A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems

This paper presents a node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems using a mesh of polygonal elements. The calculation of the system stiffness matrix is performed using strain smoothing technique over the smoothing cells associated with nodes, which leads to line integrations along the edges of the smoothing cells. The numerical results demonstrated that the NS-FEM possesses the following properties: (1) upper bound in the strain energy of the exact solution when a reasonably fine mesh is used; (2) well immune from the volumetric locking; (3) can use polygonal elements with an arbitrary number of sides; (4) insensitive to element distortion.