Buckling and postbuckling of variable angle tow composite plates under in-plane shear loading

Raju, Gangadharan; Wu, Zhang Ming; Weaver, Paul M.

doi:10.1016/j.ijsolstr.2015.01.011

Cited by 64 publications

(29 citation statements)

References 22 publications

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“…In [17], the difference in the postbuckling behavior in case of positive and negative shear loading of VAT plates is demonstrated and discussed.…”

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confidence: 99%

Lay-Up Optimality Conditions for Stiffness Maximization of Anisotropic Composite Plates in Postbuckling

Selyugin¹

2019

Preprint

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The present paper deals with the optimization of post-buckled composite plates. The plates have a symmetric lay-up. The layer orientation angles vary in the point-wise or in the platewise ways. The von Karman theory is employed. The boundary conditions are the simple support ones or the clamped ones. The structural potential energy is treated as a measure of structural stiffness. For the plate stiffness maximization problem, the first-order necessary conditions of the local optimality are derived. The mathematical treatment of the conditions is performed. The conditions contain two terms. One of them corresponds to the mid-plane strains; another one corresponds to the plate curvatures. The optimality conditions may lead to a co-axiality of some structural tensors. An illustration of the optimality conditions is presented.-2 - INTRODUCTIONPostbuckling of thin composite plates attracts the attention of numerous researchers, working in various modern application areas. Among these applications, there are the aerospace, the automotive, the marine, and the civil ones. According to design practice in composite structures, the account of the load-carrying capability "above buckling" gives an opportunity of extra weight saving, as compared to existing traditional design.Composite plates are a part of a considerable number of structures in the above applications. The loading applied to the plates is a combination of compression and shear. The compression dominates for the structures similar to the upper panels of an airplane wing structure. As the examples of known structures designed for pure shear, one may indicate airplane wing ribs and spars, as well as some fuselage panels. As a rule, the shear-loaded plates have the so-called angle-ply symmetric lay-up. For example, buckling is not allowed in airplane structures in the case of loading up to the so-called limit loads (LL) and may be allowed for the loading level between the limit loads and the so-called ultimate loads (UL).The latter loads are 1.5 times higher than the limit loads.When optimizing the composite plate, an engineer, in fact, does his best to save the structural weight, the material cost, and the production time. Due to that, the optimization problems for the composite plates attract considerable attention at the design phase. The layup optimization problem is one of them requiring a solution at the beginning of the design process. Since the last decade of the previous century, numerous papers dealt with the lay-up optimization of composite plates. The non-exhaustive list [1]-[22] contains the important publications devoted to the postbuckling analysis and optimization. The foundations of the postbuckling theory are described in [23].

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“…In [17], the difference in the postbuckling behavior in case of positive and negative shear loading of VAT plates is demonstrated and discussed.…”

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confidence: 99%

Lay-Up Optimality Conditions for Stiffness Maximization of Anisotropic Composite Plates in Postbuckling

Selyugin¹

2019

Preprint

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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%

“…(13), and that are sufficiently general to solve the boundary value problem depicted in Figure 2, are given by…”

Section: Model Implementationmentioning

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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“…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: 99%

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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Buckling and postbuckling of variable angle tow composite plates under in-plane shear loading

Cited by 64 publications

References 22 publications

Lay-Up Optimality Conditions for Stiffness Maximization of Anisotropic Composite Plates in Postbuckling

Lay-Up Optimality Conditions for Stiffness Maximization of Anisotropic Composite Plates in Postbuckling

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

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

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