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Erschienen in: Computational Mechanics 4/2013

01.10.2013 | Original Paper

Patch based recovery in finite element elastoplastic analysis

verfasst von: Federica Daghia, Stefano de Miranda, Francesco Ubertini

Erschienen in: Computational Mechanics | Ausgabe 4/2013

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Abstract

A new patch based stress recovery procedure for elastoplastic analysis is presented in this paper. The formulation derives from the extension to the elastic-perfectly plastic case of the Recovery by Compatibility in Patches procedure recently proposed by the authors. The present procedure is designed to simultaneously reconstruct both a new stress field and a new plastic strain field, so to ensure that elastoplastic consistency is satisfied. The numerical results on two common benchmark problems show the effectiveness of the new procedure.

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Literatur
1.
Zurück zum Zitat Ainsworth M, Oden JT (2000) A posteriori error estimation in finite element analysis. Wiley, New YorkCrossRefMATH Ainsworth M, Oden JT (2000) A posteriori error estimation in finite element analysis. Wiley, New YorkCrossRefMATH
2.
Zurück zum Zitat Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. Part I: the recovery technique. Int J Numer Methods Eng 33:1331–1364MathSciNetCrossRefMATH Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. Part I: the recovery technique. Int J Numer Methods Eng 33:1331–1364MathSciNetCrossRefMATH
3.
Zurück zum Zitat Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. Part II: error estimates and adaptivity. Int J Numer Methods Eng 33:1365–1382MathSciNetCrossRefMATH Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. Part II: error estimates and adaptivity. Int J Numer Methods Eng 33:1365–1382MathSciNetCrossRefMATH
4.
Zurück zum Zitat Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery (SPR) and adaptive finite element refinement. Comput Methods Appl Mech Eng 101:207–224MathSciNetCrossRefMATH Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery (SPR) and adaptive finite element refinement. Comput Methods Appl Mech Eng 101:207–224MathSciNetCrossRefMATH
5.
Zurück zum Zitat Blacker T, Belytschko T (1994) Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements. Int J Numer Methods Eng 37:517–536MathSciNetCrossRefMATH Blacker T, Belytschko T (1994) Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements. Int J Numer Methods Eng 37:517–536MathSciNetCrossRefMATH
6.
Zurück zum Zitat Wiberg N, Abdulwahab F, Li XD (1997) Error estimation and adaptive procedures based on superconvergent patch recovery (SPR) techniques. Arch Comput Methods Eng 4:203–242MathSciNetCrossRef Wiberg N, Abdulwahab F, Li XD (1997) Error estimation and adaptive procedures based on superconvergent patch recovery (SPR) techniques. Arch Comput Methods Eng 4:203–242MathSciNetCrossRef
7.
Zurück zum Zitat Lee T, Park HC, Lee SW (1997) A superconvergent stress recovery technique with equilibrium constraint. Int J Numer Methods Eng 40:1139–1160CrossRefMATH Lee T, Park HC, Lee SW (1997) A superconvergent stress recovery technique with equilibrium constraint. Int J Numer Methods Eng 40:1139–1160CrossRefMATH
8.
Zurück zum Zitat Park HC, Shin SH (1999) Element stress recovery technique with equilibrium constraints for superconvergence boundary stress extraction. AIAA J 37:623–628CrossRef Park HC, Shin SH (1999) Element stress recovery technique with equilibrium constraints for superconvergence boundary stress extraction. AIAA J 37:623–628CrossRef
9.
Zurück zum Zitat Kvamsdal T, Okstad KM (1998) Error estimation based on superconvergent patch recovery using statically admissible stress fields. Int J Numer Methods Eng 42:443–472MathSciNetCrossRefMATH Kvamsdal T, Okstad KM (1998) Error estimation based on superconvergent patch recovery using statically admissible stress fields. Int J Numer Methods Eng 42:443–472MathSciNetCrossRefMATH
10.
Zurück zum Zitat Okstad KM, Kvamsdal T, Mathisen KM (1999) Superconvergent patch recovery for plate problems using statically admissible stress resultant fields. Int J Numer Methods Eng 44:697–727CrossRefMATH Okstad KM, Kvamsdal T, Mathisen KM (1999) Superconvergent patch recovery for plate problems using statically admissible stress resultant fields. Int J Numer Methods Eng 44:697–727CrossRefMATH
11.
Zurück zum Zitat Boroomand B, Zienkiewicz OC (1997) Recovery by equilibrium in patches (REP). Int J Numer Methods Eng 40:137–164MathSciNetCrossRef Boroomand B, Zienkiewicz OC (1997) Recovery by equilibrium in patches (REP). Int J Numer Methods Eng 40:137–164MathSciNetCrossRef
12.
Zurück zum Zitat Boroomand B, Zienkiewicz OC (1997) An improved REP recovery and the effectivity robustness test. Int J Numer Methods Eng 40:3247–3277MathSciNetCrossRefMATH Boroomand B, Zienkiewicz OC (1997) An improved REP recovery and the effectivity robustness test. Int J Numer Methods Eng 40:3247–3277MathSciNetCrossRefMATH
13.
