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Boundary element analysis of stiffened panels with repair patches. (English) Zbl 1403.74161
Summary: In this paper a boundary element method for analysis of fractured stiffened panels repaired with riveted or adhesively bonded patches is presented. In order to achieve such a formulation, several boundary element formulations involving the membrane and bending of displacement, and, stress resultants are coupled together to analyse the model. The multi-region formulation is used to simulate the stiffeners, which are modelled as an assembly. They are then connected to the sheets to form the stiffened panels by means of a rivet formulation. The dual boundary element method is used to simulate the presence of cracks, and the patches, treated as independent plates, are joined to the panel either with rivets or adhesive. A boundary element formulation for adhesive bonding is implemented to model the adhesively bonded patches. The Crack Opening Displacements (COD) method and the J-integral are implemented to evaluate the required fracture parameters. Examples presented include a wing box with a three spar section, with fully stiffened skin, and, the skin is considered to have a crack and a repair patch is used on top of the crack to stop its growth.

MSC:
74S15 Boundary element methods applied to problems in solid mechanics
65N38 Boundary element methods for boundary value problems involving PDEs
74R10 Brittle fracture
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[1] Actis, R. L.; Szabò, B. A., Analysis of bonded and fastened repairs by the p-version of the finite-element method, Comput Math Appl, 46, 1-14, (2003) · Zbl 1221.74068
[2] Albuquerque, E. L.; Sollero, P.; Venturini, W. S.; Aliabadi, M. H., Boundary element analysis of anisotropic Kirchhoff plates, Int J Solids Struct, 43, 14, 4029-4046, (2006) · Zbl 1120.74840
[3] Aliabadi, M. H., Plate bending analysis with boundary elements, (1998), Computational Mechanics Publications Southampton · Zbl 0987.74006
[4] Aliabadi, M. H., The boundary element method, vol II: application to solids and structures, (2001), Wiley Winchester
[5] Aliabadi, M. H., A new generation of boundary element methods in fracture mechanics, Int J Fract, 86, 91-125, (1997)
[6] Aliabadi, M. H., Boundary element formulations in fracture mechanics, Appl Mech Rev, 50, 83-96, (1997)
[7] Baiz, P. M.; Aliabadi, M. H., Local buckling of thin-walled structures by the boundary element method, Eng Anal Bound Elem, 33, 3, 302-313, (2009) · Zbl 1244.74138
[8] Baker, A. A.; Jones, R., Bonded repair of aircraft structures, (1988), Martinus Nijhoff Publishers Dordrecht
[9] Balas, J.; Sladek, J.; Sladek, K., The boundary integral equation method for plates resting on a two-parameter foundation, Z Angew Math Mech, 64, 137-146, (1984) · Zbl 0532.73080
[10] Barcellos CA, Silva LHM. A boundary element formulation for the Mindlin׳s plate model. In: Boundary element technology. Southampton: Computational Mechanics Publications; 1989. p. 123-30.
[11] Benedetti, I.; Aliabadi, M. H., A three-dimensional cohesive-frictional grain-boundary polycrystalline materials, Comput Methods Appl Mech Eng, 265, 36-62, (2013) · Zbl 1286.74012
[12] Bezine, G., Boundary integral formulation for plate flexture with arbitrary boundary conditions, Mech Res Commun, 5, 4, 197-206, (1978) · Zbl 0399.73062
[13] Di Pisa, C.; Aliabadi, M. H., An efficient BEM formulation for analysis of bond-line cracks in thin walled aircraft structure, Int J Fract, 179, 1-2, 129-145, (2013)
[14] Di Pisa, C.; Aliabadi, M. H., Fatigue crack growth analysis of assembled plate structures with dual boundary element method, Eng Fract Mech, 98, 200-213, (2013)
[15] di Pisa, C.; Aliabadi, M. H.; Yong, A., Dual boundary method for assembled plate structures undergoing large deflection, Int J Numer Methods Eng, 89, 13, 1720-1738, (2012) · Zbl 1242.74184
[16] Dourakopoulos, J. A.; Sapountzakis, E. J., Nonlinear dynamic analysis of plates stiffened by parallel beams with deformable connection, Adv Civil Eng, 1, 942763, (2014), 22 pp
[17] Dirgantara, T.; Aliabadi, M. H., Boundary element method analysis of assembled plate-structure, Commun Numer Methods Eng, 17, 749-760, (2001) · Zbl 1017.74078
[18] Dirgantara T, Aliabadi MH. Crack growth analysis of plates loaded by bending and tension using dual boundary element method. Int J Fract 105(1):27-47.
