Shells, laminated

Work on analysis of the common structural shell element made of composite materials is very extensive. Contributions will be mentioned that parallel the developments in Chapter 5 on plates. Some of the first analyses of laminated shells are by Dong, Pister, and Taylor [6-44] and the monograph by Ambartsumyan [6-36]. Further efforts include the buckling work on laminated shells by Cheng and Ho [6-45] and on eccentrically stiffened laminated shells by Jones [6-46]. 

Classical solutions to laminated shell buckling and vibration problems in the manner of Chapter 5 were obtained by Jones and Morgan [6-47]. Their results are presented as normalized buckling loads or fundamental natural frequency versus the Batdorf shell curvature parameter. They showed that, for antisymmetrically laminated cross-ply shells as for plates, the effect of coupling between bending and extension on buckling loads and vibration frequencies dies out rapidly as the number of layers... 

Many composite stractures can be described and analysed as thin laminated shells or plates composed of several laminae stacked sequentially, each aligned at a specific angle with respect to a material reference axis, by convention the jc-axis. Classical lamination theory is quite suitable for analysing thin laminated plates or any thin laminated shell that can be reduced to an equivalent plate. 

From the mechanical point of view, the theory developed so far allows for the consideration of adaptive laminated shells subjected to arbitrary loads and strains within the framework of Remarks 6.1 to 6.6. For many applications, such a level of generality is not necessary as particular knowledge with respect to mission and design may be used to imposed simplifying assumptions. 

Another possibility to reduce the number of components in the constitutive relation of adaptive laminated shells is to employ the extended Dirichlet s principle of minimum potential energy derived in Section 3.5.1. 

With the preceding constitutive modeling, the associated electroelastic energy density ZYo, see Eq. (3.65), may now be given for adaptive laminated shells as... 

Inspection of laminate and joints between the shells and the two inner beams on each side. 

Water-borne adhesives are preferred because of restrictions on the use of solvents. Low viscosity prepolymers are emulsified in water, followed by chain extension with water-soluble glycols or diamines. As cross-linker PMDI can be used, which has a shelf life of 5 to 6 h in water. Water-borne polyurethane coatings are used for vacuum forming of PVC sheeting to ABS shells in automotive interior door panels, for the lamination of ABS/PVC film to treated polypropylene foam for use in automotive instmment panels, as metal primers for steering wheels, in flexible packaging lamination, as shoe sole adhesive, and as tie coats for polyurethane-coated fabrics. PMDI is also used as a binder for reconstituted wood products and as a foundry core binder. 

Two resin systems based on this chemical concept are commercially available from Shell Chemical Company/Technochemie under the COMPIMIDE trademark COMPIMIDE 183 (34) [98723-11-2], for use in printed circuit boards, and COMPIMIDE 796 [106856-59-1], as a resin for low pressure autoclave mol ding (35). Typical properties of COMPIMIDE 183 glass fabric—PCB laminates are provided in Table 8. COMPIMIDE 183 offers a combination of advantageous properties, such as a high glass transition temperature, low expansion coefficient, and flame resistance without bromine compound additives. 

Tubercles consisted of hard, hlack oxide shells overlaid with friable carbonate-containing deposits. In places, several laminate black magnetite shells existed. The outer crust could be crushed by gentle pressure with a finger. Tubercles were riddled with white crystalline fibers. Other detritus was incorporated into the tubercle core and crust. Metal loss was less than 0.030 in. (0.076 cm) below each tubercle. Wall thickness was almost 0.25 in. (0.64 cm). 

The two estimates, if plotted, look as shown in Fig. 6.4. This explains why fibre-reinforced composites like wood and GFRP are so stiff along the reinforced direction (the upper line of the figure) and yet so floppy at right angles to the direction of reinforcement (the lower line), that is, it explains their anisotropy. Anisotropy is sometimes what you want - as in the shaft of a squash racquet or a vaulting pole. Sometimes it is not, and then the layers of fibres can be laminated in a criss-cross way, as they are in the body shell of a Formula 1 racing car. 

Domestic and commercial furniture and fittings form another important market. Uses include stacking chairs, armchair body shells, foam upholstery and desk and cupboard drawers, whilst chipboard and decorative laminates are very widely used. The variety of finishes possible at a relatively low cost compared to traditional materials as well as ease of maintenance are important in raising standards of living around the world. As with other applications the use of plastics in furniture is not without its detractors and in particular there is concern... 

