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Topology Optimization of Structures Using an Adaptive Element-Free Galerkin Method

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Advances in Global Optimization

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 95))

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Abstract

This paper proposes a topology optimization method based on an adaptive element-free Galerkin (EFG) method. Since there are a large number of discrete design variables in the meshless based topology optimization, the adaptive EFG method is included to improve the computational efficiency. The topology optimization problem is formulated as a mean compliance design of structures, in which the nodal densities are regarded as design variable. In the proposed method, the criteria of adding node, the scheme of adaptively inserting nodes, and the method of updating the variable for any new node are discussed. A typical example is used to demonstrate the effectiveness of the proposed topology optimization method using the adaptive EFG method.

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References

  1. Bendsøe, M.P., Sigmund, O.: Topology Optimization: Theory, Methods, and Applications. Springer, Berlin (2003)

    Google Scholar 

  2. Luo, Z., Zhang, N., Wang, Y., Gao, W.: Topology optimization of structures using meshless density variable approximants. Int. J. Numer. Methods Eng. 93, 443–464 (2013)

    Article  MathSciNet  Google Scholar 

  3. Allaire, G., Jouve, F., Toader, A.M.: Structural optimization using sensitivity analysis and a level-set method. J. Comput. Phys. 194, 363–393 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  4. Luo, Z., Wang, M.Y., Wang, S., Wei, P.: A level set-based parameterization method for structural shape and topology optimization. Int. J. Numer. Methods Eng. 76, 1–16 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  5. Sigmund, O., Petersson, J.: Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct. Multidiscip. Optim. 16, 68–75 (1998)

    Article  Google Scholar 

  6. Du, Y., Luo, Z., Tian, Q., Chen, L.: Topology optimization for thermomechanical compliant actuators using mesh-free methods. Eng. Optim. 41, 753–772 (2009)

    Article  MathSciNet  Google Scholar 

  7. Xu, S., Cheng, G.D.: Structural topology optimization based on adaptive mesh. J. Dalian Univ. Technol. 49, 469–475 (2009)

    Google Scholar 

  8. Lin, C.Y., Chou, J.N.: A two-stage approach for structural topology optimization. Adv. Eng. Softw. 30, 261–271 (1999)

    Article  Google Scholar 

  9. Wu, X., Gong, S.: Research of EFGM structure topology optimization based on adaptive scheme. Ph.D. Thesis, Xiangtan University (2011)

    Google Scholar 

  10. Belytschko, T., Lu, Y.Y., Gu, L.: Element-free Galerkin methods. Int. J. Numer. Methods Eng. 37, 229–256 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  11. Liu, G.R., Gu, Y.T.: An Introduction to Meshfree Methods and Their Programming. Springer, Berlin (2005)

    Google Scholar 

  12. Dolbow, J., Belytschko, T.: An introduction to programming the meshless element free Galerkin method. Arch. Comput. Methods Eng. 5(3), 207–241 (1998)

    Article  MathSciNet  Google Scholar 

  13. Bendsøe, M.P., Sigmund, O.: Material interpolation schemes in topology optimization. Arch. Appl. Mech. 69, 635–654 (1999)

    Article  Google Scholar 

  14. Gao, D.Y.: Solutions and optimality criteria to box constrained nonconvex minimization problems. J. Ind. Manag. Optim. 3, 293–304 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  15. Gao, D.Y., Ruan, N.: Solutions to quadratic minimization problems with box and integer constraints. J. Glob. Optim. 47, 463–484 (2012)

    Article  MathSciNet  Google Scholar 

  16. Rozvany, G.I.N., Kirch, U., Bendsøe, M.P., Sigmund, O.: Layout optimization of structures. Appl. Mech. Rev. 48, 41–119 (1995)

    Article  Google Scholar 

  17. Zhou, J.X., Zou, W.: Meshless approximation combined with implicit topology description for optimization of continua. Struct. Multidiscip. Optim. 36, 347–353 (2008)

    Article  MATH  Google Scholar 

  18. Liu, G.R., Tu, Z.H.: An adaptive procedure based on background cells for meshless methods. Comput. Methods Appl. Mech. Eng. 191, 1923–1943 (2002)

    Article  MATH  Google Scholar 

  19. Feng, T., Liu, X.: Study on adaptive meshfree method in solid mechanics. Ph.D. Thesis, Zhejiang University (2007)

    Google Scholar 

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Acknowledgements

This research was partially funded by National Natural Science Foundation of China (51105229; 51305232), Natural Science Foundation of Hubei Province of China (2010CDB10805), and National Science Foundation for Distinguished Young Scholars of Hubei Province of China (2013CFA022).

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Authors and Affiliations

  1. College of Mechanical and Material Engineering, China Three Gorges University, Yichang, 443002, China

    Yixian Du, Shuangqiao Yan, De Chen, Qingping Long & Xiang Li

  2. Hubei Key Laboratory of Hydroelectric Machinery Design & Maintenance, China Three Gorges University, Yichang, 443002, China

    Yixian Du, Shuangqiao Yan, De Chen, Qingping Long & Xiang Li

  3. Collaborative Innovation Center for Energy Equipment of Three Gorges Region, China Three Gorges University, Yichang, 443002, China

    Yixian Du, Shuangqiao Yan, De Chen, Qingping Long & Xiang Li

Authors
  1. Yixian Du
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  2. Shuangqiao Yan
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  3. De Chen
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  4. Qingping Long
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  5. Xiang Li
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Corresponding author

Correspondence to Yixian Du .

Editor information

Editors and Affiliations

  1. School of Science, Information Technology and Engineering, Federation University Australia, Ballarat, Victoria, Australia

    David Gao

  2. School Science, Inform., Tech. & Engg., Federation University Australia, Ballarat, Victoria, Australia

    Ning Ruan

  3. Dept. of Mathematical Sciences, Tsinghua University, Beijing, China

    Wenxun Xing

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Du, Y., Yan, S., Chen, D., Long, Q., Li, X. (2015). Topology Optimization of Structures Using an Adaptive Element-Free Galerkin Method. In: Gao, D., Ruan, N., Xing, W. (eds) Advances in Global Optimization. Springer Proceedings in Mathematics & Statistics, vol 95. Springer, Cham. https://doi.org/10.1007/978-3-319-08377-3_24

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