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Moving Least Squares (MLS) Interpolation Based Post-processing Parametric Study in Finite Element Elastic Problems

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Computational and Experimental Simulations in Engineering (ICCES 2019)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 75))

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Abstract

The parametric effect on performance of Moving Least Squares (MLS) interpolation based recovery technique is evaluated in this paper. The Moving Least Squares (MLS) fitting recovers the field variable derivatives over nodes patch using background element meshes. The recovered errors at element and global levels in the finite element solution are presented in energy norm. The study considers three basic recovery parameters (i.e. parameters affecting the post-processed results) namely shape of influence (support) domain, dilation parameter and order of poly nominal basis function. Numerical experiments on elastic plate problems are carried out for parametric effect of interpolation based post processing technique on effectivity of error estimation and rate of convergence of the recovered solution with fineness of the meshing scheme. The linear and quadratic triangular elements have been used for the discretization of the problem domain. The circular and rectangular shape domain of influence is used to form the node patch. Six different dilation parameters and three different number of basis function terms are selected in the moving least squared interpolation formulation. The study shows that recovery parameters of MLS interpolation method have pronounced effect on the post-processing recovery of finite element solution and optimal alternatives are to be adopted for better performance of the recovery procedures.

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References

  1. Ainsworth, M., Oden, J.T.: A posteriori error estimation in finite element analysis. Comp. Methods Appl. Mech. Eng. 142, 1–88 (1997)

    Article  MathSciNet  Google Scholar 

  2. Gratsch, T., Bathe, K.: A posteriori error estimation techniques in practical finite element analysis. Comput. Struct. 83, 235–265 (2005)

    Article  MathSciNet  Google Scholar 

  3. Mirzaei, D.: Analysis of moving least squares approximation. Revisit. J. Comput. Appl. Math. 282, 237–250 (2015)

    Article  MathSciNet  Google Scholar 

  4. Xing, H.L., Wang, S., Makinouchi, A.: An adaptive mesh h-refinement algorithm for finite-element modelling of sheet forming. J. Mater. Process. Technol. 91, 183–190 (1999)

    Google Scholar 

  5. Liu, Y.C., Elmaraghy, H.A.: Assessment of discretized errors and adaptive refinement with quadrilateral finite element. Int. J. Num. Methods Eng. 33, 781–798 (1992)

    Article  Google Scholar 

  6. Zienkiewicz, O.C., Zhu, J.Z.: A simple error estimator and adaptive procedure for practical engineering analysis. Int. J. Num. Methods Eng. 24, 333–357 (1987)

    Article  MathSciNet  Google Scholar 

  7. Liu, G.R., Nguyen-Thoia, T., Lam, K.Y.: A novel alpha finite element method (αFEM) for exact solution to mechanics problems using triangular and tetrahedral elements. Comput. Methods Appl. Mech. Eng. 197, 3883–3897 (2008)

    Article  MathSciNet  Google Scholar 

  8. Kim, K.-Y., Lee, H.-C.: A posteriori error estimators for nonconforming finite element methods of the linear elasticity problem. J. Comput. Appl. Math. 235, 186–202 (2010)

    Article  MathSciNet  Google Scholar 

  9. Ullah, Z., Coombs, W.M., Augarde, C.E.: An adaptive finite element/meshless coupled method based on local maximum entropy shape functions for linear and nonlinear problems. Comput. Methods Appl. Mech. Eng. 267, 111–132 (2013)

    Article  MathSciNet  Google Scholar 

  10. Bramble, J.H., Schatz, A.H.: Higher order local accuracy by averaging in finite element method. 31, 94–111 (1977)

    Google Scholar 

  11. Hinton, E., Campbell, J.S.: Local and global smoothing of discontinuous finite element functions using a least square methods. Int. J. Num. Methods Eng. 8, 61–80 (1974)

    Article  MathSciNet  Google Scholar 

  12. Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates, part I, the error recovery technique. Int. J. Num. Methods Eng. 33, 1331–1364 (1992)

    Article  Google Scholar 

  13. Zienkiewicz, O.C., Zhu, J.Z.: The superconvergent patch recovery and a posteriori error estimates. Part II: error estimates and adaptivity. Int. J. Num. Methods Eng. 33, 1365–1382 (1992)

    Article  Google Scholar 

  14. Li, X.D., Wiberg, N.E.: An posteriori error estimate by element patch post-processing, adaptive analysis in energy and L2 norms. Comput. Struct. 53, 907–919 (1994)

