### Abstract

Original language | English |
---|---|

Pages (from-to) | 1411-1426 |

Number of pages | 16 |

Journal | International Journal for Numerical Methods in Biomedical Engineering |

Volume | 27 |

Issue number | 9 |

Early online date | 10 Mar 2010 |

DOIs | |

Publication status | Published - Sep 2011 |

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### Keywords

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

### Cite this

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**A finite-volume method for solids with a rotational degrees of freedom based on the 6-node triangle.** / Pan, Wenke; Wheel, Marcus.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A finite-volume method for solids with a rotational degrees of freedom based on the 6-node triangle

AU - Pan, Wenke

AU - Wheel, Marcus

PY - 2011/9

Y1 - 2011/9

N2 - 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.

AB - 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.

KW - finite volume method

KW - control volume

KW - vertex centred method

KW - rotational degree

KW - incompressibility

UR - http://www.scopus.com/inward/record.url?scp=77958098724&partnerID=8YFLogxK

UR - http://onlinelibrary.wiley.com/doi/10.1002/cnm.1368/full

U2 - 10.1002/cnm.1368

DO - 10.1002/cnm.1368

M3 - Article

VL - 27

SP - 1411

EP - 1426

JO - International Journal for Numerical Methods in Biomedical Engineering

JF - International Journal for Numerical Methods in Biomedical Engineering

SN - 2040-7939

IS - 9

ER -