- -

Efficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity

RiuNet: Institutional repository of the Polithecnic University of Valencia

Share/Send to

Cited by

Statistics

Efficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity

Show full item record

González Estrada, OA.; Natarajan, S.; J.J. Ródenas; Nguyen-Xuan, H.; Bordas, S. (2013). Efficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity. Computational Mechanics. 52(1):37-52. https://doi.org/10.1007/s00466-012-0795-6

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/31483

Files in this item

Item Metadata

Title: Efficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity
Author: González Estrada, Octavio Andrés Natarajan, S. J.J. Ródenas Nguyen-Xuan, H. Bordas, S.P.A.
UPV Unit: Universitat Politècnica de València. Departamento de Ingeniería Mecánica y de Materiales - Departament d'Enginyeria Mecànica i de Materials
Issued date:
Abstract:
[EN] An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown to provide ...[+]
Subjects: Smoothed finite element method , Error estimation , Statical admissibility , SPR-CX , Singularity , Recovery
Copyrigths: Reserva de todos los derechos
Source:
Computational Mechanics. (issn: 0178-7675 )
DOI: 10.1007/s00466-012-0795-6
Publisher:
Springer Verlag
Publisher version: http://dx.doi.org/10.1007/s00466-012-0795-6
Project ID:
info:eu-repo/grantAgreement/EC/FP7/289361/EU/Integrating Numerical Simulation and Geometric Design Technology/
EPSRC/ EP/G042705/1
...[+]
info:eu-repo/grantAgreement/EC/FP7/289361/EU/Integrating Numerical Simulation and Geometric Design Technology/
info:eu-repo/grantAgreement/EC/FP7/279578/EU/Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery/
info:eu-repo/grantAgreement/RCUK/EPSRC/EP/G042705/1/GB/
EPSRC/ EP/G042705/1
ERC/279578
info:eu-repo/grantAgreement/MICINN//DPI2010-20542/ES/DESARROLLO DE HERRAMIENTA 3D COMPUTACIONALMENTE EFICAZ Y DE ALTA PRECISION PARA ANALISIS Y DISEÑO ESTRUCTURAL BASADA EN MALLADOS CARTESIANOS DE EF INDEPENDIENTES DE GEOMETRIA/
GV/PROMETEO/2012/023
[-]
Thanks:
Stephane Bordas would like to thank the partial financial support of the Royal Academy of Engineering and of the Leverhulme Trust for his Senior Research Fellowship Towards the next generation surgical simulators as well ...[+]
Type: Artículo

References

Liu GR, Dai KY, Nguyen TT (2006) A smoothed finite element method for mechanics problems. Comput Mech 39(6): 859–877. doi: 10.1007/s00466-006-0075-4

Liu GR, Nguyen TT, Dai KY, Lam KY (2007) Theoretical aspects of the smoothed finite element method (SFEM). Int J Numer Methods Eng 71(8): 902–930

Nguyen-Xuan H, Bordas SPA, Nguyen-Dang H (2008) Smooth finite element methods: convergence, accuracy and properties. Int J Numer Methods Eng 74(2): 175–208. doi: 10.1002/nme [+]
Liu GR, Dai KY, Nguyen TT (2006) A smoothed finite element method for mechanics problems. Comput Mech 39(6): 859–877. doi: 10.1007/s00466-006-0075-4

Liu GR, Nguyen TT, Dai KY, Lam KY (2007) Theoretical aspects of the smoothed finite element method (SFEM). Int J Numer Methods Eng 71(8): 902–930

Nguyen-Xuan H, Bordas SPA, Nguyen-Dang H (2008) Smooth finite element methods: convergence, accuracy and properties. Int J Numer Methods Eng 74(2): 175–208. doi: 10.1002/nme

Bordas SPA, Natarajan S (2010) On the approximation in the smoothed finite element method (SFEM). Int J Numer Methods Eng 81(5): 660–670. doi: 10.1002/nme

Zhang HH, Liu SJ, Li LX (2008) On the smoothed finite element method. Int J Numer Methods Eng 76(8): 1285–1295. doi: 10.1002/nme.2460