    Article  Google Scholar 

  15. Ubertini, F.: Patch recovery based on complementary energy. Int. J. Numer. Methods Eng. 59(11), 1501–1538 (2004)

    Article  Google Scholar 

  16. Parret-Fréaud, A., Rey, V., Gosselet, P., Rey, C.: Improved recovery of admissible stress in domain decomposition methods—application to heterogeneous structures and new error bounds for FETI-DP. Int. J. Numer. Methods Eng. 111(1), 69–87 (2016)

    Article  MathSciNet  Google Scholar 

  17. Sharma, R., Zhang, J., Langelaar, M., van Keulen, F., Aragón, A.M.: An improved stress recovery technique for low-order 3D finite elements. Int. J. Numer. Methods Eng. 114, 88–103 (2018)

    Article  MathSciNet  Google Scholar 

  18. Ahmed, M., Singh, D., Desmukh, M.N.: Interpolation type stress recovery technique based error estimator for elasticity problems. Mechanika 24(5), 672–679 (2018)

    Article  Google Scholar 

  19. Rajendran, S., Liew, K.M.: Optimal stress sampling points of plane triangular elements for patch recovery of nodal stresses. Int. J. Numer. Methods Eng. 58, 579–607 (2003)

    Article  Google Scholar 

  20. Wang, J.G., Liu, G.R.: On the optimal shape parameters of radial basis functions used for 2-D meshless methods. Comput. Methods Appl. Mech. Eng., 191(23–24), 2611–2630 (2002)

    Article  MathSciNet  Google Scholar 

  21. Kanber, B., Bozkurt, O.Y., Erklig, A.: Investigation of RPIM shape parameter effects on the solution accuracy of 2D elastoplastic problems. Int. J. Comput. Methods Eng. Sci. Mech. 14, 354–366 (2013)

    Article  MathSciNet  Google Scholar 

  22. Perko, J., Šarler, B.: Weight function shape parameter optimization in meshless methods for non-uniform grids. CMES 19(1), 55–68 (2007)

    MathSciNet  MATH  Google Scholar 

  23. Nie, Y.F., Atluri, S.N., Zuo, C.W.: The optimal radius of the support of radial weights used in moving least squares approximation. CMES 12(2), 137–147 (2006)

    Google Scholar 

  24. Onate, E., Perazzo, F., Miquel, J.: A finite point method for elasticity problems. Comput. Struct. 79, 2151–2163 (2001)

    Article  Google Scholar 

  25. Ahmed, M., Singh, D.: An adaptive parametric study on mesh refinement during adaptive finite element simulation of sheet forming operations. Turk. J. Eng. Environ. Sci. 13, 1–13 (2008)

    Google Scholar 

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Acknowledgements

Authors thank Deanship of Research, Ministry of Higher Education, KSA, for financial support to carry out the research work. The authors also acknowledge to the Dean, College of Engineering for his valuable support and help.

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Authors and Affiliations

  1. College of Engineering, Main Campus, Gregar, K. K. University, Abha, 61411, Saudi Arabia

    Mohd. Ahmed, Mohamed Hechmi El Ouni & Nabil Ben Kahla

  2. Ministry of Information, Soochan Bhavan, CGO Complex, Delhi, 110003, India

    Devender Singh

Authors
  1. Mohd. Ahmed
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  2. Mohamed Hechmi El Ouni
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  3. Devender Singh
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  4. Nabil Ben Kahla
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Correspondence to Mohd. Ahmed .

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Editors and Affiliations

  1. Department of Mechanical Engineering, Tokyo University of Science, Noda, Chiba, Japan

    Hiroshi Okada

  2. Department of Mechanical Engineering, Texas Tech University, Lubbock, TX, USA

    Satya N. Atluri

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Ahmed, M., El Ouni, M.H., Singh, D., Kahla, N.B. (2020). Moving Least Squares (MLS) Interpolation Based Post-processing Parametric Study in Finite Element Elastic Problems. In: Okada, H., Atluri, S. (eds) Computational and Experimental Simulations in Engineering. ICCES 2019. Mechanisms and Machine Science, vol 75. Springer, Cham. https://doi.org/10.1007/978-3-030-27053-7_105

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  • DOI: https://doi.org/10.1007/978-3-030-27053-7_105

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-27052-0

  • Online ISBN: 978-3-030-27053-7

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