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Reliability Based Design Optimization for Multiaxial Fatigue Damage Analysis Using Robust Hybrid Method

  • A. Yaich (a1) (a2), G. Kharmanda (a3), A. El Hami (a2), L. Walha (a1) and M. Haddar (a1)...

Abstract

The purpose of the Reliability-Based Design Optimization (RBDO) is to find the best compromise between safety and cost. Therefore, several methods, such as the Hybrid Method (HM) and the Optimum Safety Factor (OSF) method, are developed to achieve this purpose. However, these methods have been applied only on static cases and some special dynamic ones. But, in real mechanical applications, structures are subject to random vibrations and these vibrations can cause a fatigue damage. So, in this paper, we propose an extension of these methods in the case of structures under random vibrations and then demonstrate their efficiency. Also, a Robust Hybrid Method (RHM) is then developed to overcome the difficulties of the classical one. A numerical application is then used to present the advantages of the modified hybrid method for treating problem of structures subject to random vibration considering fatigue damage.

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Corresponding author

*Corresponding author (ahmed.yaich@insa-rouen.fr)

References

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1. Pitoiset, X. and Preumont, A., “Spectral Methods for Multiaxial Random Fatigue Analysis of Metallic Structures,” International Journal of Fatigue, 22, pp. 541550 (2000).
2. Pitoiset, X., Rychlik, I. and Preumont, A., “Spectral Methods to Estimate Local Multiaxial Fatigue Failure for Structures Undergoing Random Vibrations,” Fatigue Fract Engng Mater Struct, 24, pp. 715727 (2001).
3. Weber, B., Labesse-Jied, F. and Robert, J., “Comparison of Multiaxial High Cycle Fatigue Criteria and Their Application to Fatigue Design of Structures,” Sixth International Conference on Biaxial/ Multiaxial Fatigue and Fracture, Lisbon (2001).
4. Wu, B., Ferraton, L., Robin, C., Mesmacque, G. and Zakarzewski, D., “Application de Critère de Fatigue Multiaxiale Aux Sturctures en Alliage D'aluminum,” Conference of G2RT, TILT (2003).
5. Pitoiset, X., “Méthodes Spectrales Pour une Analyse en Fatigue des Structures Métallique Sous Chargements Aléatoires Multiaxiaux,” PhD. Dissertation, Université Libre de Bruxelles, Bruxelles (2001).
6. Chang, T. P. and Liu, M. F., “Evaluation of Nonlinear System Parameters by Stochastic Spectral Method,” Journal of Mechanics, 23, pp. 269274 (2007).
7. Arora, J., Introduction to Optimum Design, McGraw-Hill, New York (1989).
8. Haftaka, R. and Gurdal, Z., Elements of Structural Optimization, Kluwer Academic Publications, Dordrecht (1991).
9. Kusano, I., Baldomir, A., Jurado, J. A. and Hernández, S., “Reliability Based Design Optimization of Long-Span Bridges Considering Flutter,” Journal of Wind Engineering and Industrial Aerodynamics, 135, pp. 149162 (2014).
10. Makhloufi, A., Aoues, Y. and El Hami, A., “Reliability Based Design Optimization of Wire Bonding in Power Microelectronic Devices,” Microsystem Technologies, 22, pp. 27372748 (2016).
11. Xia, B. and Yu, D., “Optimization Based on Reliability and Confidence Interval Design for the Structural-Acoustic System with Interval Probabilistic Variables,” Journal of Sound and Vibration, 336, pp. 115 (2014).
12. Aoues, Y. and Chateauneuf, A., “Benchmark Study of Numerical Methods for Reliability-Based Design Optimization,” Struct Multidisc Optim, 41, pp. 277294 (2010).
13. Kharmanda, G., Mohamed, A. and Lemaire, M., “Efficient Reliability Based Design Optimization Using a Hybrid Space with Application to Finite Element Analysis,” Struct Multidiscip Optim, 24, pp. 233245 (2002).
14. Kharmanda, G., Sharabaty, S., Ibrahim, H., Makhloufi, A. and El-Hami, A., “Reliability-Based Design Optimization Using Semi-Numerical Methods for Different Engineering Applications,” International Journal of CAD/CAM, 9, pp. 116 (2009).
15. Mohsine, A. and El Hami, A., “A Robust Study of Reliability-Based Optimization Methods under Eigen-Frequency,” Computer Methods in Applied Mechanics and Engineering, 199, pp. 10061018 (2010).
16. Kharmanda, G., Numerical and Semi-Numerical Methods for Reliability-Based Design Optimization, Structural Design Optimization Considering Uncertainties, Taylor & Francis e-Library, pp. 189216 (2008).
17. Kharmanda, G., Ibrahim, M., Abo Al-kheer, A., Guerin, F. and El-Hami, A., “Reliability-Based Design Optimization of Shank Chisel Plough Using Optimum Safety Factor Strategy,” Computers and Electronics in Agriculture, 109, pp. 162171 (2014).
