Symmetric laminate with specially orthotropic

Table 4-2 Symmetric Laminate with Five Specially Orthotropic Layers...

A very common special case of symmetric laminates with multiple specially orthotropic layers occurs when the laminae are all of the same thickness and material properties, but have their major principal material... 

Often, because specially orthotropic laminates are virtually as easy to analyze as isotropic plates, other laminates are regarded as, or approximated with, specially orthotropic laminates. This approximation will be studied by comparison of results for each type of laminate with and without the various stiffnesses that distinguish it from a specially orthotropic laminate. Specifically, the importance of the bend-twist coupling terms D,g and D26 will be examined for symmetric angle-ply laminates. Then, bending-extension coupling will be analj ed for antisym-... 

Obvious and sometimes drastic simplifications occur when the laminate is symmetric about the middle surface (By = 0), specially orthotropic (all the terms with 16 and 26 subscripts vanisn in addition to the By), homogeneous ( = 0 and Djj = Ayr/12), or isotropic. In all those cases. Equations (5.6) and (5.7) are coupled to each other, but uncoupled from Equation (5.8). That is. Equation (5.8) contains derivatives of the transverse displacement w only, and Equations (5.6) and (5.7) contain both u and V but not w. Accordingly, only Equation (5.8) must be solved to determine the transverse deflections of a plate with the aforementioned... 

Note the presence of the bend-twist coupling stiffnesses in the boundary conditions as well as in the differential et uation. As with the specially orthotropic laminated plate, the simply supported edge boundary condition cannot be further distinguished by the character of the in-plane boundary conditions on u and v because the latter do not appear in any plate problem for a symmetric laminate. 

Thus, the error from ignoring the bend-twist coupiing terms is about 24%, certainly not a negligible error. Hence, the specially orthotropic laminated plate is an unacceptable approximation to a symmetric angle-ply laminated plate. Recognize, however, that Ashton s Rayleigh-Ritz results are also approximate because only a finite number of terms were used in the deflection approximation. Thus, a comparison of his results with an exact solution would lend more confidence to the rejection of the specially orthotropic laminated plate approximation. 

The buckling load will be determined for plates with various laminations specially orthotropic, symmetric angle-ply, antisymmetric cross-ply, and antisymmetric angle-ply. The results for the different lamination types will be compared to find the influence of bend-twist coupling and bending-extension coupling. As with the deflection problems in Section 5.3, different simply supported edge boundary conditions will be used in the several problems addressed for convenience of illustration. 

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