Reference : An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order
Scientific journals : Article
Engineering, computing & technology : Multidisciplinary, general & others
Computational Sciences
An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order
Nguyen-Xuan, H. [Department of Mechanics, Faculty of Mathematics and Computer Science, University of Science, VNU-HCMC, Nguyen Van Cu Street, District 5, Ho Chi Minh City 700000, Viet Nam, Division of Computational Mechanics, Ton Duc Thang University, Nguyen Huu Tho Street, District 7, Ho Chi Minh City 700000, Viet Nam]
Liu, G. R. [School of Aerospace Systems, University of Cincinnati, 2851 Woodside Dr, Cincinnati, OH 45221, United States]
Bordas, Stéphane mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
Natarajan, S. [Department of Aerospace Engineering, Indian Institute of Science, Bangalore, India]
Rabczuk, T. [Department of Civil Engineering, Bauhaus-Universität Weimar, Germany]
Computer Methods in Applied Mechanics and Engineering
Yes (verified by ORBilu)
[en] Adaptive finite elements ; Crack propagation ; Singular ES-FEM ; Singularity ; Smoothed finite element method ; Adaptive finite element ; Adaptive procedure ; Arbitrary order ; Discretized systems ; Displacement field ; Displacement value ; Edge-based ; Numerical example ; Singular fields ; Singular stress field ; Stress field ; Triangular elements ; Finite element method ; Stiffness matrix ; Stresses
[en] 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. © 2012 Elsevier B.V.
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