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Combination of the guide-weight criterion and BESO method for fast and stable topology optimization of two-dimensional continuum structures

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Abstract

This paper proposes a new method for topology optimization of two-dimensional (2D) continuum structures by combining the features of the guide-weight criterion and the conventional bidirectional evolutionary structural optimization (BESO) method. The distribution of material is dominated by guide weights instead of sensitivity numbers. Benefitting from high computational efficiency and the existence of intermediate design variables of the guide-weight criterion, this new algorithm further improves the convergence speed and stability of the objective function. Several typical topology optimization examples of 2D continuum structures are used to demonstrate the efficiency of the proposed method. Numerical results show that convergent, mesh-independent and nearly black-and-white solutions can be achieved and that the proposed method is more stable and efficient than the conventional BESO method.

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Abbreviations

BESO:

Bidirectional evolutionary structural optimization

ESO:

Evolutionary structural optimization

ER:

Evolutionary rate

FE:

Finite element

FEA:

Finite element analysis

GA:

Geometric advantage

SIMP:

Solid isotropic material with penalization

SE:

Strain energy

2D:

Two-dimensional

References

  1. Deaton, J.D., Grandhi, R.V.: A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct. Multidiscip. Optim. 49, 1–38 (2014)

    MathSciNet  Google Scholar 

  2. Roiné, T., Montemurro, M., Pailhès, J.: Stress-based topology optimization through non-uniform rational basis spline hyper-surface. Mech. Adv. Mater. Struc. 29, 3387–3407 (2022)

    Google Scholar 

  3. Bendsøe, M.P., Kikuchi, N.: Generating optimal topologies in structural design using a homogenization method. Comput. Methods Appl. Mech. Eng. 71, 197–224 (1988)

    MathSciNet  MATH  Google Scholar 

  4. Bendsøe, M.P.: Optimal shape design as a material distribution problem. Struct. Optim. 1, 193–202 (1989)

    Google Scholar 

  5. Zhou, M., Rozvany, G.I.N.: The COC algorithm, Part II: topological, geometrical and generalized shape optimization. Comput. Methods Appl. Mech. Eng. 89, 309–336 (1991)

    Google Scholar 

  6. Xie, Y.M., Steven, G.P.: A simple evolutionary procedure for structural optimization. Comput. Struct. 49, 885–896 (1993)

    Google Scholar 

  7. Querin, O.M., Steven, G.P., Xie, Y.M.: Evolutionary structural optimization (ESO) using a bidirectional algorithm. Eng. Comput. 15, 1031–1048 (1998)

    MATH  Google Scholar 

  8. Yang, X.Y., Xie, Y.M., Steven, G.P., Querin, O.M.: Bidirectional evolutionary method for stiffness optimization. AIAA J. 37, 1483–1488 (1999)

    Google Scholar 

  9. Wang, M.Y., Wang, X.M., Guo, D.M.: A level set method for structural topology optimization. Comput. Methods Appl. Mech. Eng. 192, 227–246 (2003)

    MathSciNet  MATH  Google Scholar 

  10. Guo, X., Zhang, W.S., Zhong, W.L.: Doing topology optimization explicitly and geometrically-a new moving morphable components based framework. J. Appl. Mech. 81, 081009 (2014)

    Google Scholar 

  11. Huang, X., Xie, Y.M.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite Elem. Anal. Des. 43, 1039–1049 (2007)

    Google Scholar 

  12. Xia, L., Xia, Q., Huang, X., Xie, Y.M.: Bi-directional evolutionary structural optimization on advanced structures and materials: a comprehensive review. Arch. Comput. Methods Eng. 25, 437–478 (2018)

    MathSciNet  MATH  Google Scholar 

  13. Zhao, F.: A nodal variable ESO (BESO) method for structural topology optimization. Finite Elem. Anal. Des. 86, 34–40 (2014)

    MathSciNet  Google Scholar 

  14. Ghabraie, K.: An improved soft-kill BESO algorithm for optimal distribution of single or multiple material phases. Struct. Multidiscip. Optim. 52, 773–790 (2015)

