Effect of bending-twisting coupling on the compression and shear buckling strength of infinitely long plates

doi:10.1016/j.compstruct.2017.09.085

Composite Structures

Volume 184, 15 January 2018, Pages 18-29

https://doi.org/10.1016/j.compstruct.2017.09.085 Get rights and content

Abstract

This article describes the development of closed form polynomial equations for compression and shear buckling to assess the effect of Bending-Twisting coupling on infinitely long laminated plates with simply supported edges. The equations are used to generate contour maps, representing non-dimensional buckling factors, which are superimposed on the lamination parameter design spaces for laminates with standard ply orientations. The contour maps are applicable to two recently developed databases containing symmetric and non-symmetric laminates with either Bending-Twisting or Extension-Shearing Bending-Twisting coupling. The contour maps provide new insights into buckling performance improvements that are non-intuitive and facilitate comparison between hypothetical and practical designs. The databases are illustrated through point clouds of lamination parameter coordinates, which demonstrate the effect of applying common design heuristics, including ply angle, ply percentage and ply contiguity constraints.

Introduction

The effect of Bending-Twisting coupling continues to be ignored in studies relating to the buckling performance of plate or panel structures, which is broadly justified on the basis that the effects dissipate for laminates with a large number of plies. However, there is a significant body of research demonstrating that compression buckling strength may be overestimated (unsafe) and shear buckling strength may be overestimated or underestimated (over-designed) if the effects of Bending-Twisting coupling are ignored.

In this study, the effect of Bending-Twisting coupling on infinitely long laminated plates with simply supported edges is investigated, which complements an extensive literature on the subject, where the focus is primarily on finite length plates.

The relative buckling performance of adopting non-symmetric laminate designs is also revealed. With very few exceptions, the study of Bending-Twisting coupling effects has focussed entirely on symmetric designs.

Recent research has led to laminate design databases containing Extension-Shearing [1] and/or Bending-Twisting coupling [2]. The results have demonstrated that the design spaces contain predominantly non-symmetric stacking sequences. All are immune to thermal warping distortions by virtue of the fact that their coupling stiffness properties are null (B = 0), as would be expected from symmetric laminate configurations. Heuristic design rules [3] are now applied to these databases to assess the effect on optimum buckling performance of practical rather than hypothetical designs. The reduction in the design space is readily quantified through graphical representation of the lamination parameter design space.

New insights into compression and shear buckling strength are provided via buckling factor contour maps, which are superimposed onto the lamination parameter design spaces. Contour mapping is applied to cross-sections through the design space, to allow detailed interrogation of the effects of Bending-Twisting coupling on buckling strength. The mapping is also applied to external surfaces of the feasible domain of lamination parameters, since these surfaces represent the bounds on buckling strength. The results are applicable to infinitely long plates with simply supported edges, which represent useful lower-bound solutions for preliminary design optimisation.

Notable contributions addressing infinitely long plates [4], [5] adopted non-dimensional parameters, which differ from the lamination parameters used here. More importantly however, the buckling factor results presented were normalised by a bending stiffness parameter, which varies across the designs space, hence buckling performance is not directly comparable. Early studies on finite length plates have also adopted these non-dimensional parameters [6], as have the most recent studies [7], but a separate body of work has adopted lamination parameters [8], [9], [10] to aid optimum design. Comparisons with the infinitely long plate results of this study are therefore possible only for aspect ratios that correspond to the asymptotic result.

Section snippets

Design space interrogation

Ply angle dependent lamination parameters allow the stiffness terms to be expressed as linear variables within convenient bounds. However, the optimized lamination parameters must be matched to a corresponding laminate configuration within the feasible region, which is aided here by graphical representation of the lamination parameter design spaces [1], [2]. In practical design however, heuristic rules are commonly applied, which generally involve constraints on ply percentages, ply contiguity

Buckling of infinitely long plates

Bounds on the buckling performance of (infinitely) long, simply supported, ‘symmetric’ Bending-Twisting coupled laminates have been extensively investigated under both compression [6] and/or shear [4]. Hence, in view of the significant number of non-symmetric and other forms of sub-sequence symmetry recently identified [1], [2], which result in a vast increase in the possible design space for Bending-Twisting coupled laminate designs, the possibility of additional gains in buckling performance,

Conclusions

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The impact of the 10% rule on reducing the lamination parameter design space for extensional stiffness has been shown to be similar for both symmetric and non-symmetric designs, with standard ply orientations and up to 18 plies.
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The reduced design space, resulting from the application of the 10% rule, has been shown to virtually match to the application of the common design constraint of limiting the number of contiguous plies, i.e. adjacent plies with the same orientation, to a maximum of 3.
•
No

Acknowledgements

The Newton Research Collaboration Programme (NRCP1516/4/50) and CNPq (574004/2008-4) are gratefully acknowledged for supporting this research.

References (14)

C.B. York et al.
On extension-shearing bending-twisting coupled laminates
Compos Struct
(2017)
C.B. York
On bending-twisting coupled laminates
Compos Struct
(2017)
A. Baucke et al.
Closed-form analysis of the buckling loads of composite laminates under uniaxial compressive load explicitly accounting for bending–twisting-coupling
Compos Struct
(2015)
H. Fukunaga et al.
Buckling design of symmetrically laminated plates using lamination parameters
Comput Struct
(1995)
Bailie JA, Ley RP, Pasricha A. A summary and review of composite laminate design guidelines. Task 22, NASA Contract...
M.P. Nemeth
Buckling of symmetrically laminated plates with compression, shear, and in-plane bending
AIAA J
(1992)
J.E. Herencia et al.
Closed-form solutions for buckling of long anisotropic plates with various boundary conditions under axial compression
J Eng Mech
(2010)

There are more references available in the full text version of this article.

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Effect of bending-twisting coupling on the compression and shear buckling strength of infinitely long plates

Abstract

Introduction

Section snippets

Design space interrogation

Buckling of infinitely long plates

Conclusions

Acknowledgements

Compos Struct

Compos Struct

Compos Struct

Comput Struct

Buckling of symmetrically laminated plates with compression, shear, and in-plane bending

AIAA J

Closed-form solutions for buckling of long anisotropic plates with various boundary conditions under axial compression

J Eng Mech