Skip to main content
SpringerLink
Log in

Topology Optimization Method of Structures with Surface Corrosion Considered

  • Published:
Acta Mechanica Solida Sinica Aims and scope Submit manuscript

Abstract

Engineering equipment served in harsh environments for a long time will inevitably corrode, resulting in a loss of mechanical performance and a reduction in a lifetime, and even threatening production safety. Although conventional post-treatment anti-corrosion technologies can slow down the corrosion rate, it is important to consider the corrosion effect on the structural performance in design. This paper proposes a topology optimization method with prior consideration of structural corrosion resistance during the design phase, so the structures designed by the approach can have excellent corrosion resistance, considerably reducing the cost of post-treatment anti-corrosion technologies. First, an erosion-based method is utilized to identify the structural surface layer. In the procedure, the initial structure is eroded to generate a reduced-scale eroded structure, and then, the eroded regions are specified as the surface layer. Second, dual-material interpolation is used to create the corrosion model by modifying the material properties of elements on the structural surface layer, which is set to 0 to simulate uniform corrosion. Finally, the topology optimization method with structural surface corrosion considered is enforced through a two-step filtering/projection process. After the entire lifetime corrosion analysis, various numerical examples indicate that the structural performance of the proposed method is superior to that of the standard method (SIMP interpolation) without considering the influence of corrosion, demonstrating the effectiveness of the proposed method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Availability of Data and Materials

All data generated during this study are publicly available.

References

  1. Huang Y, Yang LJ, Xu YZ, Cao YZ, Song SD. A novel system for corrosion protection of reinforced steels in the underwater zone. Corros Eng Sci Technol. 2016;51(8):566–72.

    Article  Google Scholar 

  2. Li Q, Xia X, Pei Z, Cheng X, Zhang D, Xiao K, et al. Long-term corrosion monitoring of carbon steels and environmental correlation analysis via the random forest method. Npj Mater Degrad. 2022;6(1):1.

    Article  Google Scholar 

  3. Zhao J, Wu W, Cai J, Cheng X. Evaluating the effect of aluminum on the corrosion resistance of the structural steels used for marine engineering. J Mater Res Technol. 2022;18:4181–93.

    Article  Google Scholar 

  4. Vukelic G, Vizentin G, Brnic J, Brcic M, Sedmak F. Long-term marine environment exposure effect on butt-welded shipbuilding steel. J Mar Sci Eng. 2021;9(5):491.

    Article  Google Scholar 

  5. Popoola L, Grema A, Latinwo G, Gutti B, Balogun A. Corrosion problems during oil and gas production and its mitigation. Int J Ind Chem. 2013;4(1):35.

    Article  Google Scholar 

  6. Velázquez JC. Statistical modelling of pitting corrosion: extrapolation of the maximum pit depth-growth. Int J Electrochem Sci. 2014;9:16.

    Google Scholar 

  7. Gharaibeh A, Felhősi I, Keresztes Z, Harsányi G, Illés B, Medgyes B. Electrochemical corrosion of SAC alloys: a review. Metals. 2020;10(10):1276.

    Article  Google Scholar 

  8. Wang H, Quan X, Zeng Q, Wu Y, Liao B, Guo X. Electrochemical corrosion and protection of low-temperature sintered silver nanoparticle paste in NH4Cl solution. J Mater Sci Mater Electron. 2021;32(10):13748–60.

    Article  Google Scholar 

  9. Sathiyanarayanan S, Azim SS, Venkatachari G. A new corrosion protection coating with polyaniline–TiO2 composite for steel. Electrochim Acta. 2007;52(5):2068–74.

    Article  Google Scholar 

  10. Gopi D, Ramya S, Rajeswari D, Kavitha L. Corrosion protection performance of porous strontium hydroxyapatite coating on polypyrrole coated 316L stainless steel. Colloids Surf B Biointerfaces. 2013;107:130–6.

    Article  Google Scholar 

  11. del Olmo R, Mohedano M, Matykina E, Arrabal R. Permanganate loaded Ca-Al-LDH coating for active corrosion protection of 2024–T3 alloy. Corros Sci. 2022;198:110144.

    Article  Google Scholar 

  12. Křivý V. Design of corrosion allowances on structures from weathering steel. Procedia Eng. 2012;40:235–40.

    Article  Google Scholar 

  13. Garbatov Y. Risk-based corrosion allowance of oil tankers. Ocean Eng. 2020;213:107753.

    Article  Google Scholar 

  14. Bendsøe MP, Sigmund O. Topology optimization: theory, methods, and applications. Springer; 2003.

    MATH  Google Scholar 

  15. Guo X, Zhang WS, Wang MY, Wei P. Stress-related topology optimization via level set approach. Comput Methods Appl Mech Eng. 2011;200(47–48):3439–52.

    Article  MathSciNet  MATH  Google Scholar 

  16. da Silva GA, Beck AT, Sigmund O. Stress-constrained topology optimization considering uniform manufacturing uncertainties. Comput Methods Appl Mech Eng. 2019;344:512–37.

    Article  MathSciNet  MATH  Google Scholar 

  17. Ramani A. Multi-material topology optimization with strength constraints. Struct Multidiscip Optim. 2011;43(5):597–615.

    Article  Google Scholar 

  18. Kang Z, Luo Y. Non-probabilistic reliability-based topology optimization of geometrically nonlinear structures using convex models. Comput Methods Appl Mech Eng. 2009;198(41–44):3228–38.

    Article  MathSciNet  MATH  Google Scholar 

  19. Ma M, Wang L. Reliability-based topology optimization framework of two-dimensional phononic crystal band-gap structures based on interval series expansion and mapping conversion method. Int J Mech Sci. 2021;196:106265.

