Development of High-Order Infinite Element Method for Stress Analysis of Elastic Bodies with Singularities
Structural analysis problems are traditionally solved using the Finite Element Method (FEM). However, when the structure of interest contains discontinuities such as cracks or re-entrant corners, a large number of elements are required to accurately reproduce the stress characteristics in the region...
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| Published in | Journal of Solid Mechanics and Materials Engineering Vol. 4; no. 8; pp. 1131 - 1146 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
The Japan Society of Mechanical Engineers
2010
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1880-9871 1880-9871 |
| DOI | 10.1299/jmmp.4.1131 |
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| Abstract | Structural analysis problems are traditionally solved using the Finite Element Method (FEM). However, when the structure of interest contains discontinuities such as cracks or re-entrant corners, a large number of elements are required to accurately reproduce the stress characteristics in the region of the discontinuities. As a result, the FEM method requires a large storage space and has a slow convergence speed. It has been shown that the Infinite Element Method (IEM) overcomes these limitations and provides a feasible means of solving various types of elasticity and singularity problems. Previous studies have generally focused on the use of IEM formulations based on low-order elements (2×2). By contrast, this study develops a high-order (3×3) IEM formulation. The solutions obtained using the proposed IEM method for various 2D elasto-static problems are compared with the results obtained using the traditional low-order IEM method and the analytical solutions presented in the literature. It is shown that the results obtained using the proposed method are more accurate than those obtained using the low-order IEM method and are in excellent agreement with the analytical solutions. |
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| AbstractList | Structural analysis problems are traditionally solved using the Finite Element Method (FEM). However, when the structure of interest contains discontinuities such as cracks or re-entrant corners, a large number of elements are required to accurately reproduce the stress characteristics in the region of the discontinuities. As a result, the FEM method requires a large storage space and has a slow convergence speed. It has been shown that the Infinite Element Method (IEM) overcomes these limitations and provides a feasible means of solving various types of elasticity and singularity problems. Previous studies have generally focused on the use of IEM formulations based on low-order elements (2x2). By contrast, this study develops a high-order (3x3) IEM formulation. The solutions obtained using the proposed IEM method for various 2D elasto-static problems are compared with the results obtained using the traditional low-order IEM method and the analytical solutions presented in the literature. It is shown that the results obtained using the proposed method are more accurate than those obtained using the low-order IEM method and are in excellent agreement with the analytical solutions. Structural analysis problems are traditionally solved using the Finite Element Method (FEM). However, when the structure of interest contains discontinuities such as cracks or re-entrant corners, a large number of elements are required to accurately reproduce the stress characteristics in the region of the discontinuities. As a result, the FEM method requires a large storage space and has a slow convergence speed. It has been shown that the Infinite Element Method (IEM) overcomes these limitations and provides a feasible means of solving various types of elasticity and singularity problems. Previous studies have generally focused on the use of IEM formulations based on low-order elements (2×2). By contrast, this study develops a high-order (3×3) IEM formulation. The solutions obtained using the proposed IEM method for various 2D elasto-static problems are compared with the results obtained using the traditional low-order IEM method and the analytical solutions presented in the literature. It is shown that the results obtained using the proposed method are more accurate than those obtained using the low-order IEM method and are in excellent agreement with the analytical solutions. |
