Back
 MME  Vol.2 No.2 , May 2012
A Comparative Study of Stress Recovery Method and Error Estimation of Plate Bending Problem Using DKMQ Element
Abstract: Recovery by Equilibrium in Patches (REP) is a recovery method introduced by B. Boroomand. This method is using patch as recovery media as is used by Superconvergent Patch Recovery (SPR) which is well known as a good recovery method. In this research, a numerical study of REP implementation is held to estimate error in finite element analysis using DKMQ element. The numerical study is performed with both uniform and adaptive h-type mesh refinement. The result is compared with three other recovery method, i.e. SPR method, averaging method, and projection method.
Cite this paper: I. Katili, A. Hamdouni, O. Millet, J. Rastandi and I. Maknun, "A Comparative Study of Stress Recovery Method and Error Estimation of Plate Bending Problem Using DKMQ Element," Modern Mechanical Engineering, Vol. 2 No. 2, 2012, pp. 47-55. doi: 10.4236/mme.2012.22007.
References

[1]   O. C. Zienkiewicz and J. Z. Zhu, “The Superconvergence Patch Recovery and a Posteriori Error Estimation in the Finite Element Method, Part 1: The Recovery Technique,” International Journal for Numerical Methods in En- gineering, Vol. 33, No. 7, 1992, pp. 1331-1364. doi:10.1002/nme.1620330702

[2]   O. C. Zienkiewicz and J. Z. Zhu, “The Superconvergence Patch Recovery and a Posteriori Error Estimation in the Finite Element Method, Part 2: Error Estimates and Adaptivity,” International Journal for Numerical Methods in Engineering, Vol. 33, No. 7, 1992, pp. 1364-1382. doi:10.1002/nme.1620330703

[3]   Z. Z. Zhang, “Ultracon-vergence of the Patch Recovery Technique,” Mathematics of Computations, Vol. 65, No. 216, 1996, pp. 1431-1437. doi:10.1090/S0025-5718-96-00782-X

[4]   B. Boroomand and O. C. Zienkiewicz, “Recovery by Equilibrium in Patches (REP),” International Journal for Numerical Methods in Engineering, Vol. 40, No. 1, 1997, pp. 137-164. doi:10.1002/(SICI)1097-0207(19970115)40:1<137::AID-NME57>3.0.CO;2-5

[5]   B. Boroomand and O. C. Zienkiewicz, “An Improved REP Recovery and the Effectivity Robustness Test,” Inter- national Journal for Numerical Methods in Engineering, Vol. 40, No. 17, 1997, pp. 3247-3277. doi:10.1002/(SICI)1097-0207(19970915)40:17<3247::AID-NME211>3.0.CO;2-Z

[6]   B. Boroomand, M. Ghaffarian and O. C. Zienkiewicz, “On Application of Two Superconvergent Re-covery Procedures to Plate Problems,” International Journal for Numerical Methods in Engineering, Vol. 61, No. 10, 2004, pp. 1644-1673. doi:10.1002/nme.1128

[7]   Z. Zhang and A. Naga, “Polynomial Preserving Gradient Recovery And A Posteriori Estimate for Bilinear Element On Irregular Quadrilaterals,” International Journal of Numerical Analysis and Modeling, Vol. 1, No. 1, 2004, pp. 1-24.

[8]   O. C. Zienkiewicz and J. Z. Zhu, “The Background of Error Estimation and Adaptivity in Finite Element Computations,” Computer Methods in Applied Mechanics and Engineering, Vol. 195, No. 4-6, 2006, pp. 207-213. doi:10.1016/j.cma.2004.07.053

[9]   A. Duster, et al., “pq-Adaptive Solid Finite Elements for Three-Dimensional Plates and Shells,” Computer Methods in Applied Mechanics and Engineering, Vol. 197, No. 1-4, 2007, pp. 243-254. doi:10.1016/j.cma.2007.07.020

[10]   Ph. Destuynder, et al., “Adaptive Mesh Refinements for Thin Shells Whose Middle Surface Is Not Exactly Known,” Computer Methods in Applied Mechanics and Engineering, Vol. 197, No. 51-52, 2008, pp. 4789-4811. doi:10.1016/j.cma.2008.07.001

[11]   M. Ainsworth, et al., “A Framework for Obtaining Guar- anteed Error Bounds for Finite Element Approximations,” Journal of Computational and Ap-plied Mathematics, Vol. 234, No. 9, 2010, pp. 2618-2632. doi:10.1016/j.cam.2010.01.037

[12]   J. H. Nie, et al., “Devel-opment of an Object-Oriented Finite Element Program with Adaptive Mesh Refinement for Multi-Physics Applications,” Advances in Engineering Software, Vol. 41, No. 4, 2010, pp. 569-579. doi:10.1016/j.advengsoft.2009.11.004

[13]   V. S. Lukin, et al., “A Priori Mesh Quality Metric Error Analysis Applied to a High-Order Finite Element Method,” Journal of Computational Physics, Vol. 230, No. 14, 2011, pp. 5564-5586. doi:10.1016/j.jcp.2011.03.036

[14]   K. J. Bathe, et al., “The Use of Nodal Point Forces to Improve Element Stresses”, Computers and Structures, Vol. 89, No. 5-6, 2011, pp. 485-495. doi:10.1016/j.compstruc.2010.12.002

[15]   I. Katili, et al., “A New Discrete Kirchoff-Mindlin Element Based on Min-dlin-Reissner Plate Theory an Assumed Shear Strain Fields. Part 2: An Extended DKQ Element for Thick-Plate Bending Analysis,” International Journal for Numerical Methods in Engineering, Vol. 36, No. 11, 1993, pp. 1885-1908. doi:10.1002/nme.1620361107

[16]   J. E. Akin, “Finite Element Analysis with Error Estimators,” Elsevier Butter-worth-Heinemann, Burlinton, 2005.

 
 
Top