Abstract
Sixth and twelfth order plate theory solutions for cylindrical bending plate problems, efficiently obtained by a preliminary reduction of the twelfth order theory for general cylindrical bending to a boundary value problem for a fourth order ODE, demonstrate the adequacy of these theories for the interior of thick plates with a thickness-to-span ratio λ up to ½ (at least). In contrast. Kirchhoff's classical thin plate theory is not adequate for values of the same ratio greater than 1/10. Comparison with the corresponding interior solutions of 3-D elastostatics shows that the twelfth order theory captures the (numerically small) first order correction term in the thicknessto-span parameter ε not possible by lower order plate theories. While it is a qualitatively important feature, this additional term associated with the effect of transverse normal stress does not significantly improve the plate theory approximation quantitatively for Isotropic plates.
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