General formulation of macro-elements for the simulation of multi-layered bonded structures

References

• Hart-Smith, L. J. Technical Report AFWAL-TR-81-3154, (1982).
   Google Scholar
• Higgins, A. Adhesive bonding of aircraft structures. Int. J. Adhes. Adhes. 20 (5). 367–376 (2000). DOI:10.1016/S0143-7496(00)00006-3
   Web of Science ®Google Scholar
• Kelly, G. Quasi-static strength and fatigue life of hybrid (bonded/bolted) composite single-lap joints. Compos. Struct. 72 (1). 119–129 (2006). DOI:10.1016/j.compstruct.2004.11.002
   Web of Science ®Google Scholar
• da Silva, LFM, Öschner, A, Adams, RD (Editors), 2018. Handbook of Adhesion Technology (2 volumes), 2nd edition Springer: Heidelberg, Germany.
   Google Scholar
• van Ingen, J. W. Vlot, A. Report LR-740, (1993).
   Google Scholar
• Tsai, M. Y.; Morton, J., An evaluation of analytical and numerical solutions to the single-lap joint. Int. J. Solids Struct. 31 (18). 2537–2563 (1994). DOI:10.1016/0020-7683(94)90036-1
   Web of Science ®Google Scholar
• Da Silva, L. F. M.; Das Neves, P. J. C.; Adams, R. D.; Spelt, J. K., Analytical models of adhesively bonded joints—Part I: Literature survey. Int. J. Adhes. Adhes. 29 (3). 319–330 (2009). DOI:10.1016/j.ijadhadh.2008.06.005
   Web of Science ®Google Scholar
• Volkersen, O.; Die Nietkraftverteilung in Zugbeanspruchten Nietverbindungen mit konstanten Laschenquerschnitten. Luftfahrtforschung. 15 (24). 41–47 (1938).
   Google Scholar
• Goland, M.; Reissner, E. The stresses in cemented joints. J. Appl. Mech. 11. A17–A27 (1944).
   Google Scholar
• Hart-Smith, L. J.; NASA Technical Report CR112237, (1973).
   Google Scholar
• Hart-Smith, L. J. NASA Technical Report CR112236, (1973).
   Google Scholar
• Hart-Smith, L. J. NASA Technical Report CR112235, (1973).
   Google Scholar
• Williams, J. H. Stresses in Adhesive between Dissimilar Adherends. J. Adhes. 7 (2). 97–107 (1975). DOI:10.1080/00218467508075042
   Web of Science ®Google Scholar
• Bigwood, D. A.; Crocombe, A. D., Elastic analysis and engineering design formulae for bonded joints. Int. J. Adhes. Adhes. 9 (4). 229–242 (1989). DOI:10.1016/0143-7496(89)90066-3
   Web of Science ®Google Scholar
• Oplinger, D. W. US AMTL Technical Report MTL91-23, (1991).
   Google Scholar
• Tsai, M. Y.; Oplinger, D. W.; Morton, J., Improved theoretical solutions for adhesive lap joints. Int. J. Solids Struct. 35 (12). 1163–1185 (1998). DOI:10.1016/S0020-7683(97)00097-8
   Web of Science ®Google Scholar
• Högberg, L. Mechanical Behaviour of Single-Layer Adhesive Joints : An Integrated Approach. Licensing Graduate Thesis, Chalmers University of Technology: Sweden, 2004.
   Google Scholar
• Nemes, O.; Lachaud, F., Modeling of Cylindrical Adhesively Bonded Joints. J. Adhes. Sci. Technol. 23 (10–11). 1383–1393 (2009). DOI:10.1163/156856109X432983
   Web of Science ®Google Scholar
• Luo, Q.; Tong, L., Analytical solutions for nonlinear analysis of composite single-lap adhesive joints. Int. J. Adhes. Adhes. 29 (2). 144–154 (2009). DOI:10.1016/j.ijadhadh.2008.01.007
   Web of Science ®Google Scholar
• Weißgraeber, P.; Stein, N.; Becker, W. A general sandwich-type model for adhesive joints with composite adherends. Int. J. Adhes. Adhes. 55. 56–63 (2014). DOI: 10.1016/j.ijadhadh.2014.06.009.
