Thick laminates terms

Many early FRP marine structures were modelled on those made with traditional materials, but with substantial overdesign. Thick laminates were employed because of caution arising from unfamiliarity with the long term behaviour of the materials. Useful experience has been gained since the late 1950s which makes this caution less necessary nowadays. 

Thus the stiffness matrix for a symmetric laminate may be obtained by adding, in proportion to the ply thickness, the corresponding terms in the stiffness matrix for each of the plies. 

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. 

Start with the general expression for the force per unit width, N, In terms of the middle-surface strains and curvatures to derive the specific expression for for a two-layered, equal-thickness [0 /90°l laminate. Your final expression must be in terms of Qy and t, the laminate thickness. What Is such a laminate called What deformation characteristics does this laminate exhibit when subjected to N., i.e., what does this laminate do ... 

A cross-ply laminate in this section has N unidirectionally reinforced thotropic) layers of the same material with principal material directions srnatingly oriented at 0° and 90° to the laminate coordinate axes. The sr direction of odd-numbered layers is the x-direction of the laminate, e fiber direction of even-numbered layers is then the y-direction of the linate. Consider the special case of odd-numbered layers with equal kness and even-numbered layers also with equal thickness, but not essarily the same thickness as that of the odd-numbered layers, te that we have imposed very special requirements on how the fiber sntations change from layer to layer and on the thicknesses of the ers to define a special subclass of cross-ply laminates. Thus, these linates are termed special cross-ply laminates and will be explored his subsection. More general cross-ply laminates have no such con-ons on fiber orientation and laminae thicknesses. For example, a neral) cross-ply laminate could be described with the specification t/90° 2t/90° 2t/0° t] wherein the fiber orientations do not alter-e and the thicknesses of the odd- or even-numbered layers are not same however, this laminate is clearly a symmetric cross-ply lami-e. 

Interfaces are not only present in blends, but are also a key feature of structural joints, where it is often necessary to produce interfacial strengths comparable with the cohesive strength of the bulk materials, and of laminates, where a more modest degree of adhesion may suffice [166]. The compatibility between different components can be expressed in terms of the equilibrium interfacial thickness, w, given approximately by ... 

Substitution of Eqs. (9) into Eqs. (8) and subsequent differentiation with respect to lead to the equilibrium equations in terms of microstresses and microstrains (i.e. strains averaged across the layer thickness). To exclude the latter, constitutive equations for the damaged layer and the outer sublaminate, equations of the global equilibrium of the laminate as well as generalised plane strain conditions are employed. Finally, a system of coupled second order non-homogeneous ordinary differential equations is obtained... 

Laminar Consists of sheets of laminated carbonate, in which the laminae are on a millimetre-scale. The term is synonymous with soilstone crust . Some forms are dark in colour. They commonly occur capping hardpan layers but can also occur within chalky layers or in the host sediment or soil. They can be interlayered with pisolitic calcretes on a centimetre-scale. Most are only a few centimetres thick but some forms can reach 2 m and can be... 

Note that because AT is assumed negative and ox is typically less that m, the stress in the oxide is typically negative. For the case of a thin oxide on only one side of a thick metal substrate, it may still be reasonable to assume no bending deformation of the oxide-metal laminate. In such cases, the Equation (5.35) can be used if the factor of 2 in the last term of the denominator is removed. In cases where the oxide is very thin relative to the thickness of the metal, the last term in the denominator of Equation (5.35) can be neglected, yielding Equation (5.36),... 

Two layers were used in this example (more layers can be used as discussed in the invention). The bottom reflecting layer s properties determine performance of the laminate in terms of back surface temperature and solar radiation reflectance. Also, the ratio of thickness of both layers affects properties. 

Note that both short and continuous fibers are handled in the same manner. These calculations, while tedious, are analytically simple. The plane stress , the Qy terms, are employed because lamination neglects the mechanical properties through the ply thickness. These stiffnesses are sometimes regrouped into new constants called invariants , the Uj terms, for analytical simplicity. To compute the properties of the laminate one then sums the ply (hj ) properties through the thickness of the laminate, weighted by the thickness (h ) of each oriented ply... 

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