Two benchmarks to assess two-dimensional theories of sandwich, composite plates

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.