Skip to main content
Top
Published in: Geotechnical and Geological Engineering 4/2011

01-07-2011 | Original paper

The Case Study Analysis of Strain–Stress for Jointed Rock Mass Using Element Free Galerkin Method and Paton’s Failure

Authors: M. Hajiazizi, N. Hataf, A. Ghahramani

Published in: Geotechnical and Geological Engineering | Issue 4/2011

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this paper evaluated a case study for jointed rock mass using element free Galerkin method and Paton’s failure. The displacement field of each block is constructed by the moving least-squares interpolation with an array of points distributed in the block. The essential boundary conditions are enforced using penalty method. It is shown that excellent results are obtained and less calculation time is required as compared to finite difference method.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
go back to reference BabuŠka I, Melenk JM (1996) The partition of unity finite element method: basic theory and applications. Comput Meth Appl Mech Eng 139:289–314CrossRef BabuŠka I, Melenk JM (1996) The partition of unity finite element method: basic theory and applications. Comput Meth Appl Mech Eng 139:289–314CrossRef
go back to reference BabuŠka I, Melenk JM (1997) The partition of unity method. Int J Numer Meth Eng 40:727–758CrossRef BabuŠka I, Melenk JM (1997) The partition of unity method. Int J Numer Meth Eng 40:727–758CrossRef
go back to reference Belytschko T, Lu YY, Gu L (1994) Element-free Galerkin method. Int J Numer Methods Eng 37:229–256CrossRef Belytschko T, Lu YY, Gu L (1994) Element-free Galerkin method. Int J Numer Methods Eng 37:229–256CrossRef
go back to reference Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P (1996) Meshless methods: an overview and recent developments. Comput Meth Appl Mech Eng 139:3–47CrossRef Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P (1996) Meshless methods: an overview and recent developments. Comput Meth Appl Mech Eng 139:3–47CrossRef
go back to reference Belytschko T, Organ D, Gerlach C (2000) Element-free Galerkin methods for dynamics fracture in concrete. Comput Meth Appl Mech Eng 187:385–399CrossRef Belytschko T, Organ D, Gerlach C (2000) Element-free Galerkin methods for dynamics fracture in concrete. Comput Meth Appl Mech Eng 187:385–399CrossRef
go back to reference Chen WF (1975) Limit analysis and soil plasticity. American Elsevier Publishing Company, Inc, New York Chen WF (1975) Limit analysis and soil plasticity. American Elsevier Publishing Company, Inc, New York
go back to reference Chen J-S, Pan C, Roque MOL, Wang H-P (1998) A Lagrangian reproducing kernel particle method for metal forming analysis. Comput Mech 22:289–307CrossRef Chen J-S, Pan C, Roque MOL, Wang H-P (1998) A Lagrangian reproducing kernel particle method for metal forming analysis. Comput Mech 22:289–307CrossRef
go back to reference Duarte CAM, Oden JT (1996a) An h-p adaptive method using clouds. Comput Meth Appl Mech Eng 139:237–262CrossRef Duarte CAM, Oden JT (1996a) An h-p adaptive method using clouds. Comput Meth Appl Mech Eng 139:237–262CrossRef
go back to reference Duarte CAM, Oden JT (1996b) Hp clouds-an hp meshless method. Numer Meth Partial Diff Eqs 12:673–705CrossRef Duarte CAM, Oden JT (1996b) Hp clouds-an hp meshless method. Numer Meth Partial Diff Eqs 12:673–705CrossRef
go back to reference Fries TP, Matthies H-G (2004) Classification and Overview of Meshfree Methods. Braunschweig Institute fǘr Wissenschaftliches Rechnen Technische Universität Braunschweig Fries TP, Matthies H-G (2004) Classification and Overview of Meshfree Methods. Braunschweig Institute fǘr Wissenschaftliches Rechnen Technische Universität Braunschweig
