A finite-volume method for solids with a rotational degrees of freedom based on the 6-node triangle

Wenke Pan, Marcus Wheel

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)
22 Downloads (Pure)


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)1411-1426
Number of pages16
JournalInternational Journal for Numerical Methods in Biomedical Engineering
Issue number9
Early online date10 Mar 2010
Publication statusPublished - Sep 2011


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


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