The fast multipole boundary element method for anisotropic material problems under centrifugal loads. (English) Zbl 07855333
Keywords:
fast multipole method; boundary element method; anisotropic elastostatic problems; Leknitskii formalism; plane stress; plane strainSoftware:
AEPHReferences:
| [1] | Jaswon, M. A., Integral equation methods in potential theory. I, Proc R Soc A, 275, 1360, 23-32, 1963 · Zbl 0112.33103 |
| [2] | Symm, G. T., Integral equation methods in potential theory. II, Proc R Soc A, 275, 1360, 33-46, 1963 · Zbl 0112.33201 |
| [3] | Jaswon, M. A.; Ponter, A. R., An integral equation solution of the torsion problem, Proc R Soc A, 273, 1353, 237-246, 1963 · Zbl 0112.16703 |
| [4] | Hackbusch, W.; Nowak, Z. P., On the fast matrix multiplication in the boundary element method by panel clustering, Numer Math, 54, 4, 463-491, 1989 · Zbl 0641.65038 |
| [5] | Börm, S., Construction of data-sparse \(H^2\)-matrices by hierarchical compression, SIAM J Sci Comput, 31, 3, 1820-1839, 2009 · Zbl 1193.65043 |
| [6] | Bebendorf, M., Approximation of boundary element matrices, Numer Math, 86, 4, 565-589, 2000 · Zbl 0966.65094 |
| [7] | Bebendorf, M.; Rjasanow, S., Adaptive low-rank approximation of collocation matrices, Computing, 70, 1, 1-24, 2003 · Zbl 1068.41052 |
| [8] | Bastos, E.; de Albuquerque, É. L.; Campos, L. S.; Wrobel, L. C., Two accelerated isogeometric boundary element method formulations: fast multipole method and hierarchical matrices method, Lat Am J Solids Struct, 19, 7, 1-26, 2022 |
| [9] | Liu, Y., A new fast multipole boundary element method for solving large-scale two-dimensional elastostatic problems, Internat J Numer Methods Engrg, 65, 6, 863-881, 2006 · Zbl 1121.74061 |
| [10] | Rokhlin, V., Rapid solution of integral equations of classical potential theory, J Comput Phys, 60, 2, 187-207, 1985 · Zbl 0629.65122 |
| [11] | Greengard, L.; Rokhlin, V., A fast algorithm for particle simulations, J Comput Phys, 73, 2, 325-348, 1987 · Zbl 0629.65005 |
| [12] | Dongarra, J.; Sullivan, F., Guest editors introduction to the top 10 algorithms, Comput Sci Eng, 2, 1, 22-23, 2000 |
| [13] | Liu, Y., Fast multipole boundary element method, 2009, Cambridge University Press |
| [14] | Barnes, J.; Hut, P., A hierarchical \(O( N \log N)\) force-calculation algorithm, Nature, 324, 6096, 446-449, 1986 |
| [15] | Mullen, R. L.; Rencis, J. J., Iterative methods for solving boundary element equations, Comput Struct, 25, 5, 713-723, 1987 · Zbl 0603.73082 |
| [16] | Kane, J. H.; Keyes, D. E.; Prasad, K. G., Iterative solution techniques in boundary element analysis, Internat J Numer Methods Engrg, 31, 8, 1511-1536, 1991 · Zbl 0825.73901 |
| [17] | Mansur, W. J.; Araújo, F. C.; Malaghini, J. E.B., Solution of BEM systems of equations via iterative techniques, Internat J Numer Methods Engrg, 33, 9, 1823-1841, 1992 · Zbl 0767.73085 |
| [18] | Prasad, K. G.; Kane, J. H.; Keyes, D. E.; Balakrishna, C., Preconditioned Krylov solvers for BEA, Internat J Numer Methods Engrg, 37, 10, 1651-1672, 1994 · Zbl 0800.73504 |
| [19] | Barra, L.; Coutinho, A.; Mansur, W.; Telles, J., Iterative solution of bem equations by GMRES algorithm, Comput Struct, 44, 6, 1249-1253, 1992 |
| [20] | Greengard, L., Fast algorithms for composite materials, MRS Proc, 408, 93-97, 1995 |
| [21] | Greengard, L.; Helsing, J., On the numerical evaluation of elastostatic fields in locally isotropic two-dimensional composites, J Mech Phys Solids, 46, 8, 1441-1462, 1998 · Zbl 0955.74054 |
| [22] | Haitao, W.; Zhenhan, Y., Application of a new fast multipole BEM for simulation of 2D elastic solid with large number of inclusions, Acta Mech Sin, 20, 6, 613-622, 2004 |
| [23] | Zhu, X.; Chen, W.; Huang, Z.; Liu, Y., Fast multipole boundary element analysis of 2D viscoelastic composites with imperfect interfaces, Sci China Technol Sci, 53, 8, 2160-2171, 2010 · Zbl 1386.74147 |
| [24] | Liu, Y.; Nishimura, N.; Otani, Y., Large-scale modeling of carbon-nanotube composites by a fast multipole boundary element method, Comput Mater Sci, 34, 2, 173-187, 2005 |