   Web of Science ®Google Scholar
• Mortensen, F.; Thomsen, O. T. Simplified linear and non-linear analysis of stepped and scarfed adhesive-bonded lap-joints between composite laminates, 38 (1). 281–294 (1997). DOI: 10.1016/S0263-8223(97)00063-9.
   Google Scholar
• Mortensen, M. Development of Tools for Engineering Analysis and Design of High-Performance FRP-Composite Structural Elements. PhD Thesis, Aalborg University: Denmark, 1998.
   Google Scholar
• Mortensen, F.; Thomsen, O. T. Analysis of adhesive bonded joints: a unified approach. Compos. Sci. Technol. 62 (7–8). 1011–1031 (2002). DOI:10.1016/S0266-3538(02)00030-1
   Web of Science ®Google Scholar
• Paroissien, E. Contribution aux Assemblages Hybrides (Boulonnés/Collés) – Application aux Jonctions Aéronautiques. PhD Dissertation (in French), Université de Toulouse III: Toulouse, 2006.
   Google Scholar
• Paroissien, E.; Sartor, M.; Huet, J. Hybrid (Bolted/Bonded) Joints Applied to Aeronautic Parts: Analytical One-Dimensional Models of a Single-Lap Joint. In Advances in Integrated Design and Manufacturing in Mechanical Engineering II, Tichkiewitch, S., Tollenaere, M., Ray, P., Eds., Springer Netherlands: Dordrecht, (2007); pp 95–110. DOI: 10.1007/978-1-4020-6761-7_7.
   Google Scholar
• Paroissien, E.; Sartor, M.; Huet, J.; Lachaud, F. Analytical Two-Dimensional Model of a Hybrid (Bolted/Bonded) Single-Lap Joint. J. Aircr. 44 (2). 573–582 (2007). DOI:10.2514/1.24452
   Web of Science ®Google Scholar
• Paroissien, E.; Lachaud, F.; Jacobs, T. A Simplified Stress Analysis of Bonded Joints Using Macro-Elements. In Advances in Modeling and Design of Adhesively Bonded Systems, Kumar, S., Mittal, K. L., Eds., John Wiley & Sons, Inc.: Hoboken, NJ, USA, (2013); pp 93–146. DOI: 10.1002/9781118753682.ch4.
   Google Scholar
• Paroissien, E.; Gaubert, F.; Da Veiga, A.; Lachaud, F. Elasto-plastic analysis of bonded joints with macro-elements. J. Adhes. Sci. Technol. 27 (13). 1464–1498 (2013). DOI:10.1080/01694243.2012.745053
   Web of Science ®Google Scholar
• Lelias, G.; Paroissien, E.; Lachaud, F.; Morlier, J.; Schwartz, S.; Gavoille, C. An extended semi-analytical formulation for fast and reliable mode I/II stress analysis of adhesively bonded joints. Int. J. Solids Struct. 62. 18–38 (2015). DOI: 10.1016/j.ijsolstr.2014.12.027.
   Web of Science ®Google Scholar
• Paroissien, E.; Lachaud, F.; Schwartz, S.; Da Veiga, A.; Barrière, P. Simplified stress analysis of hybrid (bolted/bonded) joints. Int. J. Adhes. Adhes. 77. 183–197 (2017). DOI: 10.1016/j.ijadhadh.2017.05.003.
   Web of Science ®Google Scholar
• Paroissien, E.; Lachaud, F.; Morlier, J.; Schwartz, S. A Direct Method for the Assessment of Cohesive Zone Models for Thin Adhesive Layers Loaded in Mode I, Mode II, and Mixed-Mode I/II. Rev. Adhes. Adhes. 2018. DOI: 10.7569/RAA.2018.097301.
   Google Scholar
• Paroissien, E.; Da Silva, L. F. M.; Lachaud, F. Simplified stress analysis of functionally graded single-lap joints subjected to combined thermal and mechanical loads. Compos. Struct. 203. 85–100 (2018). DOI: 10.1016/j.compstruct.2018.07.015.
