Issue 29

R Massabò, Frattura ed Integrità Strutturale, 29 (2014) 230-240; DOI: 10.3221/IGF-ESIS.29.20 239 C ONCLUSIONS quilibrium equations were derived in [18,19] for multilayered composite plates with cohesive interfaces and delaminations which depend on only six unknown displacement functions (three for wide plates) for any arbitrary numbers of layers and interfaces. The equations have been particularized here to plates deforming in cylindrical bending and restated in a form similar to that of single-layer theory. This introduces a generalized transverse shear force which is directly related to the bending moment, as the shear force is in single-layer theory, and depends on the multilayered structure of the material and the status of the interfaces. The new equations explain the apparent inconsistencies which have been observed in the shear force when using zigzag theories to model plates with clamped edges. Applications to cantilevered wide plates with imperfect interfaces and delaminations confirm the accuracy of the proposed model in predicting stress and displacement fields in thick, highly anisotropic, multilayered plates. They also highlight the existence of boundary regions, near the clamped edges and at the delamination tips, where gross stress resultants and couples are accurately predicted, while stresses and displacements in the layers are not, as a consequence of the imposition of boundary/continuity conditions on the global displacement variables only. The size of the boundary region at the delamination tip in a unidirectionally reinforced laminate is very small, 50 / L  with L the characteristic inplane dimension. The presence of the boundary regions must be accounted for in the solution of the problems and fracture mechanics predictions must rely on expressions depending on gross stress resultants and couples, which should be calculated at the boundary of the region surrounding the crack tip. It is expected that improvements in the prediction of stresses and displacements in the boundary regions may be obtained through the introduction of a shear factor which depends on the status of the interfaces. A CKNOWLEDGEMENTS upport by U.S. Office of Naval Research, ONR, grant no. N00014-14-1-0229 (administered by Dr. Rajapakse). R EFERENCES [1] Pagano, N. J., Exact solutions for composite laminates in cylindrical bending, J Compos Mater, 3 (1969) 398-411. [2] Carrera, E. Theories and Finite Elements for Multilayered, Anisotropic, Composite Plates and Shell. Arch Comput Method E, 9 (2) (1997) 87–140 [3] Williams, T. O., and Addessio, F. L., A general theory for laminated plates with delaminations, Int J Solids Struct, 34 (1997) 2003-2024. [4] Allix O, Ladeveze P, Corigliano, Damage analysis of interlaminar fracture specimens, Compos Struct 31 (1995) 66-74. [5] Andrews, M.G., Massabò, R., Cavicchi, A., B.N. Cox, Dynamic interaction effects of multiple delaminations in plates subject to cylindrical bending, Int J Solids Struct, 46 (2009) 1815-1833. [6] Andrews, M.G., Massabò, R., and Cox, B.N., Elastic interaction of multiple delaminations in plates subject to cylindrical bending, Int J Solids Struct, 43(5) (2006) 855-886. [7] Massabò, R., and Cavicchi, A., Interaction effects of multiple damage mechanisms in composite sandwich beams subjected to time dependent loading, Int J Solids Struct, 49 (2012) 720-738. [8] Carrera, E., Historical review of Zig-Zag theories for multilayered plates and shells, Appl Mech Rev, 56, 3, 2003. [9] Di Sciuva, M., Bending, vibration and buckling of simply supported thick multilayered orthotropic plates: an evaluation of a new displacement model, J Sound Vib, 105 (3) (1986) 425-442. [10] Di Sciuva, M., An improved shear-deformation theory for moderately thick multilayered anisotropic shells and plates, J Appl Mech, 54 (1987) 589-596. [11] Cheng, Z. Q., Jemah, A. K., and Williams, F. W., Theory for multilayered anisotropic plates with weakened interfaces, J Appl Mech, 63 (1996) 1019-1026. [12] Schmidt, R., and Librescu, L., “Geometrically nonlinear theory of laminated anisotropic composite plates featuring interlayer slips,” Nova Journal of Mathematics, Game Theory, and Algebra, 5 (1996) 131-147. [13] Di Sciuva, M., Geom. nonlinear theory of multilayered plates with interlayer slips, AIAA J., 35 (1997) 1753-1759. E s