Authors:
Long Nguyen-Nhut-Phi,Son Nguyen-Hoai,Quan Nguyen,Phong Le-Thanh,Dai Mai-Duc,DOI NO:
https://doi.org/10.26782/jmcms.2020.05.00003Keywords:
Finite element method (FEM),Laser butt weld,Relative error,Reliability,h- refinement,p- refinement,Abstract
The finite element (FE) solutions are different from the exact ones due to the presence of various error sources, such as computer round-off error, error due to discrete of the displacement field, etc. This paper uses the h- and p-refinement of the finite element method for the laser butt weld problem, with the base metal is AISI 1018 steel highness 8 mm. The objective is to present estimation techniques the strain energy relative error and evaluate its reliability through two indices: the affectivity index and the uniformity index SD. The numerical results achieve to meet the conditions for reliability assessment. Specifically, the, , SD values of h- refinement, and p- refinement respectively: less than 6%, 0.535667, 0.019528, and less than 4%, 0.506616, 0.103834.Refference:
I. A. Düster & E. Rank, “The p-version of the finite element method compared to an adaptive h-version for the deformation theory of plasticity”, Computer Methods in Applied Mechanics and Engineering, 190(15-17), 1925–1935, 2001 (https://doi.org/10.1016/s0045-7825(00)00215-2)
II. B. A. Szabó, “Mesh design for the p-version of the finite element method”, Computer Methods in Applied Mechanics and Engineering, 55(1-2), 181–197 (https://doi.org/10.1016/0045-7825(86)90091-5), 1986
III. B. A. Szabo, P. K. Basu, and M. P. Rossow, “Adaptive Finite Element Analysis Based on P-Convergence”, Symposium on Future Trends in Computerized Structural Analysis and Synthesis, Washington, D.C., NASA Conference Publication 2059, pp. 43-50, 1978
IV. Claudio Canuto, Ricardo H. Nochetto, Rob P. Stevenson, and Marco Verani, “Convergence and Optimality of hp-AFEM”, Numer. Math. 135, 1073–1119 (https://doi.org/10.1007/s00211-016-0826-x), 2017
V. F.Cugnon & P.Beckers, “Error estimation for h- and p-methods”, 8th Mechanical Engineering Chilean Congress”, Concepción, pp.183-188, 1998
VI. F.Cugnon: Automatisation des calculs elements finis dans le cadre de la methode-p, these de doctorat, ULG, 2000
VII. F.Cugnon, M. Meyers, P.Beckers& G. Warzee, “Iterative solvers for the p-version of the finite element method”, first international conference on Advanced Computational Methods in Engineering – ACOMEN’ 98, Ghent, pp. 737-744, 1988
VIII. I. Babuška and B. A. Szabó,“On the Rates of Convergence of the Finite Element Method”, Int. J. Numer. Meth. Engng., 18, 323-341, 1982
IX. I. Babuška and W.C. Rheinboldt, “A‐posteriori error estimates for the finite element method”, Int. J. Numer. Meth. Engng, 12: 1597-1615, 1978 (http://dx.doi.org/10.1002/nme.1620121010)
X. Information on http://amet-me.mnsu.edu/ UserFilesShared/ DATA_ACQUISITION/mts/MaterialData/MaterialData_6809-1018ColdDrawn.pdf
XI. Information on http://homepages.engineering.auckland.ac.nz /~pkel015/ SolidMechanicsBooks/Part_I/BookSM_Part_I/08_Energy/08_Energy_02_Elastic_Strain_Energy.pdf
XII. Information on http://www.engr.mun.ca/~katna/5931/ STRAIN%20 ENERGY-Impact Loading.pdf
XIII. Information on http://www.yandreou.com/wp-content/uploads/2014/08/AISI-1018-Mild-Low-Carbon-Steel-PDF.pdf
XIV. J. E. Flaherty: Finite element analysis, Troy, New York, 2002
XV. Jae S. Ahn, Seung H. Yang, and Kwang S. Woo.,“Free Vibration Analysis of Patch Repaired Plates with a Through Crack by p-Convergent Layer-wise Element”, The Scientific World Journal, 2014. Article ID 427879. (http://dx.doi.org/10.1155/2014/427879)
XVI. L. Demkowicz, Ph. Devloo, J.T. Oden,“On an h-type mesh-refinement strategy based on minimization of interpolation errors”, Computer Methods in Applied Mechanics and Engineering, Volume 53, Issue 1, Pages 67-89, ISSN 0045-7825, 1985 (https://doi.org/10.1016/0045-7825(85)90076-3)
XVII. Michael R. Dörfel, Bert Jüttler, Bernd Simeon, “Adaptive isogeometric analysis by local h-refinement with T-splines”, Computer Methods in Applied Mechanics and Engineering, Volume 199, Issues 5–8, Pages 264-275, ISSN 0045-7825, 2010 (https://doi.org/10.1016/j.cma.2008.07.012)
XVIII. Son. Nguyen,“The error estimate and the convergence rate for h, p – refinement in the Finite Element Analysis”. Vietnam Journal of Mechanics, VAST, Vol. 30, No. 3, pp. 179 – 184, 2008 (https://doi.org/10.15625/0866-7136/30/3/5617)
XIX. Stephan, Ernst &Wriggers, Peter,“Modeling, Simulation, and Software Concepts for Scientific-Technological Problems”, 2011 (https://doi.org/10.1007/978-3-642-20490-6)
XX. Y. L. Kuo, W. L. Cleghorn, K. Behdinan, & R. G. Fenton, “The h–p–r-refinement finite element analysis of a planar high-speed four-bar mechanism”, Mechanism and Machine Theory, 41(5), 505–524, 2006 (https://doi.org/10.1016/j.mechmachtheory.2005.09.001)\