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A Coupled Method of Meshfree Poly-Cell Galerkin and Finite Element for Elasticity Problems

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Proceedings of the Ninth International Conference on Management Science and Engineering Management

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 362))

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Abstract

This paper developed a new method named as MPG/FEM method which is constructed by coupling the meshfree poly-cell Galerkin method (MPG) with the finite element method (FEM) for the analysis of elasticity problems. The present MPG/FEM method synthesizes the advantages of both FEM and MPG. MPG/FEM method not only simplifies the implementation of essential boundary conditions like FEM, but also inherits good accuracy from MPG. The numerical tests in the present work demonstrate that the results obtained by MPG/FEM method show an excellent agreement with the theoretical results. The coupled method is very accurate and has a promising potential for the analyses of more complicated elasticity problems.

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References

  1. Zienkiewicz O, Taylor R (2000) The finite element method. Change 50:28–73

    Google Scholar 

  2. Gu Y, Zhang L (2008) Coupling of the meshfree and finite element methods for determination of the crack tip fields. Eng Fract Mech 75:986–1004

    Article  Google Scholar 

  3. Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon Not R Astron Soc 181:375–389

    Article  Google Scholar 

  4. Lucy LB (1977) A numerical approach to the testing of the fission hypothesis. Astron J 82:1013–1024

    Article  Google Scholar 

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

    Article  Google Scholar 

  6. Liu WK, Jun S, Zhang YF (1995) Reproducing Kernel particle methods. Int J Numer Methods Fluids 20:1081–1106

    Article  Google Scholar 

  7. Atluri S, Zhu T (1998) A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput Mech 22:117–127

    Article  Google Scholar 

  8. Cai Y, Zhu H, Wang J (2003) The meshless local-Petrov Galerkin method based on the Voronoi cells. Acta Mechanica Sinica 2:010

    Google Scholar 

  9. Fries TP, Belytschko T (2008) Convergence and stabilization of stress-point integration in mesh-free and particle methods. Int J Numer Methods Eng 74:1067–1087

    Article  Google Scholar 

  10. Beissel S, Belytschko T (1996) Nodal integration of the element-free Galerkin method. Comput Methods Appl Mech Eng 139:49–74

    Article  Google Scholar 

  11. Liu G, Zhang G et al (2007) A nodal integration technique for meshfree radial point interpolation method (NI-RPIM). Int J Solids Struct 44:3840–3860

    Article  Google Scholar 

  12. Zhou J, Wen J et al (2003) A nodal integration and post-processing technique based on Voronoi diagram for Galerkin meshless methods. Comput Methods Appl Mech Eng 192:3831–3843

    Article  Google Scholar 

  13. Braun J, Sambridge M et al (1995) A numerical method for solving partial differential equations on highly irregular evolving grids. Nature 376:655–660

    Article  Google Scholar 

  14. Zheng C, Tang X et al (2009) A novel mesh-free poly-cell Galerkin method. Acta Mechanica Sinica 25:517–527

    Article  Google Scholar 

  15. Idelsohn SR, Onate E (2006) To mesh or not to mesh. that is the question. Comput Methods Appl Mech Eng 195:4681–4696

    Article  Google Scholar 

  16. Idelsohn SR, Onate E et al (2003) The meshless finite element method. Int J Numer Methods Eng 58:893–912

    Article  Google Scholar 

  17. Chao Z, Wu S et al (2008) A Meshfree Poly-cell Galerkin (MPG) approach for elasticity and fracture problems. Comput Model Eng Sci 38:149–178

    Google Scholar 

  18. Lancaster P, Salkauskas K (1981) Surfaces generated by moving least squares methods. Math Comput 37:141–158

    Article  Google Scholar 

  19. Li G, Ge J, Jie Y (2003) Free surface seepage analysis based on the element-free method. Mech Res Commun 30:9–19

    Article  Google Scholar 

  20. Liu GR (2010) Meshfree methods: moving beyond the finite element method. CRC Press, New York

    Google Scholar 

  21. Gu Y, Liu G (2005) Meshless methods coupled with other numerical methods. Tsinghua Sci Technol 10:8–15

    Article  Google Scholar 

  22. Timoshenko S, Goodier J (1970) Theory of elasticity. McGraw-Hill, New York, pp 35–39

    Google Scholar 

  23. Young WC, Budynas RG (1975) Roark’s formulas for stress and strain. McGraw-Hill, New York, pp 683–685

    Google Scholar 

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Ma, J., He, K. (2015). A Coupled Method of Meshfree Poly-Cell Galerkin and Finite Element for Elasticity Problems. In: Xu, J., Nickel, S., Machado, V., Hajiyev, A. (eds) Proceedings of the Ninth International Conference on Management Science and Engineering Management. Advances in Intelligent Systems and Computing, vol 362. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47241-5_6

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  • DOI: https://doi.org/10.1007/978-3-662-47241-5_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-47240-8

  • Online ISBN: 978-3-662-47241-5

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