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

作者：Pan Wenke^*; Wheel Marcus

来源：International Journal for Numerical Methods in Biomedical Engineering, 2011, 27(9): 1411-1426.

DOI：10.1002/cnm.1368

• vertex-centred finite-volume method
• rotational degree of freedom
• 6-node triangle element
• moment equilibrium equations

A novel vertex-centred finite-volume (FV) method is presented for determining the displacement field in loaded 2D structures. The solid is discretized into 6-node finite elements (FE) and the standard 6-node FE shape function is employed to describe the displacement variation in each element. However, the displacements of the midside nodes are replaced with the displacements and the rotations of the two neighbouring edge nodes. Thus, only the control volumes centred around each vertex node of the triangular element are required. These control volumes are constructed by joining lines between the centre of the element and the midside nodes. The force equilibrium in two perpendicular directions and one in-plane moment equilibrium equation is derived for each control volume. By solving the system of equations, the displacements and the rotations of the vertex nodes can be obtained and then the displacements of the midside nodes can be calculated. Following this, the strain and the stress can be determined through the relationship between strain and displacement, and stress and strain, respectively. The results of simulation show that this novel FV method is not only better than the previously derived 3-node triangle FV method with rotational degrees of freedom, but also better than the 3-node FE method with rotations, and can also compete with the 6-node triangle FE method. In addition, no locking problem was encountered as the value of Poisson's ratio of the elastic material approached 0.5.

• 出版日期2011-9