Abstract
A refined global-local approach based on the scaled boundary finite element method (SBFEM) is proposed to improve the accuracy of predicted singular stress field. The proposed approach is carried out in conjunction with two steps. First, the entire structure is analyzed by employing an arbitrary numerical method. Then, the interested region, which contains stress singularity, is re-solved using the SBFEM by placing the scaling center right at the singular stress point with the boundary conditions evaluated from the first step imposed along the whole boundary including the side-faces. Benefiting from the semi-analytical nature of the SBFEM, the singular stress field can be predicted accurately without highly refined meshes. It provides the FEM or other numerical methods with a rather simple and convenient way to improve the accuracy of stress analysis. Numerical examples validate the effectiveness of the proposed approach in dealing with various kinds of problems. © 2017 Published by Elsevier Ltd on behalf of Chinese Society of Theoretical and Applied Mechanics.
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References
T. Belytschko, R. Cracie, G. Ventura, A review of extended/generalized finite element methods for material modeling, Model. Simul. Mater. Sci. Eng. 17 (4) (2009) 043001.
J.P. Wolf, C.M. Song, The scaled boundary finite-element method—a primer: derivations, Comput. Struct. 78 (1) (2000) 191–210.
C. Li, L. Tong, A mixed SBFEM for stress singularities in nearly incompressible multi-materials, Comput. Struct. 157 (2015) 19–30.
C. Song, F. Tin-Loi, W. Gao, Transient dynamic analysis of interface cracks in anisotropic bimaterials by the scaled boundary finite-element method, Int. J. Solids Struct. 47 (7–8) (2010) 978–989.
X. Long, C. Jiang, X. Han, et al., The Scaled boundary finite element second order sensitivity design and fracture mechanics analysis, Chin. J. Solid Mech. 36 (01) (2015) 42–54 (in Chinese).
S.S. Chen, Q.H. Li, Y.H. Liu, et al., Mode III 2-D fracture analysis by the scaled boundary finite element method, Acta Mech. Solida Sin. 26 (6) (2013) 619–628.
Z.J. Yang, A.J. Deeks, Fully-automatic modelling of cohesive crack growth using a finite element-scaled boundary finite element coupled method, Eng. Fract. Mech. 74 (16) (2007) 2547–2573.
E.T. Ooi, C.M. Song, F. Tin-Loi, et al., Polygon scaled boundary finite elements for crack propagation modelling, Int. J. Numer. Methods Eng. 91 (3) (2012) 319–342.
Z. Yang, Application of scaled boundary finite element method in static and dynamic fracture problems, Acta Mech. Sin. 22 (3) (2006) 243–256.
M. Shi, Y. Xu, H. Zhong, et al., Modelling of crack propagation for composite materials based on polygon scaled boundary finite elements, Eng. Mech. 31 (7) (2014) 1–7.
Y. Wang, L. Gao, Z.Q. Hu, Novel nonreflecting boundary condition for an infinite reservoir based on the scaled boundary finite-element method, J. Eng. Mech. 141 (2015).
G. Lin, Y. Wang, Z.Q. Hu, An efficient approach for frequency-domain and time-domain hydrodynamic analysis of dam-reservoir systems, Earthq. Eng. Struct. Dyn. 41 (13) (2012) 1725–1749.
Chen D., Du C. Dynamic analysis of bounded domains by SBFE and the improved continued-fraction expansion. Chin. J. Theor. Appl. Mech. 2013(02): 297–301 (in Chinese).
S.M. Li, H. Liang, A.M. Li, A semi-analytical solution for characteristics of a dam-reservoir system with absorptive reservoir bottom, J. Hydrodyn. 20 (6) (2008) 727–734.
J.P. Wolf, C.M. Song, Finite-element Modeling of Unbounded Media, John Wiley, Chichester, 1996.
B. Radmanović, C. Katz, A high performance scaled boundary finite element method, IOP Conference Series: Materials Science and Engineering, 10, IOP Publishing, 1996, p. 012214.
Junyi Y., Feng J., Zhang C. Time domain coupling procedure for FE and SBFE based on linear system theory. J. Tsinghua Univ. 2003(11): 1554–1557.