| Author | ZHUANG, Zhen-Wei CHENG, Kuo-Liang LIU, De-Shin |
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| Cites_doi | 10.1016/S0013-7944(96)00051-3 10.1016/j.compstruc.2005.03.009 10.1007/BF00019768 10.1016/j.engfracmech.2006.02.003 10.1016/S0020-7683(03)00014-3 10.1016/0013-7944(95)00008-J |
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| References | (14) Gross, B. and Srawley, J.E., Stress intensity factor for single-edge-notch specimens in bending or combined bending and tension by boundary collocation of a stress function, NASA, technical note, D-2603, (1965). (18) Aliabadi, M.H., Rooke, D.P. and Carteright, D.J., Mixed-mode Bueckner weight functions using boundary element analysis, International Journal of Fracture, Vol. 34 (1987), pp.131-147. (1) Su, B., Dunn, M.L. and Lee, Y.C., Prediction of the crack initiation of GaAs in a soldered assembly, Proceedings of InterPACK'01, The PACIFIC RIM/International, Intersociety, Electronic Packaging Technical/Business Conference & Exhibition, Kauai, Hawaii, (2001), pp.8-13. (8) Guo, Z.H., Similar isoparametric elements, Chinese Science Bulletin, Vol. 24, No.13 (1979), pp.577-582. (10) Liu, D.S., Chiou, D.Y. and Lin, C.H., 3D IEM formulation with an IEM/FEM coupling scheme for solving elastostatic problems, Advances in Engineering Software, Vol. 34 (2003), pp.309-320. (12) Liu, D.S. and Chiou, D.Y., 2-D infinite element modeling for elastostatic problems with geometric singularity and unbounded domain, Computers & Structures, Vol. 83 (2005), pp.2086-2099. (13) Isida, M., Arbitrary loading problems of doubly symmetric regions containing a central crack, Engineering Fracture Mechanics, Vol. 7 (1975), pp.505-514. (19) Chan, S.K., Tuba, I.S. and Wilson, W.K., On the finite element method in linear fracture mechanics, Engineering Fracture Mechanics, Vol. 2 (1970), pp.1-17. (2) Bois-Grossiant, P. and Tan, C.L., Boundary element fracture mechanics analysis of Brazil-nut sandwich specimens with an interface crack, Engineering Analysis with Boundary Elements, Vol. 16 (1995), pp. 215-225. (20) Kwon, A.M. and Bang, H., The Finite Element Method using MATLAB, (2006), New York, CRC Press. (3) Silvester, P. and Cermark, I.A., Analysis of coaxial line discontinuities by boundary relaxation, IEFE Transaction on Microwave Theory and Techniques, Vol.17, No.8(1969), pp.489-495. (7) Ying, L.A., The infinite element method, Advances Mathematics, Vol. 11, No.4 (1982), pp.269-272. (6) Ying, L.A. and Pan, H., Computation of KI and compliance of arch shaped specimen by the infinite similar element method, Acta Mechanica Solids Sinica, Vol.1 (1981), pp.99-106. (17) Leung, A.Y.T. and Su, R.K.L., Mixed-mode two-dimensional crack problem by fractal two level finite element method, Engineering Fracture Mechanics, Vol. 51, No. 6 (1995), pp.889-895. (9) Liu, D.S. and Chiou, D.Y., A coupled IEM/FEM approach for solving elastic problems with multiple cracks, International Journal of Solids and Structures, Vol. 40 (2003), pp.1973-1993. (15) Yan, X., Cracks emanating from circular hole or square hole in rectangular plate in tension, Engineering Fracture Mechanics, Vol. 73 (2006), pp.1743-1754. (5) Han, H.D. and Ying, L.A., An iterative method in the infinite element, Mathematics Numerical Sinica, Vol. 1, No.1 (1979), pp. 91-99. (11) Liu, D.S. and Chiou, D.Y., Modeling of inclusions with interphases in heterogeneous material using the infinite element method, Computational Materials Science, Vol. 31 (2004), pp.405-420. (16) Wang, R.D., The stress intensity factors of a rectangular plate with collinear cracks under uniaxial tension, Engineering Fracture Mechanics, Vol. 56, No. 3 (1997), pp.347-356. (4) Ying, L.A., An introduction to the infinite element method, Mathematics in Practice and Theory, Vol. 2 (1992), pp.69-78. 11 12 13 14 15 16 17 18 19 1 2 3 4 5 6 7 8 9 20 10 |