go back to reference Lancaster P, Salkauskas K (1981) Surface Generated by moving least squares methods. Math Comp 37:141–158CrossRef Lancaster P, Salkauskas K (1981) Surface Generated by moving least squares methods. Math Comp 37:141–158CrossRef
go back to reference Li S, Liu WK (2000) Numerical simulations of strain localization in inelastic solids using mesh-free methods. Int J Numer Math Eng 48:1285–1309CrossRef Li S, Liu WK (2000) Numerical simulations of strain localization in inelastic solids using mesh-free methods. Int J Numer Math Eng 48:1285–1309CrossRef
go back to reference Lin J-S (2003) A mesh-based partition of unity method for discontinuity modeling. Comput Methods Appl Mech Eng 192:1515–1532CrossRef Lin J-S (2003) A mesh-based partition of unity method for discontinuity modeling. Comput Methods Appl Mech Eng 192:1515–1532CrossRef
go back to reference Liu GR (2002) Mesh free methods: moving beyond the finite element method. CRC Press, FloridaCrossRef Liu GR (2002) Mesh free methods: moving beyond the finite element method. CRC Press, FloridaCrossRef
go back to reference Liu WK, Jun S, Zhang WF (1995) Reproducing kernel particle method. Int J Numer Meth Eng 20:1081–1106CrossRef Liu WK, Jun S, Zhang WF (1995) Reproducing kernel particle method. Int J Numer Meth Eng 20:1081–1106CrossRef
go back to reference Lucy LB (1977) A numerical approach to the testing of the fission hypotheses. Astron J 8:1013–1024CrossRef Lucy LB (1977) A numerical approach to the testing of the fission hypotheses. Astron J 8:1013–1024CrossRef
go back to reference Nayroles B, Touzot G, Villon P (1992) Generalizing the finite element method: diffuse approximation and diffuse elements. Comput Mech 10:307–318CrossRef Nayroles B, Touzot G, Villon P (1992) Generalizing the finite element method: diffuse approximation and diffuse elements. Comput Mech 10:307–318CrossRef
go back to reference Noh W (1964) A time-dependent two-space-dimensional coupled Eulerian code. In: Methods in computational physics, vol 3. Academic Press, New York Noh W (1964) A time-dependent two-space-dimensional coupled Eulerian code. In: Methods in computational physics, vol 3. Academic Press, New York
go back to reference Oden JT, Duarte CAM (1997) Solution of singular problems using h-p clouds. In: Whiteman JR (ed) The mathematics of finite element and application. Wiley, New York, pp 35–54 Oden JT, Duarte CAM (1997) Solution of singular problems using h-p clouds. In: Whiteman JR (ed) The mathematics of finite element and application. Wiley, New York, pp 35–54
go back to reference Wu F, Liu J, Zhuang H, Yan Changgen (2009) A method for assessment of excavation damaged zone (EDZ) of a rock mass and its application to a dam foundation case. Eng Geol 104:254–262CrossRef Wu F, Liu J, Zhuang H, Yan Changgen (2009) A method for assessment of excavation damaged zone (EDZ) of a rock mass and its application to a dam foundation case. Eng Geol 104:254–262CrossRef
go back to reference Zhang X, Lu M, Wegner JL (2000) A 2-D meshless model for jointed rock structures. Int J Numer Methods Eng 47:1649–1661CrossRef Zhang X, Lu M, Wegner JL (2000) A 2-D meshless model for jointed rock structures. Int J Numer Methods Eng 47:1649–1661CrossRef
Metadata
Title
The Case Study Analysis of Strain–Stress for Jointed Rock Mass Using Element Free Galerkin Method and Paton’s Failure
Authors
M. Hajiazizi
N. Hataf
A. Ghahramani
Publication date
01-07-2011
Publisher
Springer Netherlands
Published in
Geotechnical and Geological Engineering / Issue 4/2011
Print ISSN: 0960-3182
Electronic ISSN: 1573-1529
DOI
https://doi.org/10.1007/s10706-011-9393-1

Other articles of this Issue 4/2011

Geotechnical and Geological Engineering 4/2011 Go to the issue