Six-node triangle finite volume method for solids with a rotational degree of freedom for incompressible material

Wenke Pan, Marcus Wheel, Yi Qin

Research output: Contribution to journalArticle

9 Citations (Scopus)
38 Downloads (Pure)

Abstract

A finite-volume (FV) cell vertex method is presented for determining the displacement field for solids exhibiting with incompressibility. The solid is discretized into six-node finite elements and the standard six-node finite-element shape function is employed for each element. Only control volumes around vertex node of the triangular element are considered. For considering the material incompressibility, a constant hydrostatic pressure as an extra unknown variable within each element is assumed. The force equilibrium in two perpendicular directions and one in-plane moment equilibrium equation are derived for each control volume. The volume conservation is satisfied by setting the integration of volumetric strain as zero within each element. By solving the system control equations, the displacements and rotations of the vertex nodes and the hydrostatic pressure for each element can be obtained and then the displacements of the midside nodes can be calculated. The simulation results show that this FV method passes the patch tests and converges to theoretical results under mesh refinement for material behaviour incompressibility.
Original languageEnglish
Pages (from-to)1506-1511
Number of pages6
JournalComputers and Structures
Volume88
Issue number23-24
DOIs
Publication statusPublished - Dec 2010

Keywords

  • finite volume method
  • control volume
  • vertex centred method
  • rotational degree
  • incompressibility

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