TY  - JOUR
A1  - Vu-Bac, N.
A1  - Nguyen-Xuan, Hung
A1  - Chen, Lei
A1  - Lee, C.K.
A1  - Zi, Goangseup
A1  - Zhuang, Xiaoying
A1  - Liu, G.R.
A1  - Rabczuk, Timon
T1  - A phantom-node method with edge-based strain smoothing for linear elastic fracture mechanics
JF  - Journal of Applied Mathematics
N2  - This paper presents a novel numerical procedure based on the combination of an edge-based smoothed finite element (ES-FEM) with a phantom-node method for 2D linear elastic fracture mechanics. In the standard phantom-node method, the cracks are formulated by adding phantom nodes, and the cracked element is replaced by two new superimposed elements. This approach is quite simple to implement into existing explicit finite element programs. The shape functions associated with discontinuous elements are similar to those of the standard finite elements, which leads to certain simplification with implementing in the existing codes. The phantom-node method allows modeling discontinuities at an arbitrary location in the mesh. The ES-FEM model owns a close-to-exact stiffness that is much softer than lower-order finite element methods (FEM). Taking advantage of both the ES-FEM and the phantom-node method, we introduce an edge-based strain smoothing technique for the phantom-node method. Numerical results show that the proposed method achieves high accuracy compared with the extended finite element method (XFEM) and other reference solutions.
KW  - Finite-Elemente-Methode
KW  - Steifigkeit
KW  - Bruchmechanik
KW  - Riss
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170426-31676
ER  - 
TY  - JOUR
A1  - Talebi, Hossein
A1  - Zi, Goangseup
A1  - Silani, Mohammad
A1  - Samaniego, Esteban
A1  - Rabczuk, Timon
T1  - A simple circular cell method for multilevel finite element analysis
JF  - Journal of Applied Mathematics
N2  - A simple multiscale analysis framework for heterogeneous solids based on a computational homogenization technique is presented. The macroscopic strain is linked kinematically to the boundary displacement of a circular or spherical representative volume which contains the microscopic information of the material. The macroscopic stress is obtained from the energy principle between the macroscopic scale and the microscopic scale. This new method is applied to several standard examples to show its accuracy and consistency of the method proposed.
KW  - Finite-Elemente-Methode
KW  - Feststoff
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170426-31639
ER  -