Summary
A system of equilibrium equations governing a twelfth-order theory for the bending of thick plates is shown to be equivalent to a biharmonic equation together with four Helmholtz equations. These equations are closely related to equations derived by Cheng for an elasticity based thick plate theory. Detailed comparisons between the solutions for the displacements and stresses predicted by the approximate plate theory and an exact theory give some basis for deciding the applicability of the plate theory. As an example of the application of the solution procedure presented here, some earlier results for the decay parameters for the end problem for finite width plates are extended to the present case of twelfth-order plate theory.
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Chen, P.S., Archer, R.R. Solutions of a twelfth order thick plate theory. Acta Mechanica 79, 97–111 (1989). https://doi.org/10.1007/BF01181482
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DOI: https://doi.org/10.1007/BF01181482