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

A finite volume (FV) cell vertex method is presented for determining the displacement field for solids exhibiting incompressibility. The solid is discretized into six-node finite elements and only control volumes around the vertex node are required. For considering the material incompressibility, a constant hydrostatic pressure as an extra unknown variable within each element is assumed. The force- and moment-equilibrium equations are derived for each control volume and the volume conservation for each element forms a constraint equation. The simulation results show that this FV method passes the patch tests and converges to theoretical results under mesh refinement.