[19] Dirgantara, T.; Aliabadi, M. H., Stress intensity factors for cracks in thin plates, Eng Fract Mech, 69, 1465-1486, (2002)
[20] Dirgantara, T.; Aliabadi, M. H., Dual boundary element formulation for fracture mechanics analysis of shear deformable shells, Int J Solids Struct, 38, 7769-7800, (2001) · Zbl 1024.74046
[21] Fedelinski, P.; Aliabadi, M. H.; Rooke, D. P., The Laplace transform DBEM for mixed-mode dynamic crack analysis, Comput Struct, 59, 6, 1021-1031, (1996) · Zbl 0918.73299
[22] Forbes DJ, Robinson AR. Numerical analysis of elastic plates and shallow shells by an integral equation method. Structural research series report no 345. Urbana, USA: University of Illinois; 1969.
[23] Fernandes, Gabriela R. A., BEM formulation for linear bending analysis of plates reinforced by beams considering different materials, Eng Anal Bound Elem, 33, 8-9, 1132-1140, (2009) · Zbl 1244.74154
[24] Goland M, Reissner E. The stresses in cemented joints. ASME, A-17 A-27; March 1944.
[25] Hartmann, F.; Zormantel, R., The direct boundary element method for plate bending, Int J Numer Methods Eng, 23, 2049-2069, (1986) · Zbl 0596.73068
[26] Huang, X.; Aliabadi, M. H.; Sharif Khodaei, Z., Fatigue crack growth reliability analysis by stochastic boundary element method, Comput Model Eng Sci, 102, 291-330, (2014) · Zbl 1356.74184
[27] Hwu, Chyanbin, Boundary element formulation for the coupled stretching-bending analysis of thin laminated plates, Eng Anal Bound Elem, 36, 6, 1027-1039, (2012) · Zbl 1351.74110
[28] Jaswon, M. A.; Maiti, M.; Symm, G. T., Numerical biharmonic analysis and some applications, Int J Solids Struct, 3, 309-332, (1967) · Zbl 0148.19403
[29] Kamiya, N.; Sawaki, Y., An integral equation approach to finite deflection of elastic plates, Int J Non-linear Mech, 17, 187-194, (1988) · Zbl 0491.73092
[30] Karam, V. J.; Telles, J. C.F., On boundary elements for reissner׳s plate theory, Eng Anal, 5, 21-27, (1988)
[31] Katsikadelis, J. T.; Nerantzaki, M. S., The boundary element method for non-linear problems, Eng Anal Bound Elem, 23, 365-373, (1999) · Zbl 0945.65132
[32] Katsikadelis, J. T.; Babouskos, N. G., Stiffness and buckling optimization of thin plates with BEM, Arch Appl Mech, 82, 10-11, 1403-1422, (2012) · Zbl 1293.74346
[33] Kirchhoff, G., Uber das gleichgewicht und die bewegung einer elastischen scheibe, J Rein Angew Math, 40, 51-88, (1850)
[34] Lei, X. Y.; Haung, M. K.; Wang, X. X., Geometrically nonlinear analysis of a Reissner type plate by the boundary element method, Comput Struct, 37, 911-916, (1990)
[35] Lucas, F. M., Multiple-site damage in riveted lap-joints: experimental simulation and finite element prediction, Int J Fatigue, 22, 319-338, (2000)
[36] Mackerle, J., Finite element analysis of fastening and joininga bibliography (1990-2002), Int J Press Vessel. Pip., 80, 253-273, (2003)
[37] Maleki, S.; Tahani, M., Non-linear analysis of moderately thick laminated plates and shell panels under thermo-mechanical loading, Z Angew Math Mech, 92, 8, 652-667, (2012) · Zbl 1405.74023
[38] Mi, Y.; Aliabadi, M. H., Dual boundary element method for three-dimensional fracture mechanics analysis, Eng Anal Bound Elem, 10, 2, 161-171, (1992)
[39] Müller RPG. An experimental and analytical investigation of the fatigue behaviour of fuselage riveted lap joints. Delft, Netherlands: Delft University of Technology; 1995.
