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This work deals with the linearized buckling analysis of laminated plates and shells. A variable-kinematics approach with hierarchical capabilities is considered to establish the accuracy of a large variety of classical and advanced plate/shell theories in order to evaluate buckling loads. So-called equivalent-single-layer as well as layerwise-variable descriptions are implemented. Interlaminar continuity of transverse shear and normal stresses are a priori fulfilled by referring to Reissner's mixed variational theorem. Stability equations are derived in compact form by referring to Carrera's unified formulation for the most general case of doubly curved shells. The eigenvalue problem is solved in the case of closed-form solutions related to simply supported boundary conditions and axially loaded multilayered plates/shells made of orthotropic layers. The cases of axial constant strains and constant stresses are considered and compared to available three-dimensional and two-dimensional results. Results related to Love and Donnell approximations are implemented for comparison purposes. The accuracy of various approximations is established for significant multilayered plate and shell problems. DOI: 10.2514/1.J050203

This paper presents a failure analysis of simply supported, orthotropic plates subjected to global/local bending loadings via the Navier-type solution. Carrera's unified formulation is adopted in order to implement a large variety of two-dimensional theories. The minimum first-ply failure loading and the failure locations are obtained via classical, refined, zig-zag, layerwise, and mixed theories. The maximum stress, Tsai-Wu, Tsai-Hill, Hoffman, and Hashin failure criteria are assumed. The accuracy of two-dimensional theories is assessed via comparison with the three-dimensional Pagano's solution, which has here been extended to the considered cases. The influence of the side-to-thickness ratio, the aspect ratio, the material properties, the lamination layup, and the loading localization is investigated. A hierarchy among the Carrera's unified formulation two-dimensional models has been established.

A study of the transverse normal strain effect on the static thermoelastic response of homogeneous and multilayered plates is presented. Numerical evaluations have been given for classical, refined, and advanced zig-zag plate theories. Constant, linear, and higher-order forms of temperature profile in the plate thickness direction have been accounted for. Basic assumptions of the considered theories are quoted. The related governing equations are not given because these were derived from a unified formulation that was described elsewhere. Closed-form solutions are discussed by addressing three plate problems: a homogeneous plate made of an isotropic layer; a two-layered plate consisting of two layers made of different isotropic materials; a multilayered composite plate made of three cross-ply layers. It has been confirmed that any refinements of classical models are generally meaningless, unless the effects of transverse shear and normal strains are both taken into account in a plate theory. Furthermore, it has been found that transverse normal strains cannot be discarded even though thin plates are considered and the accurate description of the temperature profile in the plate thickness direction could result to be meaningless, unless transverse normal strains are taken into account, and vice versa.

Two-dimensional theories and finite elements are assessed to analyze displacement and stress fields in sandwich, composites plates. Two benchmarks are used to conduct the assessment. The first benchmark is a sandwich plate loaded by harmonic distribution of transverse pressure for which a three-dimensional closed-form solution exists in the literature. The second benchmark is a rectangular sandwich plate loaded by a transverse pressure located at the center. More than 20 plate theories and finite elements were implemented in a unified formulation recently proposed by the authors. Classical theories based on displacement assumptions are compared to advanced mixed models formulated on the basis of Reissner's mixed variational theorem. Both equivalent single-layer models as well as layerwise models are considered. Analytical closed-form solutions and finite elements are given. The considered benchmarks highlight both the performance and limitations of the considered two-dimensional theories. The convenience of layerwise description and advanced mixed theories has been demonstrated. The second benchmark especially proved the need for layerwise models to capture the local effects.