is to apply the optimum design methods to the engineering tasks. This paper reviews the different methods of mathematical optimization, which are widely used for solving engineering problems, and describes the application of this method for two different cases. The first sample shows how to find the optimal dimensions of the welded, box type frame of a freight bogie, which will minimize the manufacturing cost of the structure and will satisfy several restrictions, e.g. mechanical stress limit, dimensional constraints, buckling, and fatigue conditions. The other case is to find the optimal geometric dimensions of a pipe insulation system which will result in a minimum investment and operating cost, when the heat loss and the outside surface temperature are restricted.
  1. Xie Y. M., Steven G. P. Evolutionary structural optimization. Springer, London (1997).
  2. Farkas J. Optimum design of metal structures, Academic Publisher, Budapest (1984).
  3. Antoniou A., Lu W. S. Practical optimization. Springer, New York (2007).
  4. Schumacher A. Optimization of mechanical structures. Springer, Berlin (2013), (In German).
  5. Dantzig G. B. Linear programming and extensions. Princeton University Press (1998).
  6. Belegundu A. D., Chandrupatla T. R. Optimization concepts and applications in engineering. Upper Sadle River. Prentice Hall (1999).
  7. Spillers W. R., MacBain K. M. Structural optimization. Springer, New York (2009).
  8. Kuhn H. W., Tucker A. Nonlinear programming. Proc. of the Second Berkeley Symposium on Mathematical Statistics and Probability. University of California Press, Berkeley, 481–490 (1951).
  9. Rao S. S. Optimization, Theory and applicatons. Wiley, New Delhi (1984).
  10. Schmit L. A. Structural design by systematic synthesis. Proc. of the Second Conference on Electronic Computation. ASCE, New York, 105–122 (1960).
  11. Caroll C. W. The created response surface techniques for optimizing nonlinear, restrained systems. Operations Research. 9, n. 2, 169–184 (1961).
  12. Fiacco A. V., McCormick G. P. Nonlinear programming: sequential unconstrained minimization techniques. Wiley, New York (1968).
  13. Wang L., Ng. A. H. C., Deb K. Multi-objective evolutionary optimization for product design and manufacturing. Springer, London (2011).
  14. Timár I. Optimierung ebener Fachwerke mit mehreren Zielfunktionen. Forschung im Ingenieurwesen. 68, n. 3, 121–125 (2004), (In German).
  15. Li W., Han Y. Multi-objective optimum design of structures. (Eds. Hernadez S., El-Sayed M., et al. Structural optimization. Computation Mechanics Publications), Southampton. 8, 35–42 (1995).
  16. Rao V. R., Savsani V. J. Mechanical design optimization using advenced optimization techniques. Springer, London (2012).
  17. Geike T., Parchem R. Genetische Algorithmen zur Optimierung von Schraubenverbindungen. Konstruktion. N. 1/2, 48–52 (2003), (In German).
  18. Pohlheim H. Evolutionäre Algorithmen – Verfahren, Operatoren, Hinweise aus der Praxis. Berlin, Heidelberg, New York: Springer-Verlag (1999), (In German).
  19. Yang X. S. Nature-inspired metaheuristic algorithm. Luniver Press (2008).
  20. Macsák G. Z., Jármai K. Solving constrained structural optimization problems with heuristic methods. GEP. N. 5, 25–32 (2014), (In Hungarian).
  21. Bendsoe M. P. Optimization of structural topology, shape, and material. Springer, Berlin (1995).
  22. Kulcsár T., Timár I. Mathematical optimization in design – Overwiew and application. Acta Technica Corviniensis Buletin of Engineering. Tome V. Fascicule 2, 21–26 (2012).
  23. Affolter Chr., Weisse B. Strukturoptimierung: Topologie- und Formoptimierung für ein effizientes Produktdesign. Konstruktion. N. 7/8, 59–61 (2001), (In German).
  24. Meske R., Sauter J., Gülzer Ph. Topologieoptimierung einer Linearführung mit TOSCA und ABAQUS. Konstruktion. N. 9, 52–54 (2001), (In German).
  25. Klein M. Form optimization with higher-order finite element methods FEM of continuum structures. VDI Verlag. Düsseldorf. (2000). (In German).
  26. Timár I., Horváth P., Borbély T. Optimierung von profilierten Sandwichbalken. Stahlbau. No. 2, 109–113. 72(2003). (In German).
  27. Timár I., Torski A., Schsukin V. About an optimum choise of parameters of the loaded three-layer plates by criterion of cost. Physiko-Mathematical Modelling and Informational Technologies. 10, 132–137 (2009), (In Ukrainian).
  28. Timár I., Horváth P. Optimal design of pipelines and spherical tank. Annals of the University of Oradea. Fascicle of Management and Technological Engineering. ISSUE #3, 57–60 (2014).
  29. Kulcsár T., Timár I. Optimization of a welded main frame of freight bogies considering to EN 13 749 standard. Deisign, Fabrication and Economy of Meteal Structures. International Conference Proceedings 2013. Miskolc, Hungary, April 24–26, 2013 (Eds. Jármai K., Farkas J.). Springer, Heidelberg (2013).
  30. Farkas J., Jármai K. Design and optimization of metal structures. Horwood Publishing, Chichester (2008).
  31. Timár I. Optimierung der Isolierstärke von Rohrleitungen. Forschung im Ingenieurwesen. 68, n. 2, 96–100 (2003), (In German).
Math. Model. Comput. Vol.3, No.1, pp.59-78 (2016)