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 ... 

Figure 6-16 Cylindrical Bending of an Infinitely Long Cross-Ply Strip...

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). 

To investigate the effect of passivation layer on the performances of a-Si H TFTs under mechanical stress, we stressed both TFTs by outward cylindrical bending at the radius of curvature R = 5 mm as shown in Fig. 6. Less than R = 4 mm, most of TFTs employing acrylic polymer or SiNx as passivation layer were failed. When the radius of curvature was 5 mm, the strain on the surface of aciyl and SiNx was 0.0082 (0.82 %) and 0.0077 (0.72 %), respectively. Eq. 1 considering single aciyl (3 jtan) or SiNx (substrate-insulation, te-insulation and backchannel passivation 0.9 jtan) layer calculated the strain. 

A hybrid structure which was composed of 50 nm-thick SiNx and 3 jtan-thick acrylic polymer was chosen as passivation layer as shown in the Fig. 10. TFTs were stressed by outward cylindrical bending at the radius of curvature R = 5 mm. Before bending the TFTs, electrical p>erformances measured. The TFTs were stressed for 24 hours. The transfer characteristics of... 

F. Boeykens, L. Vallozzi, H. Rogier, Cylindrical bending of deformable textile rectangular patch antennas, Int. J. Antenn. Propag. (2012) 11. 

To determine the edge loads, it was necessary to calculate the deflection of the adherends and joint area due to the tensile load. Goland and Reissner assumed that the adherends and the joint undergo cylindrical bending. This implies that deflection is not dependent on normal or shear forces but only the bending moment, such that... 

There are other significant features of the behavior illustrated in Figure 2.29. Among these are the axially symmetric response is nonlinear for values of Cm beyond about 0.3, consistent with the behavior observed in Figure 2.20 the maximum deflection at the substrate periphery reaches a value of about two times the substrate thickness before bifurcation occurs the post bifurcation deformation becomes more like cylindrical bending as Cm... 

The rectangular channel is covered by an elastic membrane that is pulled downward due to the negative pressure inside the liquid. This downward deflection can be written as u(x, z). If we make the assumption that, the z-derivatives of u are much smaller than the x-derivatives and that the length of the meniscus is not much larger than the channel width w, then the deflection in the elasticity problem is virtually independent of z and we are left with a quasi one-dimensional problem, the so-called cylindrical bending of a long, rectangular plate. The equation of elasticity for the deflection... 

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