Significance:

The presence of damage at arbitrary locations in a structure is common in aerospace components [1]. Material flaw as minor as a small surface crack can lead to fatigue failure is one of the most important failure modes in the engineering field [2], being responsible for more than 80% of all structural failures. Topology optimisation has become an effective tool for efficient light-weight design in aviation industry where design approach that treats fatigue life as design objectives is now a standard practice [3]. Fatigue life based optimum design plays a crucial role in restoring the operability of deteriorating structures and altering local structural shapes to extend their operational life beyond expectation [4]. Optimised components,   such as smart structures design of wing ribs, also showed significant weight reduction and improved safety factor [5]. Thus, development and application of optimisation system will be beneficial to existing product development methods such as conceptual and preliminary design process as it reduces manpower, time and cost of implementation [6].

Literature review

Classical optimisation methods, such as density filtering, were originally introduced since when the methodology for topology was well developed and utilised on a regular basis in industrial settings where demands for aircraft structural stiffness were high [7]. The aim of density-based topology optimisation is to find an optimal material distribution which can effectively minimise the structural compliance subject to an overall mass constraint. Such approach is both easy to implement and computationally efficient as explained in [8]. Nevertheless, major design alterations are usually required for stiffness optimal designs to meet requirements of more common design driving criteria such as stress or fatigue as mentioned in [9]. Therefore, it can be useful to introduce stress or fatigue criteria in the formulation of topology optimisation.

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 Although stiffness is not an unimportant property, the key property of a structure is often its durability. This is closely related to the stresses in the structure, and it is common engineering practice to keep the stresses in a structure below its suitable material limit [10]. Despite of its relevance in aviation industry, topology optimisation with stress constraints comes with limitations regarding singularity and computational cost due to large number of constraints [11]. Solutions to such problems; for instance, global stress measure and clustering technique, have been discussed in many papers, see [2], [3], [12]. However, the local stress control is lost and the optimisation problem becomes increasingly non-linear, resulting in impairment of structural integrity [13]. 

While stress-based topology optimisation is an old field of research, investigation in fatigue-based topology optimisation is still a relatively recent and unexplored area in aerospace structures design [14]. As reviewed in [15], this can be justified by the fact that computational cost of Finite Element Method used in analysis is high as iterations of detailed simulation have to be done for each fine mesh. Still, successful practical applications within aerospace industry are evident. For example, utilisation of topology optimisation in the design of the Airbus A380 leading edge ribs and forward strut of aircraft’s nose landing gear [16] both showed considerable decrease in weight and prolongation of fatigue life.

To date, topology optimization has proven to be the most useful, yet most complicated, structural optimization methodology [3]. However, only a few applications to real-world design problems in the aerospace industry are evident. This accounts for the difficulties in design process to ensure that the finalised design complies with the regulations and meet the airworthiness standards in aviation field [17]. Technical hardships due to the fast evolution of aerospace structural engineering have restricted the application of topology optimization from being widely used in the industry [18].

References

[1] R. Das and R. Jones, “Damage tolerance based design optimisation of a fuel flow vent hole in an aircraft structure,” Structural and Multidisciplinary Optimization, vol. 38, no. 3, pp. 245-265, 2009.

[2] O. Sigmund, “On the usefulness of non-gradient approaches in topology optimization,” Structural and Multidisciplinary Optimization, vol. 43, no. 5, pp. 589-596, 2011.

[3] J. H. Zhu, W. H. Zhang, and L. Xia, “Topology Optimization in Aircraft and Aerospace Structures Design,” Archives of Computational Methods in Engineering, vol. 23, no. 4, pp. 595-622, 2016.

[4] R. Das and R. Jones, “Development of a 3D Biological method for fatigue life based optimisation and its application to structural shape design,” International Journal of Fatigue, vol. 31, no. 2, pp. 309-321, 2009/02/01/ 2009.

[5] M. Seabra et al., “Selective laser melting (SLM) and topology optimization for lighter aerospace componentes,” in Procedia Structural Integrity, 2016, vol. 1, pp. 289-296.

[6] J. Oest, Structural Optimization with Fatigue Constraints, (Structural Optimization with Fatigue Constraints): Aalborg Universitetsforlag, 2017.

[7] S. B. Dilgen, C. B. Dilgen, D. R. Fuhrman, O. Sigmund, and B. S. Lazarov, “Density based topology optimization of turbulent flow heat transfer systems,” Structural and Multidisciplinary Optimization, vol. 57, no. 5, pp. 1905-1918, 2018/05/01 2018.

[8] U. Schramm and M. Zhou, “Recent developments in the commercial implementation of topology optimization,” in Solid Mechanics and its Applications vol. 137, ed, 2006, pp. 239-248.

[9] E. Holmberg, “Topology optimization considering stress, fatigue and load uncertainties,” 2016. 

[10] M. Bruggi, “On an alternative approach to stress constraints relaxation in topology optimization,” Structural and Multidisciplinary Optimization, vol. 36, no. 2, pp. 125-141, 2008.

[11] E. Holmberg, B. Torstenfelt, and A. Klarbring, “Stress constrained topology optimization,” Structural and Multidisciplinary Optimization, vol. 48, no. 1, pp. 33-47, 2013.

[12] J. Oest and E. Lund, “Topology optimization with finite-life fatigue constraints,” Structural and Multidisciplinary Optimization, vol. 56, no. 5, pp. 1045-1059, 2017/11/01 2017.

[13] E. Holmberg, “Stress and fatigue constrained topology optimization,” 2013. 

[14] Z. Kang, P. Liu, and M. Li, “Topology optimization considering fracture mechanics behaviors at specified locations,” Structural and Multidisciplinary Optimization, vol. 55, no. 5, pp. 1847-1864, 2017.

[15] J. W. Lee, G. H. Yoon, and S. H. Jeong, “Topology optimization considering fatigue life in the frequency domain,” Computers and Mathematics with Applications, vol. 70, no. 8, pp. 1852-1877, 2015.

[16] M. K. Leader, T. W. Chin, and G. Kennedy, “High Resolution Topology Optimization of Aerospace Structures with Stress and Frequency Constraints,” in 2018 Multidisciplinary Analysis and Optimization Conference,(AIAA AVIATION Forum: American Institute of Aeronautics and Astronautics, 2018.

[17] H. Svärd, “Topology Optimization of Fatigue-Constrained Structures,” Doctoral thesis, comprehensive summary, KTH Royal Institute of Technology, Stockholm, 2015:04, 2015. Accessed on: 2015-04-08t22:30:59.713+02:00. [Online]. Available: http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-163575Available: DiVA

[18] D. J. Munk, D. J. Auld, G. P. Steven, and G. A. Vio, “On the benefits of applying topology optimization to structural design of aircraft components,” Structural and Multidisciplinary Optimization, vol. 60, no. 3, pp. 1245-1266, 2019.

 Oest, J 2017, Structural Optimization with Fatigue Constraints. Ph.d.-serien for Det Ingeniør- og Naturvidenskabelige Fakultet, Aalborg Universitet, Aalborg Universitetsforlag.