Second-order linear plate theories: Partial differential equations, stress resultants and displacements

By combining the uniform-approximation technique with the pseudo-reduction approach, a consistent second-order plate theory is developed with recourse to neither kinematical assumptions nor to shear-correction factors by truncation of the elastic energy. The governing partial differential equations and the expressions for the stress resultants are compared with those of other authors. Free coefficients of the resulting displacement “ansatz” are determined a posteriori, in order to satisfy three-dimensional boundary conditions and local equilibrium equations.