| [25] | Wang, D. F.; Fukui, T.; Kobayashi, T., Analysis of multi-crack problems in orthotropic elastic body based on fast multipole boundary element, J Jascome, 5, 2, 183-188, 2005 |
| [26] | Wang, Q.; Miao, Y.; Zhu, H., A fast multipole hybrid boundary node method for composite materials, Comput Mech, 51, 6, 885-897, 2012 · Zbl 1366.74082 |
| [27] | Zhang, J.; Zhuang, C.; Qin, X.; Li, G.; Sheng, X., FMM-accelerated hybrid boundary node method for multi-domain problems, Eng Anal Bound Elem, 34, 5, 433-439, 2010 · Zbl 1244.74239 |
| [28] | Barbarino, M.; Bianco, D., A BEM-FMM approach applied to the combined convected Helmholtz integral formulation for the solution of aeroacoustic problems, Comput Methods Appl Mech Engrg, 342, 585-603, 2018 · Zbl 1440.76048 |
| [29] | Ptaszny, J.; Fedelińnaski, P., Numerical homogenization by using the fast multipole boundary element method, Arch Civ Mech Eng, 11, 1, 181-193, 2011 |
| [30] | Li, S.; Trevelyan, J.; Zhang, W.; Wang, D., Accelerating isogeometric boundary element analysis for 3-dimensional elastostatics problems through black-box fast multipole method with proper generalized decomposition, Internat J Numer Methods Engrg, 114, 9, 975-998, 2018 · Zbl 07878393 |
| [31] | Hwu, C., Anisotropic elasticity with matlab, 2022, Springer International Publishing |
| [32] | Fahmy, M. A., A new boundary element algorithm for modeling and simulation of nonlinear thermal stresses in micropolar FGA composites with temperature-dependent properties, Adv Model Simul Eng Sci, 8, 1, 2021 |
| [33] | Cordeiro, S. G.F.; Leonel, E. D., Cohesive crack propagation modelling in wood structures using BEM and the Tangent Operator Technique, Eng Anal Bound Elem, 64, 111-121, 2016 · Zbl 1403.74157 |
| [34] | Yin, J.; Barnett, D. M.; Fitzgerald, S. P.; Cai, W., Computing dislocation stress fields in anisotropic elastic media using fast multipole expansions, Modelling Simul Mater Sci Eng, 20, 4, Article 045015 pp., 2012 |
| [35] | Benedetti, I.; Milazzo, A.; Aliabadi, M. H., A fast dual boundary element method for 3D anisotropic crack problems, Internat J Numer Methods Engrg, 80, 10, 1356-1378, 2009 · Zbl 1183.74334 |
| [36] | Akaiwa, N.; Thornton, K.; Voorhees, P., Large-scale simulations of microstructural evolution in elastically stressed solids, J Comput Phys, 173, 1, 61-86, 2001 · Zbl 1056.74057 |
| [37] | Sollero, P.; Aliabadi, M. H., Fracture mechanics analysis of anisotropic plates by the boundary element method, Int J Fract, 64, 4, 269-284, 1993 |
| [38] | Albuquerque, E. L.; Sollero, P.; Aliabadi, M. H., Dual boundary element method for anisotropic dynamic fracture mechanics, Internat J Numer Methods Engrg, 59, 9, 1187-1205, 2004 · Zbl 1041.74555 |
| [39] | Albuquerque, E.; Sollero, P.; Fedelinski, P., Dual reciprocity boundary element method in Laplace domain applied to anisotropic dynamic crack problems, Comput Struct, 81, 17, 1703-1713, 2003 |
| [40] | Albuquerque, E.; Sollero, P.; Fedelinski, P., Free vibration analysis of anisotropic material structures using the boundary element method, Eng Anal Bound Elem, 27, 10, 977-985, 2003 · Zbl 1045.74608 |
| [41] | Albuquerque, E.; Sollero, P.; Aliabadi, M., The boundary element method applied to time dependent problems in anisotropic materials, Int J Solids Struct, 39, 5, 1405-1422, 2002 · Zbl 1039.74053 |
| [42] | García-Sánchez, F.; Sáez, A.; Domínguez, J., Two-dimensional time-harmonic BEM for cracked anisotropic solids, Eng Anal Bound Elem, 30, 2, 88-99, 2006 · Zbl 1195.74230 |
| [43] | García-Sánchez, F.; Zhang, C.; Sáez, A., A two-dimensional time-domain boundary element method for dynamic crack problems in anisotropic solids, Eng Fract Mech, 75, 6, 1412-1430, 2008 |
| [44] | Deb, A.; Banerjee, P. K., BEM for general anisotropic 2D elasticity using particular integrals, Commun Appl Numer Methods, 6, 2, 111-119, 1990 · Zbl 0693.73055 |
| [45] | Partridge, P. W.; Brebbia, C. A.; Wrobel, L. C., The dual reciprocity boundary element method, 2012, Springer Netherlands |
| [46] | Chang, C. I., A closed-form solution for an orthotropic rotating disk, J Appl Mech, 41, 4, 1122-1123, 1974 |
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