   Web of Science ®Google Scholar
• Jones, R. M. Composite materials, Mechanical behavior and structural analysis. Springer: New York, (1999).
   Google Scholar
• Berthelot, J.-M. Composite materials, Mechanical behavior and structural analysis. Springer: New York, 1999.
   Google Scholar
• Brualdi, R. A. The Jordan Canonical Form: An Old Proof. Am. Math. Mon. 94 (3). 257 (1987). DOI:10.2307/2323392
   Web of Science ®Google Scholar
• Cater, S. An Elementary Development of the Jordan Canonical Form. Am. Math. Mon. 69 (5). 391 (1962). DOI:10.2307/2312130
   Web of Science ®Google Scholar
• Fletcher, R.; Sorensen, D. C. An Algorithmic Derivation of the Jordan Canonical Form. Am. Math. Mon. 90 (1). 12 (1983). DOI:10.2307/2975686
   Web of Science ®Google Scholar
• Galperin, A.; Waksman, Z. An Elementary Approach to Jordan Theory. Am. Math. Mon. 87 (9). 728 (1980). DOI:10.2307/2321861
   Web of Science ®Google Scholar
• Gohberg, I.; Goldberg, S. A Simple Proof of the Jordan Decomposition Theorem for Matrices. Am. Math. Mon. 103 (2). 157 (1996). DOI:10.2307/2975110
   Web of Science ®Google Scholar
• Valiaho, H. An Elementary Approach to the Jordan Form of a Matrix. Am. Math. Mon. 93 (9). 711 (1986). DOI:10.2307/2322285
   Web of Science ®Google Scholar
• Beauregard, R. A. Fraleigh, J. B. A First Course in Linear Algebra with OptionalIntroduction to Groups, Rings, and Fields. Boston: Houghton Mifflin (1973).
   Google Scholar
• Golub, G. H. Van Loan, C. F. Matrix Computation, 3rd edition. The John Hopkins University Press, Baltimore, Maryland 1996.
   Google Scholar
• Nering, E. D. Linear Algebra and Matrix Theory, 2nd edition, John Wiley and Sons: New-York, (1970).
   Google Scholar
• Brechenmacher, F. Histoire Du Théorème De Jordan De La Décomposition Matricielle (1870–1930). Formes de représentation et méthodes de décomposition. PhD Thesis, Ecole des Hautes Etudes en Sciences Sociales (EHESS): France, 2006.
   Google Scholar
• Horn, R. A. Johnson, C. R. Matrix Analysis, Cambridge University Press: New York 1985.
   Google Scholar
• Gauthier-Villars., J. C.; Traité des substitutions et des équations algébriques: Paris, France (1870).
   Google Scholar
• C. Jordan, Œuvres de Camille Jordan, Gauthier-Villars: Paris, 1961.
   Google Scholar
• R. Bronson, Matrix Methods: An Introduction. Academic Press: New York, 1970.
   Google Scholar
• Lélias, G.; Paroissien, E.; Lachaud, F.; Morlier, J. Experimental characterization of cohesive zone models for thin adhesive layers loaded in mode I, mode II, and mixed-mode I/II by the use of a direct method. Int. J. Solids Struct. 158. 90–115 (2019). DOI: 10.1016/j.ijsolstr.2018.09.005.
   Web of Science ®Google Scholar
• Paroissien, E.; Lachaud, F.; Da Silva, L. F. M.; Seddiki, S. A comparison between macro-element and finite element solutions for the stress analysis of functionally graded single-lap joints. Compos. Struct. 215. 331–350 (2019). DOI:10.1016/j.compstruct.2019.02.070
   Web of Science ®Google Scholar
• Dechwayukul, C.; Rubin, C. A.; Hahn, G. T. Analysis of the Effects of Thin Sealant Layers in Aircraft Structural Joints. Aiaa J. 41 (11). 2216–2228 (2003). DOI:10.2514/2.6814
   Google Scholar