Hierarchical models for failure analysis of plates bent by distributed and localized transverse loadings

The failure analysis of simply supported, isotropic, square plates is addressed. Attention focuses on minimum failure load amplitudes and failure locations. von Mises' equivalent stress along the plate thickness is also addressed. Several distributed and localized loading conditions are considered. Loads act on the top of the plate. Bi-sinusoidal and uniform loads are taken into account for distributed loadings, while stepwise constant centric and off-centric loadings are addressed in the case of localized loadings. Analysis is performed considering plates whose length-to-thickness ratio a/h can be as high as 100 (thin plates) and as low as 2 (very thick plates). Results are obtained via several 2D plate models. Classical theories (CTs) and higher order models are applied. Those theories are based on polynomial approximation of the displacement field. Among the higher order theories (HOTs), HOTsd models account for the transverse shear deformations, while HOTs models account for both transverse shear and transverse normal deformations. LHOTs represent a local application of the higher order theories. A layerwise approach is thus assumed: by means of mathematical interfaces, the plate is considered to be made of several fictitious layers. The exact 3D solution is presented in order to determine the accuracy of the results obtained via the 2D models. In this way a hierarchy among the 2D theories is established. CTs provide highly accurate results for a/h greater than 10 in the case of distributed loadings and greater than 20 for localized loadings. Results obtained via HOTs are highly accurate in the case of very thick plates for bi-sinusoidal and centric loadings. In the case of uniform and off-centric loadings a high gradient is present in the neighborhood of the plate top. In those cases, LHOTs yield results that match the exact solution.