    MathSciNet  Google Scholar 

  15. Lin, H.D., Xu, A., Misra, A., Zhao, R.H.: An ANSYS APDL code for topology optimization of structures with multi-constraints using the BESO method with dynamic evolution rate (DER-BESO). Struct. Multidiscip. Optim. 62, 2229–2254 (2020)

    MathSciNet  Google Scholar 

  16. Zhou, E.L., Wu, Y., Lin, X.Y., Li, Q.Q., Xiang, Y.: A normalization strategy for BESO-based structural optimization and its application to frequency response suppression. Acta Mech. 232, 1307–1327 (2021)

    MathSciNet  MATH  Google Scholar 

  17. Huang, X., Xie, Y.M.: Evolutionary topology optimization of continuum structures: methods and applications. Wiley, Chichester (2010)

    MATH  Google Scholar 

  18. Zheng, Y.F., Wang, Y.J., Lu, X., Liao, Z.Y., Qu, J.P.: Evolutionary topology optimization for mechanical metamaterials with auxetic property. Int. J. Mech. Sci. 179, 105638 (2020)

    Google Scholar 

  19. Huang, X., Li, Y., Zhou, S.W., Xie, Y.M.: Topology optimization of compliant mechanisms with desired structural stiffness. Eng. Struct. 79, 13–21 (2014)

    Google Scholar 

  20. Zuo, Z.H., Xie, Y.M., Huang, X.: Combining genetic algorithms with BESO for topology optimization. Struct. Multidiscip. Optim. 38, 511–523 (2009)

    MATH  Google Scholar 

  21. He, Y., Cai, K., Zhao, Z.L., Xie, Y.M.: Stochastic approaches to generating diverse and competitive structural designs in topology optimization. Finite Elem. Anal. Des. 173, 103399 (2020)

    MathSciNet  Google Scholar 

  22. Zhu, B.L., Zhang, X.M., Fatikow, S., Wang, N.F.: Bi-directional evolutionary level set method for topology optimization. Eng. Optim. 47, 390–406 (2015)

    MathSciNet  Google Scholar 

  23. Xia, Q., Shi, T.L., Xia, L.: Topology optimization for heat conduction by combining level set method and BESO method. Int. J. Heat Mass Trans. 127, 200–209 (2018)

    Google Scholar 

  24. Gao, J.W., Song, B.W., Mao, Z.Y.: Combination of the phase filed method and BESO method for topology optimization. Struct. Multidiscip. Optim. 61, 225–237 (2020)

    MathSciNet  Google Scholar 

  25. Radman, A.: Combination of BESO and harmony search for topology optimization of microstructures for material. App. Math. Model. 90, 650–661 (2021)

    MathSciNet  MATH  Google Scholar 

  26. Chen, S.X., Ye, S.H.: Criterion method for the optimal design of antenna structure. Acta Mech. Solida Sin. 4, 482–498 (1984)

    Google Scholar 

  27. Chen, S.X., Ye, S.H.: A guide-weight criterion method for the optimal design of antenna structures. Eng. Optim. 10, 199–216 (1986)

    Google Scholar 

  28. Hong, J., Li, B.T., Chen, Y.B., Peng, H.: Study on the optimal design of engine cylinder head by parametric structure characterization with weight distribution criterion. J. Mech. Sci. Technol. 25, 2607–2614 (2011)

    Google Scholar 

  29. Liu, X.J., Li, Z.D., Wang, L.P., Wang, J.S.: Solving topology optimization problems by the Guide-Weight method. Front. Mech. Eng. 6, 136–150 (2011)

    Google Scholar 

  30. Liu, X.J., Li, Z.D., Chen, X.: A new solution for topology optimization problems with multiple loads: the guide-weight method. Sci. China Tech. Sci. 54, 1505–1514 (2011)

    MATH  Google Scholar 

  31. Xu, H.Y., Guan, L.W., Chen, X., Wang, L.P.: Guide-Weight method for topology optimization of continuum structures including body forces. Finite Elem. Anal. Des. 75, 38–49 (2013)

