Two consistent variants of a sixth-order theory for elastic plate bending are developed together with corresponding three-dimensional statically and kinematically admissible solutions. The relative mean square error of these solutions as compared with exact elasticity solutions is found to be proportional to the thickness squared in analogy with previous estimates for Reissner’s theory, but the contribution to the error governed by transverse shear deformability is reduced and shown to be of the order of the thickness cubed, this contribution being decisive in composite plates.

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