A Phantom-Node Method with Edge-Based Strain Smoothing for Linear Elastic Fracture Mechanics
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 elem...
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| Main Authors: | , , , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/978026 |
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| author | N. Vu-Bac H. Nguyen-Xuan L. Chen C. K. Lee G. Zi X. Zhuang G. R. Liu T. Rabczuk |
| author_facet | N. Vu-Bac H. Nguyen-Xuan L. Chen C. K. Lee G. Zi X. Zhuang G. R. Liu T. Rabczuk |
| author_sort | N. Vu-Bac |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-79f33cfb9d1a4bfa8fe1943cc5f4d6a2 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-79f33cfb9d1a4bfa8fe1943cc5f4d6a22025-02-03T06:15:13ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/978026978026A Phantom-Node Method with Edge-Based Strain Smoothing for Linear Elastic Fracture MechanicsN. Vu-Bac0H. Nguyen-Xuan1L. Chen2C. K. Lee3G. Zi4X. Zhuang5G. R. Liu6T. Rabczuk7Department of Geotechnical Engineering, Tongji University, Shanghai 200092, ChinaDivision of Computational Mechanics, Ton Duc Thang University, Ho Chi Minh City 70000, VietnamSchool of Chemistry, Physics and Mechanical Engineering, Queensland University of Technology, Brisbane, QLD 4001, AustraliaSchool of Engineering, Institute of Mechanics and Advanced Materials, Theoretical and Computational Mechanics, Cardiff University, Wales CF24 3AA, UKDepartment of Civil, Environmental & Architectural Engineering, Korea University, 5 Ga 1, An-Am Dong, Sung-Buk Gu, Seoul 136-701, Republic of KoreaDepartment of Geotechnical Engineering, Tongji University, Shanghai 200092, ChinaAerospace Systems Ohio Eminent Scholar, University of Cincinnati, Cincinnati, OH 45221-0070, USAInstitute of Structural Mechanics, Bauhaus-University Weimar, Marienstraße 15, D-99423 Weimar, GermanyThis 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.http://dx.doi.org/10.1155/2013/978026 |
| spellingShingle | N. Vu-Bac H. Nguyen-Xuan L. Chen C. K. Lee G. Zi X. Zhuang G. R. Liu T. Rabczuk A Phantom-Node Method with Edge-Based Strain Smoothing for Linear Elastic Fracture Mechanics Journal of Applied Mathematics |
| title | A Phantom-Node Method with Edge-Based Strain Smoothing for Linear Elastic Fracture Mechanics |
| title_full | A Phantom-Node Method with Edge-Based Strain Smoothing for Linear Elastic Fracture Mechanics |
| title_fullStr | A Phantom-Node Method with Edge-Based Strain Smoothing for Linear Elastic Fracture Mechanics |
| title_full_unstemmed | A Phantom-Node Method with Edge-Based Strain Smoothing for Linear Elastic Fracture Mechanics |
| title_short | A Phantom-Node Method with Edge-Based Strain Smoothing for Linear Elastic Fracture Mechanics |
| title_sort | phantom node method with edge based strain smoothing for linear elastic fracture mechanics |
| url | http://dx.doi.org/10.1155/2013/978026 |
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