Development of the consistent second-order plate theory for transversely isotropic plates and its analytical assessment from the three-dimensional perspective

In this paper, the consistent second-order plate theory is developed for transversely isotropic plates. It validated against three-dimensional elasticity using a well-known benchmark problem of simply-supported rectangular subjected to symmetric transverse sinusoidal loading. The choice based on fact that it allows an exact solution be derived in closed form. study, closed-form Elliot’s displacement potentials solids specifically validation purposes. Its equivalence other analytical solutions established. Expanding into power-law series with respect non-dimensionalised thickness enables direct term-by-term comparison and provides valuable mechanism validate plates purely term-by term reveals first terms above coincide exactly expressions theory. addition validation, numerical finite element method performed. A comparative analysis several theories demonstrates can predict displacements stresses thick very high degree accuracy, such even thickness-to-length ratio 0.5, deviation from less than 1%.