A.J. Deeks, Prescribed side-face displacements in the scaled boundary finite-element method, Comput. Struct. 82 (15–16) (2004) 1153–1165.
A.J. Deeks, J.P. Wolf, A virtual work derivation of the scaled boundary finite-element method for elastostatics, Comput. Mech. 28 (6) (2002) 489–504.
E.T. Ooi, Z.J. Yang, A hybrid finite element-scaled boundary finite element method for crack propagation modelling, Comput. Methods Appl. Mech. Eng. 199 (17–20) (2010) 1178–1192.
M.C. Genes, S. Kocak, A combined finite element based soil–structure interaction model for large-scale systems and applications on parallel platforms, Eng. Struct. 24 (9) (2002) 1119–1131.
E. Protopapadakis, M. Schauer, E. Pierri, et al., A genetically optimized neural classifier applied to numerical pile integrity tests considering concrete piles, Comput. Struct. 162 (2016) 68–79.
K.M. Mao, C.T. Sun, A refined global-local finite element analysis method, Int. J. Numer. Methods Eng. 32 (1991) 29–43.
C.M. Song, A matrix function solution for the scaled boundary finite-element equation in statics, Comput. Methods Appl. Mech. Eng. 193 (23–26) (2004) 2325–2356.
C.M. Song, Analysis of singular stress fields at multi-material corners under thermal loading, Int. J. Numer. Methods Eng. 65 (2006) 620–652.
C. Li, E.T. Ooi, C.M. Song, et al., SBFEM for fracture analysis of piezoelectric composites under thermal load, Int. J. Solids. Struct. 52 (2015) 114–129.
M.H. Bazyar, C.M. Song, Time-harmonic response of non-homogeneous elastic unbounded domains using the scaled boundary finite-element method, Earthq. Eng. Struct. Dyn. 35 (3) (2006) 357–383.
A. Yaseri, M.H. Bazyar, N. Hataf, 3D coupled scaled boundary finite-element/finite-element analysis of ground vibrations induced by underground train movement, Comput. Geotech. 60 (2014) 1–8.
N.M. Syed, B.K. Maheshwari, Improvement in the computational efficiency of the coupled FEM-SBFEM approach for 3D seismic SSI analysis in the time domain, Comput. Geotech. 67 (2015) 204–212.
G. Lin, Y. Zhang, Y. Wang, Z.Q. Hu, Coupled isogeometric and scaled boundary isogeometric approach for earthquake response analysis of dam-reservoir-foundation system, in: Proceedings of the 15th world conference of earth-quake engineering, Lisbon, 2012.
A.J. Deeks, J.P. Wolf, Semi-analytical elastostatic analysis of unbounded two-dimensional domains, Int. J. Numer. Anal. Methods Geomech. 26 (11) (2002) 1031–1057.
C.M. Song, F. Tin-Loi, W. Gao, A definition and evaluation procedure of generalized stress intensity factors at cracks and multi-material wedges, Eng. Fract. Mech. 77 (12) (2010) 2316–2336.
D.P. Rooke, D.J. Cartwright, Compendium of Stress Intensity Factors, Her Majesty’s Office, London, 1976, pp. 233–234.
Z.L. Xu, Elasticity (Volume One), 4th ed., Higher Education Press, Beijing, 2006, pp. 81–83.
L. Bouhala, A. Makradi, S. Belouettar, Thermal and thermo-mechanical influence on crack propagation using an extended mesh free method, Eng. Fract. Mech. 88 (2012) 35–48.
D.K.L. Tsang, S.O. Oyadiji, A.Y.T. Leung, Two-dimensional fractal-like finite element method for thermoelastic crack analysis, Int. J. Solids Struct. 44 (24) (2007) 7862–7876.
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Pang, L., Lin, G. & Hu, Z. A refined global-local approach for evaluation of singular stress field based on scaled boundary finite element method. Acta Mech. Solida Sin. 30, 123–136 (2017). https://doi.org/10.1016/j.camss.2017.03.006
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DOI: https://doi.org/10.1016/j.camss.2017.03.006