Laminate cylindrical bending

Study of transverse shearing stress effects is divided in two parts. First, some exact elasticity solutions for composite laminates in cylindrical bending are examined. These solutions are limited in their applicability to practical problems but are extremely useful as checl oints for more broadly applicable approximate theories. Second, various approximations for treatment of transverse shearing stresses in plate theory are discussed. 

Pagano studied cylindrical bending of symmetric cross-ply laminated composite plates [6-21]. Each layer is orthotropic and has principal material directions aligned with the plate axes. The plate is infinitely long in the y-direction (see Figure 6-16). When subjected to a transverse load, p(x), that is, p is independent of y, the plate deforms into a cylinder ... 

The results shown in Figure 6-21 for the present shear-deformation approach versus classical lamination theory are quite similar qualitatively to the comparison between the exact cylindrical bending solution and classical lamination theory in Figure 6-17. 

N. J. Pagano, Exact Solutions for Composite Laminates in Cylindrical Bending, Journal of Composite Materials, July 1969, pp. 398-411. 

However, the foregoing derivation is valid only for isotropic beams of rectangular cross section. For beams of nonrectangular cross section, the parabolic stress distribution is not correct. Also, for laminated beams, the parabolic distribution is most assuredly incorrect because of layer inhomogeneity. In fact, for laminated beams, we must expect different shapes of stress distribution in each layer as seen in Figure 6-19 for wide beams (there interpreted as cylindrical bending of a long strip, i.e., a special plate). 

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