Advertisement

Structural and Multidisciplinary Optimization

, Volume 59, Issue 5, pp 1747–1759 | Cite as

Stress-constrained topology optimization of continuum structures subjected to harmonic force excitation using sequential quadratic programming

  • Kai LongEmail author
  • Xuan Wang
  • Hongliang Liu
Research Paper
  • 247 Downloads

Abstract

In this paper, we propose a method for stress-constrained topology optimization of continuum structure sustaining harmonic load excitation using the reciprocal variables. In the optimization formulation, the total volume is minimized with a given stress amplitude constraint. The p-norm aggregation function is adopted to treat the vast number of local constraints imposed on all elements. In contrast to previous studies, the optimization problem is well posed as a quadratic program with second-order sensitivities, which can be solved efficiently by sequential quadratic programming. Several numerical examples demonstrate the validity of the presented method, in which the stress constrained designs are compared with traditional stiffness-based designs to illustrate the merit of considering stress constraints. It is observed that the proposed approach produces solutions that reduce stress concentration at the critical stress areas. The influences of varying excitation frequencies, damping coefficient and force amplitude on the optimized results are investigated, and also demonstrate that the consideration of stress-amplitude constraints in resonant structures is indispensable.

Keywords

Topology optimization Harmonic analysis p-norm Solid isotropic material with penalization Stress constraints Sequential quadratic programming 

Notes

Acknowledgments

This work was financially supported by the National Natural Science Foundation of Beijing (No. 2182067) and the Fundamental Research Funds for the Central Universities (No. 2017MS077, 2018ZD09). We thank Professor Krister Svanberg for providing the source code of MMA. We gratefully acknowledge the valuable remarks of the anonymous reviewers.