| References_xml | – reference: (5) Han, H.D. and Ying, L.A., An iterative method in the infinite element, Mathematics Numerical Sinica, Vol. 1, No.1 (1979), pp. 91-99. – reference: (13) Isida, M., Arbitrary loading problems of doubly symmetric regions containing a central crack, Engineering Fracture Mechanics, Vol. 7 (1975), pp.505-514. – reference: (16) Wang, R.D., The stress intensity factors of a rectangular plate with collinear cracks under uniaxial tension, Engineering Fracture Mechanics, Vol. 56, No. 3 (1997), pp.347-356. – reference: (20) Kwon, A.M. and Bang, H., The Finite Element Method using MATLAB, (2006), New York, CRC Press. – reference: (6) Ying, L.A. and Pan, H., Computation of KI and compliance of arch shaped specimen by the infinite similar element method, Acta Mechanica Solids Sinica, Vol.1 (1981), pp.99-106. – reference: (11) Liu, D.S. and Chiou, D.Y., Modeling of inclusions with interphases in heterogeneous material using the infinite element method, Computational Materials Science, Vol. 31 (2004), pp.405-420. – reference: (15) Yan, X., Cracks emanating from circular hole or square hole in rectangular plate in tension, Engineering Fracture Mechanics, Vol. 73 (2006), pp.1743-1754. – reference: (12) Liu, D.S. and Chiou, D.Y., 2-D infinite element modeling for elastostatic problems with geometric singularity and unbounded domain, Computers & Structures, Vol. 83 (2005), pp.2086-2099. – reference: (17) Leung, A.Y.T. and Su, R.K.L., Mixed-mode two-dimensional crack problem by fractal two level finite element method, Engineering Fracture Mechanics, Vol. 51, No. 6 (1995), pp.889-895. – reference: (10) Liu, D.S., Chiou, D.Y. and Lin, C.H., 3D IEM formulation with an IEM/FEM coupling scheme for solving elastostatic problems, Advances in Engineering Software, Vol. 34 (2003), pp.309-320. – reference: (4) Ying, L.A., An introduction to the infinite element method, Mathematics in Practice and Theory, Vol. 2 (1992), pp.69-78. – reference: (8) Guo, Z.H., Similar isoparametric elements, Chinese Science Bulletin, Vol. 24, No.13 (1979), pp.577-582. – reference: (2) Bois-Grossiant, P. and Tan, C.L., Boundary element fracture mechanics analysis of Brazil-nut sandwich specimens with an interface crack, Engineering Analysis with Boundary Elements, Vol. 16 (1995), pp. 215-225. – reference: (18) Aliabadi, M.H., Rooke, D.P. and Carteright, D.J., Mixed-mode Bueckner weight functions using boundary element analysis, International Journal of Fracture, Vol. 34 (1987), pp.131-147. – reference: (14) Gross, B. and Srawley, J.E., Stress intensity factor for single-edge-notch specimens in bending or combined bending and tension by boundary collocation of a stress function, NASA, technical note, D-2603, (1965). – reference: (3) Silvester, P. and Cermark, I.A., Analysis of coaxial line discontinuities by boundary relaxation, IEFE Transaction on Microwave Theory and Techniques, Vol.17, No.8(1969), pp.489-495. – reference: (7) Ying, L.A., The infinite element method, Advances Mathematics, Vol. 11, No.4 (1982), pp.269-272. – reference: (9) Liu, D.S. and Chiou, D.Y., A coupled IEM/FEM approach for solving elastic problems with multiple cracks, International Journal of Solids and Structures, Vol. 40 (2003), pp.1973-1993. – reference: (1) Su, B., Dunn, M.L. and Lee, Y.C., Prediction of the crack initiation of GaAs in a soldered assembly, Proceedings of InterPACK'01, The PACIFIC RIM/International, Intersociety, Electronic Packaging Technical/Business Conference & Exhibition, Kauai, Hawaii, (2001), pp.8-13. – reference: (19) Chan, S.K., Tuba, I.S. and Wilson, W.K., On the finite element method in linear fracture mechanics, Engineering Fracture Mechanics, Vol. 2 (1970), pp.1-17. – ident: 2 – ident: 3 – ident: 16 doi: 10.1016/S0013-7944(96)00051-3 – ident: 5 – ident: 4 – ident: 12 doi: 10.1016/j.compstruc.2005.03.009 – ident: 18 doi: 10.1007/BF00019768 – ident: 1 – ident: 11 – ident: 10 – ident: 19 – ident: 13 – ident: 14 – ident: 15 doi: 10.1016/j.engfracmech.2006.02.003 – ident: 9 doi: 10.1016/S0020-7683(03)00014-3 – ident: 17 doi: 10.1016/0013-7944(95)00008-J – ident: 6 – ident: 7 – ident: 8 – ident: 20 |
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| SubjectTerms | Convergence Discontinuity Finite Element Method Formulations Infinite Element Method Materials engineering Mathematical analysis Mathematical models Singularities Stress Intensity Factor Stress Singularity |
| Title | Development of High-Order Infinite Element Method for Stress Analysis of Elastic Bodies with Singularities |
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