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Design Optimisation of Lower-Bound Buckling Capacities for FRP-Laminated Cylindrical Shells  [PDF]
Hongtao Wang,James G. A. Croll
ISRN Mechanical Engineering , 2012, DOI: 10.5402/2012/636898
Abstract: The imperfection sensitive buckling loads of fibre reinforced polymeric (FRP) composite cylindrical shells under axial compression can be optimised with respect to many material and geometric parameters. Current approaches, using mathematical algorithms to optimise the linearised classical critical loads with respect to many design variables, generally ignore the potential reductions in elastic load carrying capacities that result from the severe sensitivities of buckling loads to the effects of initial imperfections. This paper applies a lower-bound design philosophy called the reduced stiffness method (RSM) to the optimisation design of FRP shell buckling. A physical optimisation in terms of parametric studies is carried out for simply supported, 6-ply symmetric, glass-epoxy circular cylindrical shells under uniform axial load. It is shown that under the guidance of RSM, safe lower-bound buckling loads can be enhanced greatly by choosing appropriate combinations of design parameters. It is demonstrated how this approach encourages the delineation of those components of the shell’s membrane and bending stiffness that are important and those that are unimportant within each of the prospective buckling modes. On this basis, it is argued that the RSM provides not only a safe but also a more rational strategy for better design decision making. 1. Introduction Due to their high strength-to-stiffness and strength-to-weight ratios, fibre-reinforced-polymeric- (FRP-) laminated shells are widely used in the weight sensitive industries such as aerospace, automobile, and offshore engineering. For thin FRP-laminated shells, the typically low elastic stiffness-to-strength ratios result in the elastic buckling playing a greater role in the design process compared with equivalent metallic structures. Relative to conventional metallic shells, the buckling capacities of FRP laminated shells will depend upon a much larger number of additional design variables, such as fibre distribution and orientation, lamina stacking sequence and thickness, and material selections. Identifying optimum design choices is consequently a more complex problem than for metallic shells. Current approaches [1–5] to the problem share a methodology based upon mathematical optimisation algorithms seeking the maximum linear classical critical loads of perfect FRP-laminated shells with respect to many design parameters. These approaches have inherent defects. Firstly they heavily rely on immense mathematical and computational efforts. Secondly they usually leave basic understanding of the
Buckling Analysis of Laminated Composite Panel with Elliptical Cutout Subject to Axial Compression  [PDF]
Hamidreza Allahbakhsh,Ali Dadrasi
Modelling and Simulation in Engineering , 2012, DOI: 10.1155/2012/171953
Abstract: A buckling analysis has been carried out to investigate the response of laminated composite cylindrical panel with an elliptical cutout subject to axial loading. The numerical analysis was performed using the Abaqus finite-element software. The effect of the location and size of the cutout and also the composite ply angle on the buckling load of laminated composite cylindrical panel is investigated. Finally, simple equations, in the form of a buckling load reduction factor, were presented by using the least square regression method. The results give useful information into designing a laminated composite cylindrical panel, which can be used to improve the load capacity of cylindrical panels. 1. Introduction Laminated composite shells are widely used in many industrial structures including automotive and aviation due to their lower weights compared to metal structures [1]. Many of these shell structures have cutouts or openings that serve as doors, windows, or access ports, and these cutouts or openings often require some type of reinforcing structure to control local structural deformations and stresses near the cutout. In addition, these structures may experience compression loads during operation, and thus their buckling response characteristics must be understood and accurately predicted in order to determine effective designs and safe operating conditions for these structures. For predicting the buckling load and buckling mode of a structure in the finite-element program, the linear (or eigenvalue) buckling analysis is an existing technique for estimation [2]. In general, the analysis of composite laminated shell is more complicated than the analysis of homogeneous isotropic ones [3]. In the literature, many published studies investigated the buckling of laminated composite plates with a cutout [4–10]. Few studies are available on buckling of composite panel. Kim and Noor [11] studied the buckling and postbuckling responses of composite panels with central circular cutouts subjected to various combinations of mechanical and thermal loads. They investigated the effect of variations in the hole diameter; the aspect ratio of the panel; the laminate stacking sequence; the fiber orientation on the stability boundary; postbuckling response and sensitivity coefficients. Mallela and Upadhyay [12] presented some parametric studies on simply supported laminated composite panels subjected to in-plane shear loading. They analyzed many models using ANSYS, and a database was prepared for different plate and stiffener combinations. Studies are carried out by
Review of Recent Literature on Static Analyses of Composite Shells: 2000-2010  [PDF]
Mohammad S. Qatu, Ebrahim Asadi, Wenchao Wang
Open Journal of Composite Materials (OJCM) , 2012, DOI: 10.4236/ojcm.2012.23009
Abstract: Laminated composite shells are frequently used in various engineering applications including aerospace, mechanical, marine, and automotive engineering. This article reviews the recent literature on the static analysis of composite shells. It follows up with the previous work published by the first author [1-4] and it is a continuation of another recent article that focused on the dynamics of composite shells [3]. This paper reviews most of the research done in recent years (2000-2010) on the static and buckling behavior (including postbuckling) of composite shells. This review is conducted with an emphasis on the analysis performed (static, buckling, postbuckling, and others), complicating effects in both material (e.g. piezoelectric) and structure (e.g. stiffened shells), and the various shell geometries (cylindrical, conical, spherical and others). Attention is also given to the theory being applied (thin, thick, 3D, nonlinear …). However, more details regarding the theories have been described in previous work [1,3].
