Exact Solutions for Cylindrical Bending

the plate is in a state of generalized plane strain in the x-z plane. 

Pagano s exact solution for the stresses and displacements is too complex to present here. The corresponding classical lamination theory result stems from the equilibrium equations, Equations (5.6) to (5.8), which simplify to 

Even though in classical lamination theory by virtue of the Kirchhoff hypothesis we assume the stresses and are zero, we can still obtain these stresses approximately by integration of the stress equilibrium equations 

Pagano presented numerical results for several laminates made of a high-modulus graphite-epoxy composite material with 

Obviously, the classical lamination theory stresses in Pagano s example converge to the exact solution much more rapidly than do the displacements as the span-to-thickness ratio increases. The stress errors are on the order of 10% or less for S as low as 20. The displacements are severely underestimated for S between 4 and 30, which are common values for laboratory characterization specimens. Thus, a practical means of accounting for transverse shearing deformations is required. That objective is attacked in the next section. 

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