A novel singular node-based smoothed finite element method (NS-FEM) for upper bound solutions of fracture problems

Abstract

It is well known that the lower bound to exact solutions in linear fracture problems can be easily obtained by the displacement compatible finite element method (FEM) together with the singular crack tip elements. It is, however, much more difficult to obtain the upper bound solutions for these problems. This paper aims to formulate a novel singular node-based smoothed finite element method (NS-FEM) to obtain the upper bound solutions for fracture problems. In the present singular NS-FEM, the calculation of the system stiffness matrix is performed using the strain smoothing technique over the smoothing domains (SDs) associated with nodes, which leads to the line integrations using only the shape function values along the boundaries of the SDs. A five-node singular crack tip element is used within the framework of NS-FEM to construct singular shape functions via direct point interpolation with proper order of fractional basis. The mix-mode stress intensity factors are evaluated using the domain forms of the interaction integrals. The upper bound solutions of the present singular NS-FEM are demonstrated via benchmark examples for a wide range of material combinations and boundary conditions. © 2010 John Wiley & Sons, Ltd.