Scaling instability of the buckling load in axially compressed circular cylindrical shells  [PDF]
Yury Grabovsky,Davit Harutyunyan
Mathematics , 2014, DOI: 10.1007/s00332-015-9270-9
Abstract: In this paper we initiate a program of rigorous analytical investigation of the paradoxical buckling behavior of circular cylindrical shells under axial compression. This is done by the development and systematic application of general theory of "near-flip" buckling of 3D slender bodies to cylindrical shells. The theory predicts scaling instability of the buckling load due to imperfections of load. It also suggests a more dramatic scaling instability caused by shape imperfections. The experimentally determined scaling exponent 1.5 of the critical stress as a function of shell thickness appears in our analysis as the scaling of the lower bound on safe loads given by the Korn constant. While the results of this paper fall short of a definitive explanation of the buckling behavior of cylindrical shells, we believe that our approach is capable of providing reliable estimates of the buckling loads of axially compressed cylindrical shells.
Rigorous derivation of the formula for the buckling load in axially compressed circular cylindrical shells  [PDF]
Yury Grabovsky,Davit Harutyunyan
Mathematics , 2014,
Abstract: The goal of this paper is to apply the recently developed theory of buckling of arbitrary slender bodies to a tractable yet non-trivial example of buckling in axially compressed circular cylindrical shells, regarded as three-dimensional hyperelastic bodies. The theory is based on a mathematically rigorous asymptotic analysis of the second variation of 3D, fully nonlinear elastic energy, as the shell's slenderness parameter goes to zero. Our main results are a rigorous proof of the classical formula for buckling load and the explicit expressions for the relative amplitudes of displacement components in single Fourier harmonics buckling modes, whose wave numbers are described by Koiter's circle. This work is also a part of an effort to quantify the sensitivity of the buckling load of axially compressed cylindrical shells to imperfections of load and shape.
The secondary buckling transition: wrinkling of buckled spherical shells  [PDF]
Sebastian Knoche,Jan Kierfeld
Physics , 2014, DOI: 10.1140/epje/i2014-14062-9
Abstract: We theoretically explain the complete sequence of shapes of deflated spherical shells. Decreasing the volume, the shell remains spherical initially, then undergoes the classical buckling instability, where an axisymmetric dimple appears, and, finally, loses its axisymmetry by wrinkles developing in the vicinity of the dimple edge in a secondary buckling transition. We describe the first axisymmetric buckling transition by numerical integration of the complete set of shape equations and an approximate analytic model due to Pogorelov. In the buckled shape, both approaches exhibit a locally compressive hoop stress in a region where experiments and simulations show the development of polygonal wrinkles, along the dimple edge. In a simplified model based on the stability equations of shallow shells, a critical value for the compressive hoop stress is derived, for which the compressed circumferential fibres will buckle out of their circular shape in order to release the compression. By applying this wrinkling criterion to the solutions of the axisymmetric models, we can calculate the critical volume for the secondary buckling transition. Using the Pogorelov approach, we also obtain an analytical expression for the critical volume at the secondary buckling transition: The critical volume difference scales linearly with the bending stiffness, whereas the critical volume reduction at the classical axisymmetric buckling transition scales with the square root of the bending stiffness. These results are confirmed by another stability analysis in the framework of Donnel, Mushtari and Vlasov (DMV) shell theory, and by numerical simulations available in the literature.
