Buckling analysis and optimization of blade stiffened variable stiffness panels

Coburn, Broderick H.; Wu, Zhangming

doi:10.2514/6.2015-1438

Cited by 18 publications

(22 citation statements)

References 28 publications

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“…This work shows that non-intuitive localized stress fields can also occur in tow-steered laminates remote from any boundaries. The significance of this finding is twofold (i) Optimization studies on tow-steered laminates have predominantly focused on improving the structural stability of plates [44–46], shells [47] and stiffened panels [48]. The fibre paths are tailored to redistribute in-plane stresses over the planform to preempt the onset of buckling.…”

Section: Resultsmentioning

confidence: 99%

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

Groh¹

2016

Proc. R. Soc. A.

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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 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.

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Section: Resultsmentioning

confidence: 99%

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

Groh¹

2016

Proc. R. Soc. A.

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“…A summary of the required shape function boundary conditions for w, γ xz and γ yz for given edge boundary conditions are provided in Table 1 . The required boundary conditions are implemented through circulation functions applied to the Legendre polynomials ( Coburn and Weaver, 2015;Wu et al, 2012b ) in the form:…”

Section: Shape Functionsmentioning

confidence: 99%

“…Recently, Coburn et al (2014a ); 2014b ) developed an analytical model based on the Ritz energy method for the buckling of stiffened VS panels including a first-order shear deformation theory (FSDT) to enable the study of thick laminate sections. Using the model in a follow-up optimisation study ( Coburn and Weaver, 2015 ), it was shown that stiffened VS panels can achieve mass reductions when compared to straight-fibre stiffened panels, albeit to a lesser extent than plates considered in isolation IJsselmuiden et al, 2010;Olmedo and Gürdal, 1993;Wu et al, 2012b ).…”

Section: Introductionmentioning

confidence: 96%

“…However, recent advancements of automated fibre placement (AFP) and tape laying technologies have led to the possibility of steering fibres in the plane of a ply, thus creating variable-stiffness laminates and significantly increasing the design space available to engineers. In recent times, performance benefits of VS laminates have been shown for: the buckling and post-buckling of plates ( Groh et al, 2013;IJsselmuiden et al, 2010;Olmedo and Gürdal, 1993;Raju et al, 2015;Weaver et al, 2009;Wu et al, 2013;2012b ), shells ( White et al, 2014 ) and stiffened panels ( Coburn and Weaver, 2015;Coburn et al, 2014a;2014b ); the stress distribution around discontinuities ( Hyer and Lee, 1991;Khani et al, 2011 ); * Corresponding author. Tel.…”

Section: Introductionmentioning

confidence: 98%

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Buckling analysis, design and optimisation of variable-stiffness sandwich panels

Coburn

Weaver

2016

International Journal of Solids and Structures

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a b s t r a c tIn recent years variable-stiffness (VS) technology has been shown to offer significant potential weight savings and/or performance gains for both monolithic and stiffened plate structures when buckling is a driving consideration. As yet, little work has been reported on VS sandwich structures. As such, a semianalytical model is developed based on the Ritz energy method for the buckling of sandwich panels with fibre-steered VS face-sheets. The model captures both global and shear crimping instabilities and is shown to explain both types of buckling responses observed and the mode switching between them. Quantitative agreement with detailed three-dimensional finite element analysis was found to be within 13% . Subsequent parametric and optimisation studies, which were performed for many practical geometries using the developed model, reveal that, whilst VS sandwich panels show a significant improvement in global buckling performance, they suffer a reduction in shear crimping performance when compared to their straight-fibre counterparts. This behaviour is found to be due to the VS face-sheets creating a pre-buckling load redistribution where regions locally exceed the critical shear crimping load and induce the short wavelength instability at a reduced panel level load. For VS sandwich panels with modest to low transverse shear moduli of the core, shear crimping can become the critical mode diminishing performance benefits relative to straight-fibre configurations. Cores with sufficient rigidity, thus preventing shear crimping, showed improvements in critical buckling load in the order of 80% when using VS, however this improvement reduces to a negligible amount with decreasing core transverse shear moduli. The transverse shear flexibility and load redistribution are thus two key parameters that must be considered carefully in the design of sandwich panels, in order to exploit the benefits of VS fully in this novel structural configuration.

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“…In further work, Akhavan and Ribeiro [24] extended the vibrational analysis into the nonlinear regime using a first-order model. Coburn et al [25,26] accounted for the effect of transverse shear deformation on the buckling behaviour of tow-steered, blade-stiffened wing panels. Akbarzadeh et al [27] studied the effects of transverse shear deformation on the vibrational and buckling response of moderately thick AFP panels with gaps and overlaps using a Reddy-type third-order shear deformable theory.…”

Section: Variable-stiffness Laminated Compositesmentioning

confidence: 99%

A computationally efficient 2D model for inherently equilibrated 3D stress predictions in heterogeneous laminated plates. Part II: Model validation

Groh

2016

Composite Structures

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. AbstractThe higher-order, equivalent single-layer model developed in Part I is applied to the stretching and bending of exemplar multilayered flat plates, where the results are compared with different 3D models, and trends and insights are subsequently drawn. The present mixed displacement/stress-based model is derived from inherently equilibrated 3D stress fields that satisfy the interlaminar and surface traction equilibrium conditions. A new set of governing equations is derived from a contracted Hellinger-Reissner functional that only enforces the classical membrane and bending equations via Lagrange multipliers. Combined with the fact that the same set of stress resultants is used for all stress fields, the number of unknown variables of the theory reduces, while maintaining sufficient fidelity to capture higher-order transverse shearing and zig-zag effects. A wide range of stacking sequences are considered ranging from orthotropic straight-fibre laminates to sandwich panels with variable-stiffness face sheets, i.e. composite plies in which the reinforcing fibres describe curvilinear paths. Hence, the model is used to study laminated plates with 3D heterogeneity, that is laminates comprising layers with material properties that can differ by multiple orders of magnitude and that vary continuously in-plane. The governing equations are solved both analytically using trigonometric expansions and numerically using the pseudo-spectral differential quadrature method. The 3D stress fields predictions correlate closely with 3D elasticity and 3D finite element solutions and are accurate to within a few percent for thick plates with characteristic length to thickness ratios as small as 5:1. In fact, the results suggest that 3D stress fields from our model satisfy Cauchy's 3D equilibrium equations more accurately, and at a three-order degree of freedom reduction in computational cost, compared to high-fidelity 3D FEM models.

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Buckling analysis and optimization of blade stiffened variable stiffness panels

Cited by 18 publications

References 28 publications

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

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

Buckling analysis, design and optimisation of variable-stiffness sandwich panels

A computationally efficient 2D model for inherently equilibrated 3D stress predictions in heterogeneous laminated plates. Part II: Model validation

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