18. Crossland, B., “Effect of Large Hydrostatic Pressures on the Torsional Fatigue Strength of an Alloy Steel,” Proceeding of International Conference on Fatigue of Metals, 1, pp. 138149 (1956).
19. Sines, G., Behaviour of Metals under Complex Static and Alternationg Stress, McGraw-Hill, New York, pp. 145169 (1959).
20. Weber, B., “Fatigue Multiaxiale des Structures Industrielles Sous Chargement Quelconque,” PhD. Dissertation, INSA de Lyon, Lyon (1999).
21. Lambert, S., Pagnacco, E. and Khalij, L., “A Probabilistic Model for the Fatigue Reliability of Structures under Random Loadings with Phase Shift Effects,” International Journal of Fatigue, 32, pp. 463474 (2010).
22. Li, B. and Freitas, M., “A Procedure for Fast Evaluation of High-Cycle Fatigue under Multiaxial Random Loading,” Journal of Mechanical Design, 124, pp. 558563 (2002).
23. Balthazar, J. and Malcher, L., A Review on the Main Approaches for Determination of the Multiaxial High Cycle Fatigue Strengh, Marcilio Alves & da costa Mattos, Brazil (2007).
24. Bernasconi, A., “Efficient Algorithms for Calculation of Shear Stress Amplitude and Amplitude of the Second Invariant of the Stress Deviator in Fatigue Criteria Applications,” International Journal of Fatigue, 24, pp. 649657 (2002).
25. Papuga, J., “Mapping of Fatigue Damages Program Shell of FE-Calculation,” PhD. Dissertation, Faculty of Mechanical Engineering, Prague (2005).
26. Cristofori, A., Susmel, L. and Tovo, A., “A Stress Invariant Based Criterion to Estimate Fatigue Damage under Multiaxial Loading,” International Journal of Fatigue, 30, pp. 16461658 (2008).
27. Liu, J. and Zenner, H., “Fatigue Llimit of Ductile Metals under Multiaxial Loading,” Biaxial/ Multiaxial Fatigue and Fracture, 6 International Conference on Biaxial/Multiaxial Fatigue and Fracture, Elsevier, Lisbon, Portugal, 31, pp. 147164 (2003).
28. Gonçalves, C., Araujo, J. and Mamiya, E., “A Simple Multiaxial Fatigue Criterion for Metals,” Comptes Rendus Mécanique, 332, pp. 963968 (2004).
29. Zouain, N., Mamiya, E. and Comes, F., “Using Enclosing Ellipsoids in Multiaxial Fatigue Strength Criteria,” European Journal of Mechanics - A/Solids, 25, pp. 5171 (2006).
30. Davenport, A. G., “Note on the Distribution of Largest Values of Random Function with Application to Gust Loading” Proceedings of the Institution of Civil Engineers, 28, pp. 187196 (1964).
31. Arora, J. S., Introduction to Optimum Design, Second Edition, Elsevier, Amsterdam (2004).
32. Bhatti, M. A., Practical Optimization Methods with Mathematical Applications, Springer-Verlag, New York (2000).
33. Lange, K., Optimization, Springer-Verlag, New York (2004).
34. Pedregal, K., Introduction to Optimization, Springer-Verlag, New York (2004).
35. Stevenson, J., Reliability Analysis and Optimum Design of Structural Systems with Applications to Rigid Frames, Division of Solid Mechanics and Structures, 14, Case Western Reserve University, Cleveland, Ohio (1967).
36. Moses, F., “Structural System Reliability and Optimization,” Comput Struct, 7, pp. 283290 (1977).
37. Feng, Y. and Moses, F., “A Method of Structural Optimization Based on Structural System Reliability,” Journal of Structural Mechanics, 14, pp. 437453 (1986).
38. Chandu, S. and Grandhi, R., “General Purpose Procedure for Reliability Structural Optimization under Parametric Uncertainties,” Advances in Engineering Software, 23, pp. 714 (1995).
39. Du, X. and Chen, W., “Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design,” Journal of Mechanical Design, 126, pp. 225233 (2004).
40. Steenackers, G., Versluys, R., Runacres, M. and Guillaume, P., “Reliability-Based Design Optimization of Computation-Intensive Models Making Use of Response Surface Models,” Quality and Reliability Engineering International, 27, pp. 555568 (2011).
41. Lemaire, M., Fiabilité des Structures, HERMES-LAVOISIER, Paris, p. 506 (2005).
42. Kharmanda, G., Olhoff, N. and El-Hami, A., “Optimum Values of Structural Safety Factors for a Predefined Reliability Level with Extension to Multiple Limit States,” Structural and Multidisciplinary Optimization, 27, pp. 421434 (2004).
43. Kharmanda, G. and Olhoff, N., “Extension of Optimum Safety Factor Method to Nnonlinear Reliability-Based Design Optimization,” Journal of Structural and Multidisciplinary Optimization, 43, pp. 367380 (2007).
44. Lopez, R. H., Lemosse, D., Cursi, E. S., Rojas, J. E. and El-Hami, A., “An Approach for the Reliability Based Design Optimization of Laminated Composite Plates,” Engineering Optimization, 43, pp. 10791094 (2011).
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Journal of Mechanics
  • ISSN: 1727-7191
  • EISSN: 1811-8216
  • URL: /core/journals/journal-of-mechanics
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