Experimental Investigation on the Buckling Process of Water-filled Metal Cylindrical Shells under Axial Impact

LEI Jian-ping,CHENG Guo-qiang,ZHANG Shan-yuan,

实验力学 , 2002,
Abstract: Experimental results for the buckling process of cylindrical shells fully filled with water under axial impact are reported. Low velocity and large mass impact tests are carried out by means of a dropping hammer device. The experiment indicates that the buckling of shells takes place in an axisymmetric mode, and the whole impact process can be divided into three stages, i.e. dynamic loading, dynamic post-buckling and elastic unloading. The effect of the height and thickness of the cylindrical shells on the phenomena is discussed.
Soft modes near the buckling transition of icosahedral shells  [PDF]
M. Widom,J. Lidmar,D. R. Nelson
Physics , 2007, DOI: 10.1103/PhysRevE.76.031911
Abstract: Icosahedral shells undergo a buckling transition as the ratio of Young's modulus to bending stiffness increases. Strong bending stiffness favors smooth, nearly spherical shapes, while weak bending stiffness leads to a sharply faceted icosahedral shape. Based on the phonon spectrum of a simplified mass-and-spring model of the shell, we interpret the transition from smooth to faceted as a soft-mode transition. In contrast to the case of a disclinated planar network where the transition is sharply defined, the mean curvature of the sphere smooths the transitition. We define elastic susceptibilities as the response to forces applied at vertices, edges and faces of an icosahedron. At the soft-mode transition the vertex susceptibility is the largest, but as the shell becomes more faceted the edge and face susceptibilities greatly exceed the vertex susceptibility. Limiting behaviors of the susceptibilities are analyzed and related to the ridge-scaling behavior of elastic sheets. Our results apply to virus capsids, liposomes with crystalline order and other shell-like structures with icosahedral symmetry.
Parametric study on buckling behaviour of thin stainless steel cylindrical shells for circular dent dimensional variations under uniform axial compression
B Prabu, A Raviprakash, N Rathinam
International Journal of Engineering, Science and Technology , 2010,
Abstract: It is well known that thin cylindrical shell structures have wide applications as one of the important structural elements in many engineering fields and its load carrying capacity is decided by its buckling strength which in turn predominantly depends on geometrical imperfections present in it. Geometrical imperfections can be classified as local and distributed geometrical imperfections. But in this work, only local geometrical imperfection namely dent is considered for analysis. The main aim of this study is to determine the more influential dimensional parameter out of two dent dimensional parameters, one is the extent of dent present over a surface area and the other is dent depth, which affect the buckling strength of the cylindrical shells drastically. To account for the parameter “extent of dent present over an area”, the dent is considered as circular dent and its amplitude is considered as dent depth. For this purpose, finite element (FE) models of cylindrical shells with a circular dent at half the height of cylindrical shells having different dent sizes are generated. These FE models are analyzed using ANSYS nonlinear buckling analysis. It is concluded that extent of dent present over an area is more influential than dent depth. To verify this conclusion further, FE models of cylindrical shells with two circular dents at half the height of cylindrical shell placed at 180° apart having different dent sizes are generated and analyzed.
Virus shapes and buckling transitions in spherical shells  [PDF]
Jack Lidmar,Leonid Mirny,David R. Nelson
Quantitative Biology , 2003, DOI: 10.1103/PhysRevE.68.051910
Abstract: We show that the icosahedral packings of protein capsomeres proposed by Caspar and Klug for spherical viruses become unstable to faceting for sufficiently large virus size, in analogy with the buckling instability of disclinations in two-dimensional crystals. Our model, based on the nonlinear physics of thin elastic shells, produces excellent one parameter fits in real space to the full three-dimensional shape of large spherical viruses. The faceted shape depends only on the dimensionless Foppl-von Karman number \gamma=YR^2/\kappa, where Y is the two-dimensional Young's modulus of the protein shell, \kappa is its bending rigidity and R is the mean virus radius. The shape can be parameterized more quantitatively in terms of a spherical harmonic expansion. We also investigate elastic shell theory for extremely large \gamma, 10^3 < \gamma < 10^8, and find results applicable to icosahedral shapes of large vesicles studied with freeze fracture and electron microscopy.
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