N-objective genetic algorithm to obtain accurate equivalent single layer models with layerwise capabilities for challenging sandwich plates

This paper presents refined equivalent single layer plate theories develop by an effective N-objective optimization method, considering multiple displacements and stresses as output parameters. The refined plate theories reported belong to Best Theory Diagrams (BTDs), in which the minimum number of terms that have to be used to achieve a desired accuracy can be read. Maclaurin, high order zig-zag, trigonometric, exponential and hyperbolic terms are employed in order to investigate their influence on several static mechanical studies for sandwich plates. The used refined models are develop via the Unified Formulation developed by Carrera. The governing equations are derived from the Principle of Virtual Displacement (PVD), and Navier-type closed form solutions have been obtained in the case of simply supported plates subjected to bisinuisoidal transverse pressure. BTDs have been constructed using the Axiomatic/Asymptotic Method (AAM) and genetic algorithms (GA). The results are compared with the layer-wise solution in several benchmarks proposed in the literature. It is shown that the ESL plate models can accurately describe the displacement field and the mechanical stress fields predicted by a LW model with less computational effort, even for extreme theoretical cases. Furthermore, the method presented allows the user to analyze the influence of numerous test functions in a single run. The combined use of CUF, AAM and GA is a powerful tool to evaluate the accuracy of any structural theory.