On variational formulations with rigid-body constraints for finite elasticity: Applications to 2D and 3D finite element simulations

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate a recently proposed variational principle with rigid-body constraints and present an extension of its implementation in three dimensional finite elasticity problems. Through numerical examples, we illustrate that the proposed variational principle with rigid-body constraints is applicable to both single field and mixed finite elements of arbitrary order and geometry, e.g. triangular/tetrahedral and quadrilateral/hexagonal elements, in two and three dimensions. Moreover, we demonstrate that, as compared to the commonly adopted approach of discretizing the rigid domains with standard finite elements, the proposed formulation requires neither discretization nor numerical integration in the interior of each rigid domain. As a comparative result, the variational formulation may reduce the total number of degrees of freedom of the resulting finite element system and provide improved accuracy.

Original languageEnglish (US)
Pages (from-to)15-26
Number of pages12
JournalMechanics Research Communications
Volume78
DOIs
StatePublished - Dec 1 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Keywords

  • 3D FEA
  • Finite elastostatics
  • Rigid inclusions
  • Variational principles

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