Buckling analysis and optimisation of variable angle tow composite plates

Wu, Zhang Ming; Weaver, Paul M.; Raju, Gangadharan; Kim, Byung Chul

doi:10.1016/j.tws.2012.07.008

Cited by 251 publications

(165 citation statements)

References 29 publications

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“…Numerous works have shown that tailoring the in-plane stiffness of a plate allows prebuckling stresses to be redistributed to supported regions, thereby increasing the critical buckling load [5][6][7][8][9][10][11][12][13]. Specifically, Gürdal et al [6] have shown that varying the stiffness of the panel perpendicular to the direction of applied end compression results in greater improvements than varying the stiffness in the direction of loading.…”

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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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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“…Various studies have shown that fiber variations perpendicular to applied end-compression provide greater improvements in buckling load than fiber variations along the load direction. [5][6][7] This occurs due to the favorable redistribution of prebuckling stresses towards supported edges that do not buckle. Referring to Figure 1 with axial compression applied in the x-direction, such an effect is achieved with fiber variations in the y-direction, requiring φ k = 90…”

Section: Iia Modeling the Variable Thickness Cross-sectionmentioning

confidence: 99%

“…Wu et al 6 used a genetic algorithm (GA) in combination with the Rayleigh-Ritz solution technique. The novelty of Wu's approach is the use of Lagrange polynomials to define the fiber paths based on a finite number of grid points, allowing any order of nonlinear fiber variation to be represented.…”

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confidence: 99%

Mass Optimisation of Variable Angle Tow, Variable Thickness Panels with Static Failure and Buckling Constraints

Groh

2015

56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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By taking advantage of curved fiber paths, Variable Angle Tow (VAT) laminates increase the design space for tailoring the structural behavior of thin-walled aerospace structures. In recent years, advancements in Automated Fiber Placement (AFP) and Continuous Tow Shearing (CTS) have facilitated the manufacture of these laminates. The CTS technique holds the advantage of reducing many of the manufacturing defects characteristic of the AFP process such as fiber wrinkling, tow gaps and tow overlaps, while also allowing for tighter steering radii. On the other hand, the CTS process features added complexity due to the coupling of fiber steering angle with tow thickness. In this study, a minimummass design of a typical aircraft wing panel under end-compression subject to pre-defined manufacturing, static failure and buckling load constraints is sought. The geometric effects of the asymmetric thickness distribution of the CTS panel on the critical buckling loads, postbuckling paths and static failure behavior are captured for the first time. A hybrid optimization scheme that couples a genetic algorithm with a pattern-search algorithm is used to define a VAT laminate that reduces the mass of both square and rectangular aircraft panels by 31% compared to a baseline straight fiber design. The optimization of the fiber paths is driven by two distinct requirements, namely local and global stiffness tailoring that influence the buckling performance and static strength, respectively. Finally, the initial postbuckling behavior of the optimized designs is investigated using Koiter's perturbation approach, which reveals that postbuckling stability should be considered when optimising VAT panels manufactured by the CTS technique.

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“…• Unlike the vast majority of works reported in literature [40], the optimum bres-path for each ply is very general. In the framework of the proposed approach, the point- linear or parabolic variations (with respect to laminate global frame) as in [40], rather it is described by a general B-spline surface, see Eq.…”

mentioning

confidence: 99%

“…In the framework of the proposed approach, the point- linear or parabolic variations (with respect to laminate global frame) as in [40], rather it is described by a general B-spline surface, see Eq. (12).…”

mentioning

confidence: 99%