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

Pan, Wenke and Wheel, Marcus (2011) A finite-volume method for solids with a rotational degrees of freedom based on the 6-node triangle. International Journal for Numerical Methods in Biomedical Engineering, 27 (9). pp. 1411-1426. ISSN 2040-7939 (https://doi.org/10.1002/cnm.1368) Microsoft Word. Filename: Pan_W_Wheel_MA_Pure_A_finite_volume_method_for_solids_with_a_rotation_degree_of_freedom_based_on_the_node_triangle_Mar_2010.doc Preprint Download (219kB)

## 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.

#### ORCID iDs

Pan, Wenke and ;
• Item type: Article 29108 DateEventSeptember 2011Published10 March 2010Published Online finite volume method, control volume, vertex centred method, rotational degree, incompressibility, Mechanical engineering and machinery, Mechanical Engineering, Computational Mechanics, Theoretical Computer Science Technology > Mechanical engineering and machinery Faculty of Engineering > Mechanical and Aerospace Engineering Pure Administrator 07 Mar 2011 23:25 22 Sep 2022 00:43 https://strathprints.strath.ac.uk/id/eprint/29108