Nguyen-Thoi T, Liu G, Lam K, Zhang G. (2009) A face-based smoothed finite element method (FS-FEM) for 3D linear and nonlinear solid mechanics using 4-node tetrahedral elements. Int J Numer Methods Eng 78: 324–353

Liu G, Nguyen-Thoi T, Lam K (2009) An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids. J Sound Vib 320: 1100–1130

Liu G, Nguyen-Thoi T, Nguyen-Xuan H, Lam K (2009) A node based smoothed finite element method (NS-FEM) for upper bound solution to solid mechanics problems. Comput Struct 87: 14–26

Liu G. Smoothed Finite Element Methods. CRC Press, 2010

Liu G, Nguyen-Xuan H, Nguyen-Thoi T (2010) A theoretical study on the smoothed FEM (SFEM) models: Properties, accuracy and convergence rates. Int J Numer Methods Biomed Eng 84: 1222–1256

Nguyen T, Liu G, Dai K, Lam K (2007) smoothed finite element method. Tsinghua Sci Technol 12: 497–508

Hung NX, Bordas S, Hung N (2009) Addressing volumetric locking and instabilities by selective integration in smoothed finite element. Commun Numer Methods Eng 25: 19–34

Nguyen-Xuan H, Rabczuk T, Bordas S, Debongnie JF (2008) A smoothed finite element method for plate analysis. Comput Methods Appl Mech Eng 197: 1184–1203

Nguyen NT, Rabczuk T, Nguyen-Xuan H, Bordas S (2008) A smoothed finite element method for shell analysis. Comput Methods Appl Mech Eng 198: 165–177

Bordas SPA, Rabczuk T, Hung NX, Nguyen VP, Natarajan S, Bog T, óuan DM, Hiep NV (2010) Strain smoothing in FEM and XFEM. Comput Struct 88(23–24): 1419–1443. doi: 10.1016/j.compstruc.2008.07.006

Bordas SP, Natarajan S, Kerfriden P, Augarde CE, Mahapatra DR, Rabczuk T, Pont SD (2011) On the performance of strain smoothing for óuadratic and enriched finite element approximations (XFEM/GFEM/PUFEM). Int J Numer Methods Biomed Eng 86: 637–666

Liu G, Nguyen-Thoi T, Nguyen-Xuan H, Dai K, Lam K (2009) On the essence and the evaluation of the shape functions for the smoothed finite element method (SFEM). Int J Numer Methods Eng 77: 1863–1869. doi: 10.1002/nme.2587

Strouboulis T, Zhang L, Wang D, Babuška I. (2006) A posteriori error estimation for generalized finite element methods. Comput Methods Appl Mech Eng 195(9–12): 852–879

Bordas SPA, Duflot M (2007) Derivative recovery and a posteriori error estimate for extended finite elements. Comput Methods Appl Mech Eng 196(35–36): 3381–3399

Xiao óZ, Karihaloo BL (2004) Statically admissible stress recovery using the moving least sóuares technique. In: Topping BHV, Soares CAM (eds) Progress in computational structures technology. Saxe-Coburg Publications, Stirling, pp 111–138

Ródenas JJ, González-Estrada OA, Tarancón JE, Fuenmayor FJ (2008) A recovery-type error estimator for the extended finite element method based on singular + smooth stress field splitting. Int J Numer Methods Eng 76(4): 545–571. doi: 10.1002/nme.2313

Panetier J, Ladevèze P, Chamoin L (2010) Strict and effective bounds in goal-oriented error estimation applied to fracture mechanics problems solved with XFEM. Int J Numer Methods Eng 81(6): 671–700

Barros FB, Proenca SPB, de Barcellos CS (2004) On error estimator and p-adaptivity in the generalized finite element method. Int J Numer Methods Eng 60(14):2373–2398. doi: 10.1002/nme.1048

Nguyen-Thoi T, Liu G, Nguyen-Xuan H, Nguyen-Tran C (2011) Adaptive analysis using the node-based smoothed finite element method (NS-FEM). Int J Numer Methods Biomed Eng 27(2): 198–218. doi: 10.1002/cnm

González-Estrada OA, Ródenas JJ, Bordas SPA, Duflot M, Kerfriden P, Giner E (2012) On the role of enrichment and statical admissibility of recovered fields in a-posteriori error estimation for enriched finite element methods. Eng Comput 29(8)

