Variable-node finite elements with smoothed integration techniques and their applications for multiscale mechanics problems

In this paper, variable-node finite elements with smoothed integration are proposed with emphasis on their applications for multiscale mechanics problems. The smoothed integration, which picks up strain matrix at discrete points along the cell boundary to form stiffness matrix, is combined with the variable-node finite elements, which have an arbitrary number of nodes on element side. Hence, they effectively link meshes of different resolution along their nonmatching interface. Particularly, they provide a powerful tool, when combined with homogenization schemes, for multiscale computing for complex heterogeneous structures. We show some applications of variable-node elements for multiscale problems to demonstrate their effectiveness.