[40] (Murakami, Y., Stress intensity factors handbook, (1987), Oxford Pergamon Press)
[41] Panzeca, T.; Milana, V.; Salerno, M., A symmetric Galerkin BEM for plate bending analysis, Eur J Mech A/Solids, 28, 1, 62-74, (2009) · Zbl 1155.74424
[42] Pavia, J. B.; Aliabadi, M. H., Boundary element analysis of zoned plates in bending, Comput Mech, 25, 560-566, (2000) · Zbl 0993.74076
[43] Poe CC. The effect of riveted and uniformly spaced stringers on the stress intensity factors of a cracked sheet [M.Sc. thesis]. Virginia Polytechnic Institute; 1969.
[44] Provatidis, C. G.; Angelidis, D. I., Performance of coons׳ macroelements in plate bending analysis, Int J Comput Methods Eng Sci Mech, 15, 2, 110-125, (2014)
[45] Purbolaksono, J.; Aliabadi, M. H., Buckling analysis of shear deformable plates by boundary element method, Int J Numer Methods Eng, 62, 4, 537-563, (2005) · Zbl 1077.74055
[46] Purbolaksono, J.; Aliabadi, M. H., Sourcedual boundary element method for instability analysis of cracked plates, Comput Model Eng Sci, 8, 1, 73-90, (2005) · Zbl 1107.74048
[47] Portela, A.; Aliabadi, M. H., The dual boundary element methodeffective implementation for crack problems, Int J Numer Methods Eng, 33, 1269-1287, (1992) · Zbl 0825.73908
[48] Rashed, Y. F.; Aliabadi, M. H.; Brebbia, C. A., The boundary element method for thick plates on a Winkler foundation, Int J Numer Methods Eng, 41, 1435-1462, (1998) · Zbl 0907.73075
[49] Ratwani, M. N., Analysis of cracked adhesively bonded laminate structures, AIAA J, 17, 988-994, (1979) · Zbl 0414.73073
[50] Reissner, E., On bending of elastic plates, Q J Appl Math, 5, 55-68, (1947) · Zbl 0030.04302
[51] Rigby, R. H.; Aliabadi, M. H., Mixed-mode J-integral method for analysis of 3D fracture problems using BEM, Eng Anal Bound Elem, 11, 239-256, (1993)
[52] Salgado, N. K.; Aliabadi, M. H., The application of the dual boundary element method to the analysis of cracked stiffened panels, Eng Fract Mech, 54, 91-105, (1996)
[53] Salgado, N. K.; Aliabadi, M. H., Boundary element analysis of cracked stiffened sheets, reinforced by adhesively bonded patches, Int J Numer Methods Eng, 42, 195-217, (1998) · Zbl 0911.73074
[54] Salgado, N. K.; Aliabadi, M. H., The analysis of riveted repairs and lap joints, Fatigue Fract Eng Mater Struct, 20, 4, 583-593, (1996)
[55] Sapountzakis, E. J.; Dikaros, I. C., Large deflection analysis of plates stiffened by parallel beams, Eng Struct, 35, 254-271, (2012)
[56] Sfantos, G. K.; Aliabadi, M. H., A boundary cohesive grain element formulation for modelling intergranular microfracture in polycrystalline brittle materials, Int J Numer Methods Eng, 69, 1590-1626, (2007) · Zbl 1194.74503
[57] Sharif Khodaei, Z.; Ghajari, M.; Aliabadi, M. H., Determination of impact location on composite stiffened panels, Smart Mater Struct, 21, 10, 105026, (2012), (14 pp.)
