Bending of composites and sandwich plates subjected to localized lateral loadings: a comparison of various theories

A unified compact formulation of theories for multilayered structures analyses, that has recently been proposed by the first author, is, in this paper, extended to study the response of composites and sandwich plates subjected to localized distribution of transverse pressure and to point loadings. Closed form `exactʹ solutions are presented by expanding the applied loadings in Fourier series. Relevant plate theories are compared. These theories cover the most significant aspects of two-dimensional modeling of layered structures: layer-wise and equivalent single layer variable descriptions are compared; classical models formulated with only displacement unknowns are compared to advanced ones that were obtained by employing the Reissner mixed variational theorem. Furthermore, the considered plate theories permit to evaluate the effect of both zig-zag form of the displacement field in the thickness plate direction and interlaminar continuity of transverse shear and normal stresses to be evaluated, as well as the role played by the transverse normal strain to be assessed. Four distinct benchmarks were examined in the numerical investigation: BM1 is related to a sandwich plate loaded by uniform distribution of transverse pressure on the top surface; BM2 and BM3 restrict the application of the transverse pressure of the BM1 case to a smaller areas located in the center of the plate; BM4 is related to a three layered plate subject to point loading. The stress and displacement fields in the vicinity of the loaded areas were compared to three-dimensional elasticity solutions and to available finite element analyses. It has been concluded in particular that: the issues that are already know for classical problems require amendment if localized loadings problems are analyzed; layer-wise analyses are required to capture localized stress/fields in the neighborhood of the loading area; transverse normal deformation must be taken into account to accurately predict behaviors of the sandwich core.