Classical laminate plate theory

Actually, because of the stress and deformation hypotheses that are an inseparable part of classical lamination theory, a more correct name would be classical thin lamination theory, or even classical laminated plate theory. We wiiruS ffi bmmon term classical lamination theory, but recognize that it is a convenient oversimplification of the rigorous nomenclature. In the composite materials literature, classical laminationtheoryls en abbreviated as CLT. 

CLPT classical laminate plate theory CPET chlorinated polyethylene terephthalate... 

Alternatively, tests can be used to obtain the basic stiffness properties of the material form and their corresponding range measured by some statistical property such as the standard deviation. In two-dimensional cases where there are no significant loads in the out-of-plane direction, the basic orthotropic stiffness properties in Eqn (6.1) can be measured experimentally. Then, the classical laminated plate theory described in previous sections for determination of stiffness can be used effectively to model these sttuctures. Alternatively, the four basic stiffiiesses for 3-D woven composites can be... 

However, especially for three-dimensional stmcture, or, even, in two-dimensional stmcture with significant out-of-plane loads, the stiffness averaging of the classical laminated plate theory is not sufficient. In such cases, a specialized finite element model such as the binary model by Cox, Carter, and Fleck [25] can be used. In this model, Monte Carlo simulation allows the user to randomly orient tows and to randomly assign strength properties to the different components. 

Once the new matrix properties accounting for porosity are known, the ply-level stiffnesses can be determined using micromechanics, and then the classical laminated plate theory outlined in previous sections can be used. 

For the case of an orthotropic laminate under conditions of plane stress, which can be assumed when the thickness of a laminate ply is small compared to its length and width, the stress in each constituent ply of a laminate can be determined with the aid of classical laminate plate theory [5-7]. The elastic stress-strain relationship for an orthotropic unidirectional plate then becomes... 

Classical laminated plate tlieoiy is used to determine the stiffness of laminated composites. Details of the Kitchoff-Love hypothesis on which the theory is based can be found in standard texts (1,7,51). Essentially, the strains in each ply of the laminate ate represented as middle surface strains plus... 

The laminated plates discussed in this code are symmetric laminates, there is no extension/bending coupling, hence By=0, and classical thin plate theory can be used. Membrane action is not considered. 

From a fundamental imderstanding of the mechanics of winding fibers onto a cylinder, it is possible to predict, nsing micromechanics and the classical composite laminate plate theory, the effective elastic properties of the finished filament wormd catheter/tubing. 

Note that no assumptions involve fiber-reinforced composite materials explicitly. Instead, only the restriction to orthotropic materials at various orientations is significant because we treat the macroscopic behavior of an individual orthotropic (easily extended to anisotropic) lamina. Therefore, what follows is essentially a classical plate theory for laminated materials. Actually, interlaminar stresses cannot be entirely disregarded in laminated plates, but this refinement will not be treated in this book other than what was studied in Section 4.6. Transverse shear effects away from the edges will be addressed briefly in Section 6.6. 

The preceding subsection was devoted to a comparison of a special exact elasticity solution with classical lamination theory results. The importance of transverse shear effects was clearly demonstrated. However, that demonstration was for a special problem of rather narrow interest. The objective of this subsection is to display approaches and results for the approximate consideration of transverse shear effects for general laminated plates. 

The treatment of transverse shear stress effects in plates made of isotropic materials stems from the classical papers by Reissner [6-26] and Mindlin [6-27. Extension of Reissner s theory to plates made of orthotropic materials is due to Girkmann and Beer [6-28], Ambartsumyan [6-29] treated symmetrically laminated plates with orthotropic laminae having their principal material directions aligned with the plate axes. Whitney [6-30] extended Ambartsumyan s analysis to symmetrically laminated plates with orthotropic laminae of arbitrary orientation. 

However, these transverse shearing stresses were neglected implicitly when we adopted the Kirchhoff hypothesis of lines that were normal to the undeformed middle surface remaining normal after deformation in Section 4.2.2 on classical lamination theory. That hypothesis is interpreted to mean that transverse shearing strains are zero, and, hence, by the stress-strain relations, the transverse shearing stresses are zero. The Kirchhoff hypothesis was also adopted as part of classical plate theory in Section 5.2.1. 

Laminate plate and shell stiffness classical lamination theory (CLT)... 

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. 

The classical lamination theory was then briefly presented. This is an analytical tool suitable for modelling thin laminated plates in an effective way. Laminate examples were given to illustrate the dependence of in-plane and flexural engineering constants on direction. 

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