Abstract
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 fibre-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 laminae 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 localized 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.
Highlights
A third-order ZZ version of the model derived in §2 denoted by HR3-refined ZZ theory (RZT) is used from hereon to study boundary layer effects at clamped edges of constant-stiffness laminates
This work demonstrates that the proposed higher-order model derived from the Hellinger– Reissner mixed variational principle accurately predicts local variations in the 3D stresses towards clamped edges
The observed boundary layer effects arise due to local variations in the higher-order stress resultants
Summary
Composite laminates are typically modelled as thin plates and shells because the thickness dimension t is at least an order of magnitude smaller than representative in-plane dimensions Lx and Ly. & Vidoli [21] and Batra et al [22], one of the major advantages of using the HR principle is that independent assumptions of stress and displacement fields allow prescribed traction conditions to be satisfied exactly This means that boundary layer effects and localized stress gradients towards boundaries can be captured accurately. The use of a spectral Chebychev–Gauss–Lobatto grid biases the collocation points towards the boundaries and eliminates oscillations in the numerical solution that occur for spaced grids (the Runge effect) These particular features of the spectral mesh, coupled with strong-form solutions of the governing equations at each collocation point, allow accurate representations of the steep stress gradients towards clamped edges.
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