Zurück zum Zitat Boroomand B, Zienkiewicz OC, Zhu JZ (1999) Recovery procedures in error estimation and adaptivity. Part I: adaptivity in linear problems. Comput Methods Appl Mech Eng 176:111–125MathSciNetCrossRefMATH Boroomand B, Zienkiewicz OC, Zhu JZ (1999) Recovery procedures in error estimation and adaptivity. Part I: adaptivity in linear problems. Comput Methods Appl Mech Eng 176:111–125MathSciNetCrossRefMATH
14.
Zurück zum Zitat Boroomand B, Zienkiewicz OC (1999) Recovery procedures in error estimation and adaptivity. Part II: Adaptivity in nonlinear problems of elasto-plasticity behaviour. Comput Methods Appl Mech Eng 176:127–146MathSciNetCrossRefMATH Boroomand B, Zienkiewicz OC (1999) Recovery procedures in error estimation and adaptivity. Part II: Adaptivity in nonlinear problems of elasto-plasticity behaviour. Comput Methods Appl Mech Eng 176:127–146MathSciNetCrossRefMATH
15.
Zurück zum Zitat Prange C, Loehnert S, Wriggers P (2012) Error estimation for crack simulations using the XFEM. Int J Numer Methods Eng 91: 1459–1474 Prange C, Loehnert S, Wriggers P (2012) Error estimation for crack simulations using the XFEM. Int J Numer Methods Eng 91: 1459–1474
16.
Zurück zum Zitat Payen DJ, Bathe K-J (2011) The use of nodal point forces to improve element stresses. Comput Struct 89:485–495CrossRef Payen DJ, Bathe K-J (2011) The use of nodal point forces to improve element stresses. Comput Struct 89:485–495CrossRef
18.
Zurück zum Zitat Ubertini F (2004) Patch recovery based on complementary energy. Int J Numer Methods Eng 59:1501–1538CrossRefMATH Ubertini F (2004) Patch recovery based on complementary energy. Int J Numer Methods Eng 59:1501–1538CrossRefMATH
19.
Zurück zum Zitat Benedetti A, de Miranda S, Ubertini F (2006) A posteriori error estimation based on the superconvergent recovery by compatibility in patches. Int J Numer Methods Eng 67:108–131CrossRefMATH Benedetti A, de Miranda S, Ubertini F (2006) A posteriori error estimation based on the superconvergent recovery by compatibility in patches. Int J Numer Methods Eng 67:108–131CrossRefMATH
20.
Zurück zum Zitat Daghia F, de Miranda S, Ubertini F, Viola E (2008) A hybrid stress approach for laminated composite plates within the First-order Shear Deformation Theory. Int J Solids Struct 45:1766–1787CrossRefMATH Daghia F, de Miranda S, Ubertini F, Viola E (2008) A hybrid stress approach for laminated composite plates within the First-order Shear Deformation Theory. Int J Solids Struct 45:1766–1787CrossRefMATH
21.
Zurück zum Zitat de Miranda S, Garikipati K, Molari L, Ubertini F (2009) A simple solution strategy for coupled piezo-diffusion in elastic solids. Comput Mech 44:191–203CrossRefMATH de Miranda S, Garikipati K, Molari L, Ubertini F (2009) A simple solution strategy for coupled piezo-diffusion in elastic solids. Comput Mech 44:191–203CrossRefMATH
22.
Zurück zum Zitat Castellazzi G, de Miranda S, Ubertini F (2010) Adaptivity based on the recovery by compatibility in patches. Finite Elem Anal Des 46:379–390CrossRef Castellazzi G, de Miranda S, Ubertini F (2010) Adaptivity based on the recovery by compatibility in patches. Finite Elem Anal Des 46:379–390CrossRef
23.
Zurück zum Zitat Castellazzi G, de Miranda S, Ubertini F (2011) Patch based stress recovery for plate structures. Comput Mech 47:379–394CrossRefMATH Castellazzi G, de Miranda S, Ubertini F (2011) Patch based stress recovery for plate structures. Comput Mech 47:379–394CrossRefMATH
24.
Zurück zum Zitat de Miranda S, Patruno L, Ubertini F (2012) Transverse stress profiles reconstruction for finite element analysis of laminated plates. Composite Struct 94:2706–2715CrossRef de Miranda S, Patruno L, Ubertini F (2012) Transverse stress profiles reconstruction for finite element analysis of laminated plates. Composite Struct 94:2706–2715CrossRef
25.
Zurück zum Zitat Carstensen C, Funken SA (2003) Averaging techniques for reliable a posteriori FE-error control in elastoplasticity with hardening. Comput Methods Appl Mech Eng 192:1435–1450CrossRefMATH Carstensen C, Funken SA (2003) Averaging techniques for reliable a posteriori FE-error control in elastoplasticity with hardening. Comput Methods Appl Mech Eng 192:1435–1450CrossRefMATH
26.
Zurück zum Zitat Simo JC, Kennedy JG, Taylor RL (1989) Complementary mixed finite element formulations for elastoplasticity. Comput Methods Appl Mech Eng 74:177–206MathSciNetCrossRefMATH Simo JC, Kennedy JG, Taylor RL (1989) Complementary mixed finite element formulations for elastoplasticity. Comput Methods Appl Mech Eng 74:177–206MathSciNetCrossRefMATH
27.
Zurück zum Zitat Bilotta A, Leonetti L, Garcea G (2011) Three field finite elements for the elastoplastic analysis of 2D continua. Finite Elem Anal Des 47:1119–1130MathSciNetCrossRef Bilotta A, Leonetti L, Garcea G (2011) Three field finite elements for the elastoplastic analysis of 2D continua. Finite Elem Anal Des 47:1119–1130MathSciNetCrossRef
Metadaten
Titel
Patch based recovery in finite element elastoplastic analysis
verfasst von
Federica Daghia
Stefano de Miranda
Francesco Ubertini
Publikationsdatum
01.10.2013
Verlag
Springer Berlin Heidelberg
Erschienen in
Computational Mechanics / Ausgabe 4/2013
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-013-0847-6

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