PSI - Issue 2_A

J. Felger et al. / Procedia Structural Integrity 2 (2016) 2504–2511 J. Felger, W. Becker / Structural Integrity Procedia 00 (2016) 000–000

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which are significantly a ff ected by the fibre orientation and the boundary conditions. For the case of simply supported notch faces forming a nearly straight edge, singularities stronger than the classical crack tip singularity have been observed. Moreover, it has been shown that the range of notch opening angles leading to singularities varies with the fibre orientation. Consequently, a variation of the fibre direction could lead to an elimination of singularities. Finally, a comparison of the resulting asymptotic near-tip fields with finite element calculations has shown a very good agreement. The proposed complex potential method further allows for an embedding in numerical methods as e.g. an e ffi cient calculation of generalised stress intensity factors. Knowles, J. K., Wang, N.-M., 1960. On the bending of an elastic plate containing a crack. Journal of Mathematics and Physics 39 (4), 223–236. Joseph, P., Erdogan, F., 1991. Bending of a thin Reissner plate with a through crack. Journal of Applied Mechanics 58 (3), 842–846. Hui, C., Zehnder, A. T., 1993. A theory for the fracture of thin plates subjected to bending and twisting moments. International Journal of Fracture 61 (3), 211–229. Sosa, H., Herrmann, G., 1989. On invariant integrals in the analysis of cracked plates. International Journal of Fracture 40 (2), 111–126. Burton, W., Sinclair, G., 1986. On the singularities in Reissner’s theory for the bending of elastic plates. Journal of Applied Mechanics 53 (1), 220–222. Huang, C., 2003. Stress singularities at angular corners in first-order shear deformation plate theory. International Journal of Mechanical Sciences 45 (1), 1–20. Ro¨ssle, A., Sa¨ndig, A.-M., 2011. Corner singularities and regularity results for the Reissner / Mindlin plate model. Journal of Elasticity 103 (2), 113–135. Manticˇ, V., Paris, F., Canas, J., 1997. Stress singularities in 2D orthotropic corners. International Journal of Fracture 83 (1), 67–90. Chue, C.-H., Liu, C.-I., 2001. On stress singularities in an anisotropic wedge for various boundary conditions. Composite Structures 54 (1), 87–102. Lekhnitskii, S., 1963. Theory of elasticity of an anisotropic elastic body. San Francisco: Holden-Day. Lauke, B., Barroso, A., 2011. Notched-butt test for the determination of adhesion strength at bimaterial interfaces. Composite Interfaces 18 (8), 661–669. Muskhelishvili, N., 1966. Some basic problems of mathematical elasticity theory. Izd-vo Nauka, Moscow. Reddy, J. N., 1997. Mechanics of laminated composite plates: theory and analysis. CRC press. Williams, M., 1951. Surface stress singularities resulting from various boundary conditions in angular corners of plates under bending. Journal of Applied Mechanics 18, 320–320. Williams, M., 1961. The bending stress distribution at the base of a stationary crack. Journal of Applied Mechanics 28 (1), 78–82. Timoshenko, SP., Woinowsky-Krieger, S., 1959. Theory of plates and shells. New York: McGraw-Hill. Reissner, E., 1945. The e ff ect of transverse shear deformation on the bending of elastic plates. Journal of Aplied Mechanics 12, 69–77. Mindlin, RD., 1951. Influence of rotary inertia and shear on flexural motions of isotropic elastic plates. Journal of Applied Mechanics 73, 31–38. Barnett, DM., Kirchner, HOK. , 1997. A proof of the equivalence of the Stroh and Lekhnitskii sextic equations for plane anisotropic elastostatics. Philosophical Magazine A 76 (1), 231–239. Stroh, AN., 1958. Dislocations and cracks in anisotropic elasticity. Philosophical magazine 30 (3), 625–646. Savin, N., 1961. Stress concentration around holes. New York: Pergamon Press. Becker, W. , 1993. Complex method for the elliptical hole in an unsymmetric laminate. Archive of Applied Mechanics 62 (3), 159–169. Ting, TCT., 1996. Anisotropic elasticity: Theory and applications. Oxford University Press. Dolbow, J., Moe¨s, N., Belytschko, T., 2000. Modeling fracture in Mindlin–Reissner plates with the extended finite element method. International Journal of Solids and Structures 37 (48), 7161–7183. Rhee, H., Atluri, S., 1982. Hybrid stress finite element analysis of bending of a plate with a through flaw. International Journal for Numerical Methods in Engineering 18 (2), 259–271. Grisvard, P., 1980. Boundary value problems in non-smooth domains. Vol. 19. University of Maryland, Dept. of Mathematics. Kondrat’ev, V. A., 1967. Boundary value problems for elliptic equations in domains with conical or angular points. Proc. of the Moscow Math. Soc. V. 16 16, 209–292. References