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

Published online by Cambridge University Press:  06 July 2017

A. Yaich ,
G. Kharmanda ,
A. El Hami ,
L. Walha  and
M. Haddar
A. Yaich*
Affiliation:
Laboratory of Mechanics, Modeling and ManufacturingNational School of Engineers of SfaxSfax, Tunisia Laboratory of Optimization and Reliability in Structural MechanicsNormandie UniversitéINSA of RouenRouen, France
G. Kharmanda
Affiliation:
Biomedical Engineering DepartmentLund UniversityLund, Sweden
A. El Hami
Affiliation:
Laboratory of Optimization and Reliability in Structural MechanicsNormandie UniversitéINSA of RouenRouen, France
L. Walha
Affiliation:
Laboratory of Mechanics, Modeling and ManufacturingNational School of Engineers of SfaxSfax, Tunisia
M. Haddar
Affiliation:
Laboratory of Mechanics, Modeling and ManufacturingNational School of Engineers of SfaxSfax, Tunisia
*
*Corresponding author (ahmed.yaich@insa-rouen.fr)
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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.

Keywords

Reliability Based Design OptimizationMultiaxial fatigue damageRobust Hybrid MethodRandom vibrations
Type
Research Article
Information
Journal of Mechanics , Volume 34 , Issue 5 , October 2018 , pp. 551 - 566
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

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References

1. Pitoiset, X. and Preumont, A., “Spectral Methods for Multiaxial Random Fatigue Analysis of Metallic Structures,” International Journal of Fatigue, 22, pp. 541–550 (2000).Google Scholar
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. 715–727 (2001).Google Scholar
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).Google Scholar
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).Google Scholar
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).Google Scholar
6. Chang, T. P. and Liu, M. F., “Evaluation of Nonlinear System Parameters by Stochastic Spectral Method,” Journal of Mechanics, 23, pp. 269–274 (2007).Google Scholar
7. Arora, J., Introduction to Optimum Design, McGraw-Hill, New York (1989).Google Scholar
8. Haftaka, R. and Gurdal, Z., Elements of Structural Optimization, Kluwer Academic Publications, Dordrecht (1991).Google Scholar
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. 149–162 (2014).Google Scholar
10. Makhloufi, A., Aoues, Y. and El Hami, A., “Reliability Based Design Optimization of Wire Bonding in Power Microelectronic Devices,” Microsystem Technologies, 22, pp. 2737–2748 (2016).Google Scholar
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. 1–15 (2014).Google Scholar
12. Aoues, Y. and Chateauneuf, A., “Benchmark Study of Numerical Methods for Reliability-Based Design Optimization,” Struct Multidisc Optim, 41, pp. 277–294 (2010).Google Scholar
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. 233–245 (2002).Google Scholar
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. 1–16 (2009).Google Scholar
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. 1006–1018 (2010).Google Scholar
16. Kharmanda, G., Numerical and Semi-Numerical Methods for Reliability-Based Design Optimization, Structural Design Optimization Considering Uncertainties, Taylor & Francis e-Library, pp. 189–216 (2008).Google Scholar
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. 162–171 (2014).Google Scholar
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. 138–149 (1956).Google Scholar
19. Sines, G., Behaviour of Metals under Complex Static and Alternationg Stress, McGraw-Hill, New York, pp. 145–169 (1959).Google Scholar
20. Weber, B., “Fatigue Multiaxiale des Structures Industrielles Sous Chargement Quelconque,” PhD. Dissertation, INSA de Lyon, Lyon (1999).Google Scholar
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. 463–474 (2010).Google Scholar
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. 558–563 (2002).Google Scholar
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).Google Scholar
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. 649–657 (2002).Google Scholar
25. Papuga, J., “Mapping of Fatigue Damages Program Shell of FE-Calculation,” PhD. Dissertation, Faculty of Mechanical Engineering, Prague (2005).Google Scholar
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. 1646–1658 (2008).Google Scholar
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. 147–164 (2003).Google Scholar
28. Gonçalves, C., Araujo, J. and Mamiya, E., “A Simple Multiaxial Fatigue Criterion for Metals,” Comptes Rendus Mécanique, 332, pp. 963–968 (2004).Google Scholar
29. Zouain, N., Mamiya, E. and Comes, F., “Using Enclosing Ellipsoids in Multiaxial Fatigue Strength Criteria,” European Journal of Mechanics - A/Solids, 25, pp. 51–71 (2006).Google Scholar
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. 187–196 (1964).Google Scholar
31. Arora, J. S., Introduction to Optimum Design, Second Edition, Elsevier, Amsterdam (2004).Google Scholar
32. Bhatti, M. A., Practical Optimization Methods with Mathematical Applications, Springer-Verlag, New York (2000).Google Scholar
33. Lange, K., Optimization, Springer-Verlag, New York (2004).Google Scholar
34. Pedregal, K., Introduction to Optimization, Springer-Verlag, New York (2004).Google Scholar
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).Google Scholar
36. Moses, F., “Structural System Reliability and Optimization,” Comput Struct, 7, pp. 283–290 (1977).Google Scholar
37. Feng, Y. and Moses, F., “A Method of Structural Optimization Based on Structural System Reliability,” Journal of Structural Mechanics, 14, pp. 437–453 (1986).Google Scholar
38. Chandu, S. and Grandhi, R., “General Purpose Procedure for Reliability Structural Optimization under Parametric Uncertainties,” Advances in Engineering Software, 23, pp. 7–14 (1995).Google Scholar
39. Du, X. and Chen, W., “Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design,” Journal of Mechanical Design, 126, pp. 225–233 (2004).Google Scholar
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. 555–568 (2011).Google Scholar
41. Lemaire, M., Fiabilité des Structures, HERMES-LAVOISIER, Paris, p. 506 (2005).Google Scholar
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. 421–434 (2004).Google Scholar
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. 367–380 (2007).Google Scholar
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. 1079–1094 (2011).Google Scholar