A novel asymptotic approach to the problem of laminated fibrous composites with free edges is proposed in this article. Commonly, this type of composites is modeled on the assumption of homogenized individual plies. In the presence of free edges, the elastic fields in the individual plies need additional investigation. Our approach is based on the asymptotic splitting of the governing biharmonic problem into two harmonic problems. All solutions are obtained in the closed analytical form. In particular, the obtained results can be used in the analysis of fracture of composite materials as well as for the analytical modeling of the pull-out and push-out tests.
Cox B. and Vang Q. In quest of virtual tests for structural composites. Science2006; 314: 1102-1107.
2.
Kalamkarov AL , Andrianov IV and Danishevs’kyy VVAsymptotic homogenization of composite materials and structures. Appl Mech Rev2009; 62(3): 030802-1-030802-20.
3.
Andrianov IV , Danishevs’kyy VV and Weichert D.Analytical study of the load transfer in fibre-reinforced 2D composite materials. Int J Solids Struct2008; 45: 1217-1243.
4.
Tranter CJIntegral transforms in mathematical physics. London: Chapman and Hall, 1971.
5.
Prudnikov AP, Brichkov YA and Marichev OIIntegrals and series: Vol. 1: Elementary functions. New York: Gordon & Breach, 1986.
6.
Abramowitz M and Stegun IA (eds) Handbook of mathematical functions, with formulas, graphs, and mathematical tables. New York: Dover Publications, 1965.
7.
Muki R. and Sternberg E.On the diffusion of load from a transverse tension-bar into a semi-infinite elastic sheet. J Appl Mech1968; 35(12): 737-746.
8.
Sternberg E.Load-transfer and load-diffusion in elastostatics. In: Proceedings of the 6th US National Congress on Applied Mechanics, 1970, Harvard University, Cambridge, MA, USA, 15-19 June, New York, NY: ASME, pp.34-61.
9.
Christensen RMMechanics of composite materials. Minneola, New York: Dover Publications, 2005 .
10.
Manevitch LI and Pavlenko AVAsymptotic methods in micromechanics of composite materials. Kiev: Naukova Dumka, 1991(in Russian).
11.
Andrianov IV , Danishevs’kyy VV and Weichert D.Load-transfer from fibre to anisotropic half-space for dilute composites. Acta Mech2008; 200: 69-78.
12.
Slivker V.Mechanics of structural elements: theory and applications. Berlin, New York: Springer-Verlag , 2007.
13.
Koiter WTOn the diffusion of load from a stiffener into a sheet. Q J Mech Appl Math1955; 8(2): 164-178.
14.
Benveniste Y. and Miloh T.Imperfect soft and stiff interfaces in two-dimensional elasticity. Mech Mater2001; 33: 309-324.
15.
Hashin Z.Thin interphase imperfect interface in elasticity with application to coated fiber composites. J Mech Phys Solids2002; 50: 2509-2537.
16.
Golland M. and Reissner E.The stresses in cemented joints. J Appl Mech1944; 11: A17-A27.
17.
Geymonat G. , Krasucki F. and Lenci S.Mathematical analysis of a bonded joint with a soft thin adhesive. Math Mech Solids1999 ; 4: 201-225.
18.
Kalamkarov ALComposite and reinforced elements of construction . Chichester, New York: Wiley, 1992.
19.
Kalamkarov AL and Kolpakov AGAnalysis, design and optimization of composite structures. Chichester, New York : Wiley, 1997.
20.
Sinclair GBStress singularities in classical elasticity - I: removal, interpretation and analysis. Appl Mech Rev2004; 57(4): 251-297.
