Deleterious localised stress fields: the effects of boundaries and stiffness tailoring in anisotropic laminated plates

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The safe design of primary load-bearing structures requires accurate prediction of stresses, especially in the vicinity of geometric discontinuities where deleterious three-dimensional stress fields can be induced. Even for thin-walled structures significant through-thickness stresses arise at edges and boundaries, and this is especially precarious for laminates of advanced bre-reinforced composites because through-thickness stresses are the predominant drivers in delamination failure. Here we use a higher-order equivalent single-layer model derived from the Hellinger-Reissner mixed variational principle to examine boundary layer effects in laminated plates comprising constant-stiffness and variable-stiffness laminate and deforming statically in cylindrical bending. The results show that zigzag deformations, which arise due to layerwise differences in the transverse shear moduli, drive boundary layers towards clamped edges and are therefore critically important in quantifying localised stress gradients. The relative significance of the boundary layer scales with the degree of layerwise anisotropy and the thickness to characteristic length ratio. Finally, we demonstrate that the phenomenon of alternating positive and negative transverse shearing deformation through the thickness of composite laminates, previously only observed at clamped boundaries, can also occur at other locations as a result of smoothly varying the material properties over the in-plane dimensions of the laminate.
Original languageEnglish
Article number20160391
Number of pages22
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2194
Early online date5 Oct 2016
Publication statusPublished - Oct 2016


  • boundary layer effects
  • composite laminates
  • higher-order plate theory
  • variable stiffness


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