Abstract
We develop a topology optimization method including high-cycle fatigue as a constraint. The fatigue model is based on a continuous-time approach, which uses the concept of a moving endurance surface as a function of the stress history and back stress evolution. The development of damage only occurs when the stress state lies outside the endurance surface. Furthermore, an aggregation function, which approximates the maximum fatigue damage, is implemented. As the optimization workflow is sensitivity-based, the fatigue sensitivities are determined using an adjoint sensitivity analysis. The capabilities of the presented approach are tested on numerical models where the problem is to maximize the stiffness subject to high-cycle fatigue constraints.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Amzallag, C., Gerey, J., Robert, J., Bahuaud, J.: Standardization of the rainflow counting method for fatigue analysis. Int. J. Fatigue 16(4), 287–293 (1994)
Bendsoe, M.P., Sigmund, O.: Topology Optimization: Theory, Methods, and Applications. Springer Science & Business Media (2004)
Bruns, T.E., Tortorelli, D.A.: Topology optimization of non-linear elastic structures and compliant mechanisms. Comput. Methods Appl. Mech. Eng. 190(26), 3443–3459 (2001)
Collet, M., Bruggi, M., Duysinx, P.: Topology optimization for minimum weight with compliance and simplified nominal stress constraints for fatigue resistance. Struct. Multidiscip. Optim. 55(3), 839–855 (2017)
Dong, P.: A structural stress definition and numerical implementation for fatigue analysis of welded joints. Int. J. Fatigue 23(10), 865–876 (2001)
Franchi, A., Genna, F., Riva, P.: Incremental Elastic-Ziegler kinematic hardening plasticity formulations and an algorithm for the numerical integration with an “a priori” error control. In: Grierson, D.E., Franchi, A., Riva, P. (eds.) Progress in Structural Engineering, pp. 407–421. Springer, Dordrecht (1991)
Gerzen, N., Clausen, P., Suresh, S., Pedersen, C.:. Fatigue sensitivities for sizing optimization of shell structures. In: 12th World Congress on Structural and Multidisciplinary Optimization (2017)
Haftka, R.T., Adelman, H.M.: Recent developments in structural sensitivity analysis. Struct. Optim. 1, 137–151 (1989)
Holmberg, E., Torstenfelt, B., Klarbring, A.: Stress constrained topology optimization. Struct. Multidiscip. Optim. 48(1), 33–47 (2013)
Holmberg, E., Torstenfelt, B., Klarbring, A.: Fatigue constrained topology optimization. Struct. Multidiscip. Optim. 50(2), 207–219 (2014)
Holopainen, S., Kouhia, R., Saksala, T.: Continuum approach for modelling transversely isotropic high-cycle fatigue. Eur. J. Mech. A/Solids 60, 183–195 (2016)
Jeong, S.H., Lee, J.W., Yoon, G.H., Choi, D.H.: Topology optimization considering the fatigue constraint of variable amplitude load based on the equivalent static load approach. Appl. Math. Modell. 56, 626–647 (2018)
Kennedy, G.J., Hicken, J.E.: Improved constraint-aggregation methods. Comput. Methods Appl. Mech. Eng. 289, 332–354 (2015)
Oest, J., Overgaard, L.C.T., Lund, E.: Gradient based structural optimization with fatigue constraints of jacket structures for offshore wind turbines. In: 11th World Congress on Structural and Multidisciplinary Optimization, 7th–12th (2015)
Ottosen, N.S., Stenström, R., Ristinmaa, M.: Continuum approach to high-cycle fatigue modeling. Int. J. Fatigue 30(6), 996–1006 (2008)
Michaleris, P., Tortorelli, D.A., Vidal, C.A.: Tangent operators and design sensitivity formulations for transient nonlinear coupled problems with applications to elastoplasticity. Int. J. Numer. Methods Eng. 37(14), 2471–2499 (1994)
Svanberg, K.: The method of moving asymptotes - a new method for structural optimization. Int. J. Numer. Methods Eng. 24(2), 359–373 (1987)
Torstenfelt, B.: (2012) The TRINITAS. https://www.solid.iei.liu.se/Offered_services/Trinitas
Tortorelli, D.A., Michaleris, P.: Design sensitivity analysis: overview and review. Inverse Probl. Eng. 1(1), 71–105 (1994)
van Keulen, F., Haftka, R.T., Kim, N.-H.: Review of options for structural design sensitivity analysis. Part 1: linear systems. Comput. Methods Appl. Mech. Eng. 194, 3213–3243 (2005)
Acknowledgements
The work was performed within the AddMan project, funded by the Clean Sky 2 joint undertaking under the European Unions Horizon 2020 research and innovation programme under grant agreement No 738002, and within the Centre for Additive Manufacturing-Metal (CAM\(^2\)) financed by Sweden’s innovation agency under grant agreement No 2016-05175.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Suresh, S., Lindström, S.B., Thore, CJ., Torstenfelt, B., Klarbring, A. (2019). An Evolution-Based High-Cycle Fatigue Constraint in Topology Optimization. In: Rodrigues, H., et al. EngOpt 2018 Proceedings of the 6th International Conference on Engineering Optimization. EngOpt 2018. Springer, Cham. https://doi.org/10.1007/978-3-319-97773-7_73
Download citation
DOI: https://doi.org/10.1007/978-3-319-97773-7_73
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-97772-0
Online ISBN: 978-3-319-97773-7
eBook Packages: EngineeringEngineering (R0)