An r-h adaptive kinematic approach for 3D limit analysis

Zhenhao Shi, James P. Hambleton*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


This paper explores a pathway for increasing efficiency in numerical 3D limit analysis through r-h adaptivity, wherein nodal positions (r) and element lengths (h) are successively refined. The approach uses an iterative, nested optimization procedure involving three components: (1) determination of velocities for a fixed mesh of rigid, translational elements (blocks) using second-order cone programming; (2) adaptation of nodal positions using non-linear optimization (r adaptivity); and (3) subdivision of elements based on the magnitude of the velocity jumps (h adaptivity). Examples show that the method can compute reasonably accurate limit loads at relatively low computational cost.

Original languageEnglish (US)
Article number103531
JournalComputers and Geotechnics
StatePublished - Aug 2020


  • 3D
  • Adaptivity
  • Kinematic method
  • Limit analysis
  • Upper bound

ASJC Scopus subject areas

  • Geotechnical Engineering and Engineering Geology
  • Computer Science Applications


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