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This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded linear triangular (T3) elements and a special layer of five-noded singular triangular elements (sT5) connected to the singular-point of the stress field. The sT5 element has an additional node on each of the two edges connected to the singular-point. It allows us to represent simple and efficient enrichment with desired terms for the displacement field near the singular-point with the satisfaction of partition-of-unity property. The stiffness matrix of the discretized system is then obtained using the assumed displacement values (not the derivatives) over smoothing domains associated with the edges of elements. An adaptive procedure for the sES-FEM is proposed to enhance the quality of the solution with minimized number of nodes. Several numerical examples are provided to validate the reliability of the present sES-FEM method.

Keywords: Adaptive finite elements , Smoothed finite element method , Singular ES-FEM, Singularity, Crack propagation 3. G.R. Liu, W. Zeng, H. Nguyen-Xuan , Generalized stochastic cell-based smoothed finite element method for solid mechanics , Finite Element in Analysis and Design , Vol. 63, p. 51-61, doi.org/10.1016/j.finel.2012.08.007 , 2013 .