References

  1. Amstutz S, Novotny AA (2010) Topological optimization of structures subject to von mises constraints. Struct Multidiscip Optim 41(3):407–420MathSciNetzbMATHGoogle Scholar
  2. Andreassen E, Clausen A, Schevenels M, Lazarov BS, Sigmund O (2011) Efficient topology optimization in MATLAB using 88 lines of code. Struct Multidiscip Optim 43(1):1–16zbMATHGoogle Scholar
  3. Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224MathSciNetzbMATHGoogle Scholar
  4. Bendsøe MP, Sigmund O (2004) Topology optimization - theory, methods and applications. Springer, BerlinzbMATHGoogle Scholar
  5. Bourdin B (2001) Filters in topology optimization. Int J Numer Methods Eng 50(9):2143–2158MathSciNetzbMATHGoogle Scholar
  6. Bruggi M (2008) On an alternative approach to stress constraints relaxation in topology optimization. Struct Multidiscip Optim 36(2):125–141MathSciNetzbMATHGoogle Scholar
  7. Bruggi M, Duysinx P (2012) Topology optimization for minimum weight with compliance and stress constraints. Struct Multidiscip Optim 46(3):369–384MathSciNetzbMATHGoogle Scholar
  8. Bruns TE, Tortorelli DA (2001) Topology optimization of nonlinear elastic structures and compliant mechanisms. Comput Methods Appl Mech Eng 190(26–27):3443–3459zbMATHGoogle Scholar
  9. Cheng G, Guo X (1997) Epsilon-relaxed approach in structural topology optimization. Struct Optim 13(4):258–266Google Scholar
  10. Collet M, Bruggi M, Duysinx P (2017) Topology optimization for minimum weight with compliance and simplified nominal stress constraints for fatigue resistance. Struct Multidiscip Optim 55(3):839–855MathSciNetGoogle Scholar
  11. De Leon DM, Alexandersen J, Fonseca JSO, Sigmund O (2015) Stress-constrained topology optimization for compliant mechanism design. Struct Multidiscip Optim 52(5):929–943MathSciNetGoogle Scholar
  12. Deaton J, Grandhi RV (2014) A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct Multidiscip Optim 49(1):1–38MathSciNetGoogle Scholar
  13. Du J, Olhoff N (2007) Minimization of sound radiation from vibrating bi-material structures using topology optimization. Struct Multidiscip Optim 33(4–5):305–321Google Scholar
  14. Duysinx P, Bendsøe M (1998) Topology optimization of continuum structures with local stress constraints. Int J Number Methods Engrg 43(8):1453–1478MathSciNetzbMATHGoogle Scholar
  15. Duysinx P, Sigmund O (1998) New developments in handling stress constraints in handling stress constraints in optimal material distribution. In: Proceedings of 7th AIAA/USAF/NASA/ISSMO symposium on multidisciplinary design optimization, AIAA, Saint Louis, Missouri, AIAA Paper 98–4906Google Scholar
  16. Duysinx P, Van ML, Lemarie E, Bruls O, Bruyneel M (2008) Topology and generalized shape optimization: why stress constrains are so important? Int J Simul Multidisci Des Optim 2(4):253–258Google Scholar
  17. Francello EA (2006) Topology optimization for minimum mass design considering local failure constraints and contact boundary conditions. Struct Multidiscip Optim 32(3):229–240MathSciNetGoogle Scholar
  18. Guo X, Zhang W, Wang M, Wei P (2011) Stress-related topology optimization via level set approach. Comput Methods Appl Mech Eng 200(47):3439–3452MathSciNetzbMATHGoogle Scholar
  19. Holmberg E, Torstenfelt B, Klarbring A (2013) Stress constrained topology optimization. Struct Multidiscip Optim 48(1):33–47MathSciNetzbMATHGoogle Scholar
  20. Holmberg E, Torstenfelt B, Klarbring A (2014) Fatigue constrained topology optimization. Struct Multidiscip Optim 50(2):207–219MathSciNetzbMATHGoogle Scholar
  21. Huang X, Zuo ZH, Xie YM (2010) Evolutionary topological optimization of vibrating continuum structures for natural frequencies. Comput Struct 88(5–6):357–364Google Scholar
  22. Jeong SH, Choi DH, Yoon GH (2014) Separable stress interpolation scheme for stress-based topology optimization with multiple homogenous materials. Finite Elem Anal Des 82(4):16–31MathSciNetGoogle Scholar
  23. Kiyono CY, Vatanabe SL, Silva ECN, Reddy JN (2016) A new multi-p-norm formulation approach for stress-based topology optimization design. Compos Struct 156:10–19Google Scholar
  24. Le C, Norato J, Bruns T (2010) Stress-based topology optimization for continua. Struct Multidiscip Optim 41(4):605–620Google Scholar
  25. Lee E, James KA, Martins JRA (2012) Stress-constrained topology optimization with design-dependent loading. Struct Multidiscip Optim 46(5):647–661MathSciNetzbMATHGoogle Scholar
  26. Liu H, Zhang W, Gao T (2015) A comparative study of dynamic analysis methods for structural topology optimization under harmonic force excitations. Struct Multidiscip Optim 51(6):1321–1333MathSciNetGoogle Scholar
  27. Long K, Wang X, Gu X (2018a) Local optimum in multi-material topology optimization and solution by reciprocal variables. Struct Multidiscip Optim 57(3):1–13MathSciNetGoogle Scholar
  28. Long K, Wang X, Gu X (2018b) Multi-material topology optimization for transient heat conduction problem using SQP algorithm. Eng Optim 50(12):2091–2107MathSciNetGoogle Scholar
  29. Long K, Wang X, Gu X (2018c) Concurrent topology optimization for minimization of total mass considering load carrying capabilities and thermal insulation simultaneously. Acta Mech Sinica 34(2):315–326MathSciNetzbMATHGoogle Scholar
  30. Luo Y, Wang MY, Kang Z (2013) An enhanced aggregation method for topology optimization with local stress constraints. Comput Methods Appl Mech Eng 254:31–41MathSciNetzbMATHGoogle Scholar
  31. Niu B, He X, Shan Y, Yang R (2017) On objective functions of minimizing the vibration response of continuum structures subjected to external harmonic excitation. Struct Multidiscip Optim 57(28):1–17MathSciNetGoogle Scholar
  32. Oest J, Lund E (2017) Topology optimization with finite-life fatigue constraints. Struct Multidiscip Optim 56(5):1045–1059MathSciNetGoogle Scholar
  33. Olhoff N, Du J (2016) Generalized incremental frequency method for topological design of continuum structures for minimum dynamic compliance subjected to forced vibration at a prescribed low or high value of the excitation frequency. Struct Multidiscip Optim 54(5):1–29Google Scholar
  34. Paris J, Navarrina F, Colominas I, Casteleiro M (2009) Topology optimization of continuum structures with local and global stress constraints. Struct Multidiscip Optim 39(4):419–437MathSciNetzbMATHGoogle Scholar
  35. Paris J, Navarrina F, Colominas I, Casteleiro M (2010) Block aggregation of stress constraints in topology optimization of structures. Adv Eng Softw 41(3):433–441zbMATHGoogle Scholar
  36. Pedersen NL (2000) Maximization of eigenvalues using topology optimization. Struct Multidiscip Optim 20(1):2–11Google Scholar
  37. Ramani A (2011) Multi-material topology optimization with strength constraints. Struct Multidiscip Optim 43(5):597–615Google Scholar
  38. Rozvany G (2009) A critical review of established methods of structural topology optimization. Struct Multidiscip Optim 37(3):217–237MathSciNetzbMATHGoogle Scholar
  39. Sigmund O, Maute K (2013) Topology optimization approaches. Struct Multidiscip Optim 48(6):1031–1055MathSciNetGoogle Scholar
  40. Silva GA, Beck AT, Cardoso EL (2018) Topology optimization of continuum structure with stress constraints and uncertainties in loading. Int J Numer Methods Eng 113(1):1–34MathSciNetGoogle Scholar
  41. Svanberg K (1987) The method of moving asymptotes – a new method for structural optimization. Int J Number Methods Eng 24(2):359–373MathSciNetzbMATHGoogle Scholar
  42. Xia Q, Shi T, Liu S, Wang MY (2012) A level set solution to the stress-based structural shape and topology optimization. Comput Struct 90-91(1):55–64Google Scholar
  43. Xia Q, Shi T, Liu S, Wang MY (2013a) Shape and topology optimization for tailoring stress in a local region to enhance performance of piezoresistive sensors. Comput Struct 114-115:98–105Google Scholar
  44. Xia Q, Shi T, Liu S, Wang MY (2013b) Optimization of stresses in a local region for the maximization of sensitivity and minimization of cross-sensitivity of piezoresistive sensors. Struct Multidiscip Optim 48(5):927–938MathSciNetGoogle Scholar
  45. Yang RJ, Chen CJ (1996) Stress-based topology optimization. Struct Optim 12(2–3):98–105Google Scholar
  46. Yang D, Liu H, Zhang W, Li S (2018) Stress-constrained topology optimization based on maximum stress measures. Comput Struct 198:23–39Google Scholar
  47. Zhou M, Rozvany GIN (1991) The COC algorithm, part II: topological, geometry and generalized shape optimization. Comput Methods Appl Mech Eng 89(1–3):309–336Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Beijing Key Laboratory of Energy Safety and Clean UtilizationNorth China Electric Power UniversityBeijingChina
  2. 2.State Key Laboratory for Alternate Electrical Power System with Renewable Energy SourcesNorth China Electric Power UniversityBeijingChina
  3. 3.State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering MechanicsDalian University of TechnologyDalianChina

Personalised recommendations