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  • Rabczuk, Timon (12)
  • Zi, Goangseup (12)
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A simple circular cell method for multilevel finite element analysis (2012)
Talebi, Hossein ; Zi, Goangseup ; Silani, Mohammad ; Samaniego, Esteban ; Rabczuk, Timon
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.
A phantom-node method with edge-based strain smoothing for linear elastic fracture mechanics (2013)
Vu-Bac, N. ; Nguyen-Xuan, Hung ; Chen, Lei ; Lee, C.K. ; Zi, Goangseup ; Zhuang, Xiaoying ; Liu, G.R. ; Rabczuk, Timon
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.
A stochastic computational method based on goal-oriented error estimation for heterogeneous geological materials (2016)
Ghorashi, Seyed Shahram ; Lahmer, Tom ; Bagherzadeh, Amir Saboor ; Zi, Goangseup ; Rabczuk, Timon
A stochastic computational method based on goal-oriented error estimation for heterogeneous geological materials
Detection of material interfaces using a regularized level set method in piezoelectric structures (2016)
Nanthakumar, S.S. ; Lahmer, Tom ; Zhuang, Xiaoying ; Zi, Goangseup ; Rabczuk, Timon
Detection of material interfaces using a regularized level set method in piezoelectric structures
Detection of material interfaces using a regularized level set method in piezoelectric structures (2015)
Nanthakumar, S.S. ; Lahmer, Tom ; Zhuang, Xiaoying ; Zi, Goangseup ; Rabczuk, Timon
Detection of material interfaces using a regularized level set method in piezoelectric structures
A three dimensional Extended Arlequin Method for Dynamic Fracture (2015)
Silani, Mohammad ; Talebi, Hossein ; Ziaei-Rad, S. ; Hamouda, A.M.S. ; Zi, Goangseup ; Rabczuk, Timon
A three dimensional Extended Arlequin Method for Dynamic Fracture
Phantom-node method for shell models with arbitrary cracks (2012)
Chau-Dinh, T. ; Zi, Goangseup ; Lee, P.S. ; Song, Jeong-Hoon ; Rabczuk, Timon
A phantom-node method is developed for three-node shell elements to describe cracks. This method can treat arbitrary cracks independently of the mesh. The crack may cut elements completely or partially. Elements are overlapped on the position of the crack, and they are partially integrated to implement the discontinuous displacement across the crack. To consider the element containing a crack tip, a new kinematical relation between the overlapped elements is developed. There is no enrichment function for the discontinuous displacement field. Several numerical examples are presented to illustrate the proposed method.
A simple circular cell method for multilevel finite element analysis (2012)
Talebi, Hossein ; Zi, Goangseup ; Silani, Mohammad ; Samaniego, Esteban ; Rabczuk, Timon
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.
An extended isogeometric thin shell analysis based on Kirchhoff-Love theory (2015)
Nguyen-Thanh, Nhon ; Valizadeh, N. ; Nguyen, Manh Hung ; Nguyen-Xuan, Hung ; Zhuang, Xiaoying ; Areias, Pedro ; Zi, Goangseup ; Bazilevs, Yuri ; De Lorenzis, Laura ; Rabczuk, Timon
An extended isogeometric thin shell analysis based on Kirchho_-Love theory
Extended Finite Element Method for Dynamic Fracture of Piezo-Electric Materials (2012)
Nguyen-Vinh, H. ; Bakar, I. ; Msekh, Mohammed Abdulrazzak ; Song, Jeong-Hoon ; Muthu, Jacob ; Zi, Goangseup ; Le, P. ; Bordas, Stéphane Pierre Alain ; Simpson, R. ; Natarajan, S. ; Lahmer, Tom ; Rabczuk, Timon
We present an extended finite element formulation for dynamic fracture of piezo-electric materials. The method is developed in the context of linear elastic fracture mechanics. It is applied to mode I and mixed mode-fracture for quasi-steady cracks. An implicit time integration scheme is exploited. The results are compared to results obtained with the boundary element method and show excellent agreement.
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