Adhesives based on isocyanate (especially PMDl, polymethylene diisocyanate, more exactly polymeric 4,4 -diphenylmethane diisocyanate) have been used for more than 25 years in the wood-based panel industry [88], but still have a low market value in the wood-working industry compared to systems based on UF-, MUF- or PF-resins. The main application is the production of waterproof panels, but also the production of panels from raw materials that are difficult to glue, like straw, bagasse, rice shells or sugar cane bagasse. They can be used as adhesives for wood-based products like particleboard, oriented strandboard (OSB), laminated strand lumber (LSL), medium-density fiberboard (MDF) or... 

The Mosquito was a laminated wood monocoque design that although unusual, was not new. More uniquely, the monocoque shell was fabricated by gluing plywood skins to balsa wood core. This construction foreshadowed the popular honeycomb core/facesheet aluminum and composite designs of later years. Fuselage halves of the Mosquito were formed in closed wooden female tools (tools... 

A laminate is a bonded stack of laminae with various orientations of principal material directions in the laminae as in Figure 1-9. Note that the fiber orientation of the layers in Figure 1-9 is not symmetric about the middle surface of the laminate. The layers of a laminate are usually bonded together by the same matrix material that is used in the individual laminae. That is, some of the matrix material in a lamina coats the surfaces of a lamina and is used to bond the lamina to its adjacent laminae without the addition of more matrix material. Laminates can be composed of plates of different materials or, in the present context, layers of fiber-reinforced laminae. A laminated circular cylindrical shell can be constructed by winding resin-coated fibers on a removable core structure called a mandrel first with one orientation to the shell axis, then another, and so on until the desired thickness is achieved. 

Stiffnesses for single-layered configurations are treated first to provide a baseline for subsequent discussion. Such stiffnesses should be recognizable in terms of concepts previously encountered by the reader in his study of plates and shells. Next, laminates that are symmetric about their middle surface are discussed and classified. Then, laminates with laminae that are antisymmetrically arranged about their middle surface are described. Finally, laminates with complete lack of middle-surface symmetry, i.e., unsymmetric laminates, are discussed. For all laminates, the question of laminae thicknesses arises. Regular laminates have equal-thickness laminae, and irregular laminates have non-equal-thickness laminae. 

For plate problems, whether the specially orthotropic laminate has a single layer or multiple layers is essentially immaterial the laminate need only be characterized by 0 2, D22. and Dgg in Equation (5.2). That is, because there is no bending-extension coupling, the force-strain relations, Equation (5.1), are not used in plate analysis for transverse loading causing only bending. However, note that force-strain relations are needed in shell analysis because of the differences between deformation characteristics of plates as opposed to shells. 

Robert M. Jones and Jose C. F. Hennemann, Effect of Prebuckling Deformations on Buckling of Laminated Composite Circular Cylindrical Shells, AIM Journal, January 1980, pp. 110-115. 

Whitney and Pagano [6-32] extended Yang, Norris, and Stavsky s work [6-33] to the treatment of coupling between bending and extension. Whitney uses a higher order stress theory to obtain improved predictions of a, and and displacements at low width-to-thickness ratios [6-34], Meissner used his variational theorem to derive a consistent set of equations for inclusion of transverse shearing deformation effects in symmetrically laminated plates [6-35]. Finally, Ambartsumyan extended his treatment of transverse shearing deformation effects from plates to shells [6-36]. 

S. B. Dong, K. S. Rster, and R. L. Taylor, On the Theory of Laminated Anisotropic Shells and Rates, Journal of Aerospace Sciences, August 1962, pp. 969-975. 

Robert M. Jones and Harold S. Morgem, Buckling and Vibration of Cross-Ry Laminated Circular Cylindrical Shells, AIAA Journal, May 1975, pp. 664-671. 

Experiments made at higher degrees of aggregation have provided strong evidence192 for ring-like structures for mixed neutral clusters. For example, under a wide variety of experimental conditions, mixed cluster ions display a maximum intensity atm = 2(n + 1) whenn<5 for (NH3)II (M)mH+, andm = n + 2 whenn<4 for (H20)B(M)mH+ M is a proton acceptor such as acetone, pyridine, and trimethy-lamine. These findings reveal that the cluster ions with these compositions have stable solvation shell structures as discussed above. 

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