Zienkiewicz OC, Zhu JZ (1987) A simple error estimator and adaptive procedure for practical engineering analysis. Int J Numer Methods Eng 24(2): 337–357

Ródenas JJ, González-Estrada OA, Díez P, Fuenmayor FJ (2010) Accurate recovery-based upper error bounds for the extended finite element framework. Comput Methods Appl Mech Eng 199(37–40): 2607–2621

Williams ML (1952) Stress singularities resulting from various boundary conditions in angular corners of plate in extension. J Appl Mech 19: 526–534

Szabó BA, Babuška I (1991) Finite element analysis. Wiley, New York

Barber JR. (2010) Elasticity. Series: solid mechanics and its application, 3rd edn. Springer, Dordrecht

Chen JS, Wu CT, Yoon S, You Y (2001) A stabilized conforming nodal integration for Galerki mesh-free methods. Int J Numer Methods Eng 50: 435–466

Yoo J, Moran B, Chen J (2004) Stabilized conforming nodal integration in the natural element method. Int J Numer Methods Eng 60: 861–890

Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique. Int J Numer Methods Eng 33(7): 1331–1364

Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity. Int J Numer Methods Eng 33(7): 1365–1382

Wiberg NE, Abdulwahab F (1993) Patch recovery based on superconvergent derivatives and eóuilibrium. Int J Numer Methods Eng 36(16): 2703–2724. doi: 10.1002/nme.1620361603

Blacker T, Belytschko T (1994) Superconvergent patch recovery with eóuilibrium and conjoint interpolant enhancements. Int J Numer Methods Eng 37(3): 517–536

Stein E, Ramm E, Rannacher R (2003) Error-controlled adaptive finite elements in solid mechanics. Wiley, Chichester

Duflot M, Bordas SPA (2008) A posteriori error estimation for extended finite elements by an extended global recovery. Int J Numer Methods Eng 76: 1123–1138. doi: 10.1002/nme

Bordas SPA, Duflot M, Le P (2008) A simple error estimator for extended finite elements. Commun Numer Methods Eng 24(11): 961–971

Ródenas JJ, Tur M, Fuenmayor FJ, Vercher A (2007) Improvement of the superconvergent patch recovery technique by the use of constraint eóuations: the SPR-C technique. Int J Numer Methods Eng 70(6): 705–727. doi: 10.1002/nme.1903

Díez P, Ródenas JJ, Zienkiewicz OC (2007) Eóuilibrated patch recovery error estimates: simple and accurate upper bounds of the error. Int J Numer Methods Eng 69(10): 2075–2098. doi: 10.1002/nme

Yau J, Wang S, Corten H (1980) A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity. J Appl Mech 47(2): 335–341

Ródenas JJ, González-Estrada OA, Fuenmayor FJ, Chinesta F (2010) Upper bounds of the error in X-FEM based on a moving least sóuares (MLS) recovery technique. In: Khalili N, Valliappan S, Li ó, Russell A (eds) 9th World congress on computational mechanics (WCCM9). 4th Asian Pacific Congress on computational methods (APCOM2010). Centre for Infrastructure Engineering and Safety

Ródenas JJ, González-Estrada OA, Díez P, Fuenmayor FJ (2007) Upper bounds of the error in the extended finite element method by using an eóuilibrated-stress patch recovery technique. In: International conference on adaptive modeling and simulation (ADMOS 2007). International Center for Numerical Methods in Engineering (CIMNE), pp 210–213

Menk A, Bordas S (2010) Numerically determined enrichment function for the extended finite element method and applications to bi-material anisotropic fracture and polycrystals. Int J Numer Methods Eng 83: 805–828

Menk A, Bordas S (2011) Crack growth calculations in solder joints based on microstructural phenomena with X-FEM. Comput Mater Sci 3: 1145–1156

Ródenas JJ (2001) Error de discretización en el cálculo de sensibilidades mediante el método de los elementos finitos. PhD Thesis, Universidad Politécnica de Valencia

Ainsworth M, Oden JT (2000) A posteriori error estimation in finite element analysis. Wiley, Chichester

[-]

This item appears in the following Collection(s)

Show full item record