[58] Shi, G.; Bezine, G., A general boundary integral formulation for the anisotropic plate bending problems, J Compos Mater, 22, 694-716, (1988)
[59] Stern, M., A general boundary integral formulation for plate bending problems, Int J Solids Struct, 15, 769-782, (1979) · Zbl 0405.73054
[60] Syngellakis, S.; Elzein, A., Plate buckling loads by the boundary element method, Int J Numer Methods Eng, 37, 1736-1778, (1994) · Zbl 0804.73073
[61] Swift T. Development of the fail-safe design feature on DC-10, ASMT_STP 486; 1971. p. 164-214.
[62] Tanaka M, Miyazaki K. A direct BEM for elastic plate-structure subjected to arbitrary loadings. In: Boundary elements VII. Berlin: Springer Verlag; 1985. p. 4-3, 4-16.
[63] Tanaka, M.; Matsumoto, T.; Yamamura, H., Application of BEM with extended Kalman filter to parameter identification of an elastic plate under dynamic loading, Eng Anal Bound Elem, 28, 3, 213-219, (2004) · Zbl 1075.74081
[64] Telles JCF, Karam VJ. Nonlinear material analysis of Reissner׳s plates. In: Plate bending with boundary elements. Southampton: Computational Mechanics Publications; 1998. p. 127-64.
[65] Tottenham H. The boundary element method for plates and shells. In: Developments in boundary element methods—I. London: Applied Science; 1979. p. 173-205.
[66] Useche, J.; Albuquerque, E. L., Dynamic analysis of shear deformable plates using the dual reciprocity method, Eng Anal Bound Elem, 36, 5, 627-632, (2012) · Zbl 1351.74059
[67] Vander Weeen, F., Application of the boundary integral equation method to reissner׳s plate model, Int J Numer Methods Eng, 18, 1-10, (1982) · Zbl 0466.73107
[68] Fernandes, G. R.; Venturini, W. S., Stiffened plate bending analysis by the boundary element method, Comput Mech, 28, 3-4, 275-281, (2002) · Zbl 1076.74564
[69] Young, A.; Cartwright, D. J.; Rooke, D. P., The boundary element method for analyzing repairs patches of cracked finite sheets, Aeronaut J, 92, 17, 416-421, (1988)
[70] Young, A.; Rooke, D. P.; Cartwright, D. J., Analysis of patched and stiffened cracked panels using the boundary element method, Int J Solids Struct, 29, 17, 2201-2216, (1992) · Zbl 0764.73094
[71] Wen, P. H.; Aliabadi, M. H.; Young, A., Boundary element analysis of flat cracked panels with adhesively bonded patches, Eng Fract Mech, 69, 2129-2146, (2002)
[72] Westphal T Jr, Barcellos CA. Application of the boundary element method to Reissner׳s and Mindlin׳s plate model. In Boundary elements XII, vol. 1. Southampton: Computational Mechanics Publication; 1990. p. 467-77.
[73] Wen, P. H.; Aliabadi, M. H.; Young, A., A boundary element method for dynamic plate bending problems, Int J Solids Struct, 37, 37, 5177-5188, (2000) · Zbl 0972.74075
[74] Wen, P. H.; Aliabadi, M. H.; Young, A., Fracture mechanics analysis of curved stiffened panels using BEM, Int J Solids Struct, 40, 219-236, (2003) · Zbl 1083.74604
[75] Widagdo, D.; Aliabadi, M. H., Boundary element analysis of cracked panels repaired by mechanically fastened composite patches, Eng Anal Bound Elem, 25, 339-345, (2001) · Zbl 1014.74077
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