    Article  Google Scholar 

  20. Wu S, Zhang Y, Liu S. Transient thermal dissipation efficiency based method for topology optimization of transient heat conduction structures. Int J Heat Mass Transf. 2021;170:121004.

    Article  Google Scholar 

  21. Jensen JS. Topology optimization of dynamics problems with Padé approximants. Int J Numer Methods Eng. 2007;72(13):1605–30.

    Article  MATH  Google Scholar 

  22. Clausen A, Aage N, Sigmund O. Topology optimization of coated structures and material interface problems. Comput Methods Appl Mech Eng. 2015;290:524–41.

    Article  MathSciNet  MATH  Google Scholar 

  23. Clausen A, Aage N, Sigmund O. Exploiting additive manufacturing infill in topology optimization for improved buckling load. Engineering. 2016;2(2):250–7.

    Article  Google Scholar 

  24. Groen JP, Wu J, Sigmund O. Homogenization-based stiffness optimization and projection of 2D coated structures with orthotropic infill. Comput Methods Appl Mech Eng. 2019;349:722–42.

    Article  MathSciNet  MATH  Google Scholar 

  25. Harvey D, Hubert P. Extensions of the coating approach for topology optimization of composite sandwich structures. Compos Struct. 2020;252:112682.

    Article  Google Scholar 

  26. Luo Y, Li Q, Liu S. Topology optimization of shell–infill structures using an erosion-based interface identification method. Comput Methods Appl Mech Eng. 2019;355:94–112.

    Article  MathSciNet  MATH  Google Scholar 

  27. Hu J. Two-scale concurrent topology optimization method of hierarchical structures with self-connected multiple lattice-material domains. Compos Struct. 2021. https://doi.org/10.1016/j.compstruct.2021.114224.

    Article  Google Scholar 

  28. Hu J, Liu Y, Luo Y, Huang H, Liu S. Topology optimization of multi-material structures considering a piecewise interface stress constraint. Comput Methods Appl Mech Eng. 2022. https://doi.org/10.1016/j.cma.2022.115274.

    Article  MathSciNet  MATH  Google Scholar 

  29. Wang Y, Kang Z. A level set method for shape and topology optimization of coated structures. Comput Methods Appl Mech Eng. 2018;329:553–74.

    Article  MathSciNet  MATH  Google Scholar 

  30. Fu J, Li H, Gao L, Xiao M. Design of shell-infill structures by a multiscale level set topology optimization method. Comput Struct. 2019;212:162–72.

    Article  Google Scholar 

  31. Liu C, Du Z, Zhu Y, Zhang W, Zhang X, Guo X. Optimal design of shell-graded-infill structures by a hybrid MMC-MMV approach. Comput Methods Appl Mech Eng. 2020;369:113187.

    Article  MathSciNet  MATH  Google Scholar 

  32. Wang XJ, Zheng B, Huang HZ, Xu H, Wang Z. Structural topology optimization method considering reliability and corrosion. In: 2011 International conference on quality, reliability, risk, maintenance, and safety engineering [Internet]. Xi’an, China: IEEE; 2011 [cited 2022 May 19]. pp 819–23. Available from: http://ieeexplore.ieee.org/document/5976736/

  33. Zheng B, Wang X jun, Huang HZ. Reliability-based topology optimization considering corrosion. In: 2012 Proceedings annual reliability and maintainability symposium [Internet]. Reno, NV, USA: IEEE; 2012 [cited 2022 May 19]. pp 1–7. Available from: http://ieeexplore.ieee.org/document/6175463/

  34. Li Z, Shi T, Xia L, Xia Q. Maximizing the first eigenfrequency of structures subjected to uniform boundary erosion through the level set method. Eng Comput. 2019;35(1):21–33.

    Article  Google Scholar 

  35. Lazarov BS, Sigmund O. Filters in topology optimization based on Helmholtz-type differential equations. Int J Numer Methods Eng. 2011;86(6):765–81.

    Article  MathSciNet  MATH  Google Scholar 

  36. Wang F, Lazarov BS, Sigmund O. On projection methods, convergence and robust formulations in topology optimization. Struct Multidiscip Optim. 2011;43(6):767–84.

    Article  MATH  Google Scholar 

  37. Svanberg K. The method of moving asymptotes—a new method for structural optimization. Int J Numer Methods Eng. 1987;24(2):359–73.

    Article  MathSciNet  MATH  Google Scholar 

  38. Clausen A, Andreassen E. On filter boundary conditions in topology optimization. Struct Multidiscip Optim. 2017;56(5):1147–55.

    Article  MathSciNet  Google Scholar 

  39. Sigmund O. A 99 line topology optimization code written in Matlab. Struct Multidiscip Optim. 2001;21(2):120–7.

    Article  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the financial support to this work by the National Natural Science Foundation of China (Grant Nos. U1808215 and 11821202), the 111 Project (B14013) and the Fundamental Research Funds for the Central Universities of China (DUT21GF101).

Author information

Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, China

    Ran Li & Shutian Liu

Authors
  1. Ran Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shutian Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

RL provided all the data for this paper and was a significant contributor to writing this paper. SL conceived the main idea of this paper and put forward valuable suggestions for the revision of this paper.

Corresponding author

Correspondence to Shutian Liu.

Ethics declarations

Conflict of interest

The authors declare that they have no conflicts of interest.

Consent for publication

All authors approved the final manuscript and submission to the journal.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, R., Liu, S. Topology Optimization Method of Structures with Surface Corrosion Considered. Acta Mech. Solida Sin. 36, 241–253 (2023). https://doi.org/10.1007/s10338-022-00375-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10338-022-00375-8

Keywords

Search

Navigation