    MathSciNet  MATH  Google Scholar 

  32. Liao, J.P., Huang, G., Chen, X.C., Yu, Z.G., Huang, Q.: A guide-weight criterion-based topology optimization method for maximizing the fundamental eigenfrequency of the continuum structure. Struct. Multidiscip. Optim. 64, 2135–2148 (2021)

    MathSciNet  Google Scholar 

  33. Cui, M.T., Wang, J., Li, P.J., Pan, M.: Topology optimization of plates with constrained layer damping treatments using a modified guide-weight method. J. Vib. Eng. Technol. 1–18 (2021)

  34. Querin, O.M., Steven, G.P., Xie, Y.M.: Evolutionary structural optimization using an additive algorithm. Finite Elem. Anal. Des. 34, 291–308 (2000)

    MATH  Google Scholar 

  35. Da, D.C., Xia, L., Li, G.Y., Huang, X.D.: Evolutionary topology optimization of continuum structures with smooth boundary representation. Struct. Multidiscip. Optim. 57, 2143–2159 (2018)

    MathSciNet  Google Scholar 

  36. Huang, X.: Smooth topological design of structures using the floating projection. Eng. Struct. 208, 110330 (2020)

    Google Scholar 

  37. Montemurro, M.: On the structural stiffness maximisation of anisotropic continua under inhomogeneous Neumann-Dirichlet boundary conditions. Compos. Struct. 287, 115289 (2022)

    Google Scholar 

  38. Montemurro, M., Rodriguez, T., Pailhès, J., Texier, P.L.: On multi-material topology optimisation problems under inhomogeneous Neumann-Dirichlet boundary conditions. Finite Elem. Anal. Des. 214, 103867 (2023)

    MathSciNet  Google Scholar 

  39. Bendsøe, M.P., Sigmund, O.: Topology optimization: theory methods and applications. Springer, Berlin (2003)

    MATH  Google Scholar 

  40. Pedersen, N.L.: Maximization of eigenvalues using topology optimization. Struct. Multidiscip. Optim. 20, 2–11 (2000)

    Google Scholar 

  41. Huang, X., Zuo, Z.H., Xie, Y.M.: Evolutionary topological optimization of vibrating continuum structures for natural frequencies. Comput. Struct. 88, 357–364 (2010)

    Google Scholar 

  42. Costa, G., Montemurro, M.: Eigen-frequencies and harmonic responses in topology optimisation: a CAD-compatible algorithm. Eng. Struct. 214, 110602 (2020)

    Google Scholar 

  43. Li, Y., Huang, X., Xie, Y.M., Zhou, S.W.: Evolutionary topology optimization of hinge-free compliant mechanisms. Int. J. Mech. Sci. 86, 69–75 (2014)

    Google Scholar 

  44. Xu, S.L., Cai, Y.W., Cheng, G.D.: Volume preserving nonlinear density filter based on heaviside functions. Struct. Multidiscip. Optim. 41, 495–505 (2010)

    MathSciNet  MATH  Google Scholar 

  45. Wang, F.W., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Struct. Multidiscip. Optim. 43, 767–784 (2011)

    MATH  Google Scholar 

  46. Sigmund, O.: Morphology-based black and white filters for topology optimization. Struct. Multidiscip. Optim. 33, 401–424 (2007)

    Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Number 62103053) and the Beijing Municipal Science and Technology Project (Grant Number Z221100000222016).

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Authors and Affiliations

  1. CCTEG Chinese Institute of Coal Science, China Coal Technology and Engineering Group, Beijing, 100013, China

    Jingping Liao

  2. Faculty of Information Technology, Beijing University of Technology, Beijing, 100124, China

    Gao Huang & Guoyu Zuo

  3. Beijing Advanced Innovation Center for Intelligent Robots and Systems, Beijing Institute of Technology, Beijing, 100081, China

    Gao Huang & Xuxiao Fan

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  1. Jingping Liao
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  2. Gao Huang
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  4. Xuxiao Fan
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Correspondence to Gao Huang.

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Liao, J., Huang, G., Zuo, G. et al. Combination of the guide-weight criterion and BESO method for fast and stable topology optimization of two-dimensional continuum structures. Acta Mech 234, 5131–5146 (2023). https://doi.org/10.1007/s00707-023-03653-9

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