Results on best theories for metallic and laminated shells including layer-wise models

This paper deals with Best Theory Diagrams (BTDs) for metallic and laminated shells. The BTD is a curve that is defined over a 2D reference frame in which the horizontal axis indicates the error of a shell model with respect to a reference solution whereas the vertical axis indicates the number of displacement variables of the model. The best reduced model is a refined model that offers the lowest possible error for a given number of variables. The relevant terms of a model are detected by means of the axiomatic/asymptotic method (AAM), and the error is related to a given variable with respect to an exact or quasi-exact solution. In this work, a genetic algorithm has been used to obtain the BTD. The Carrera Unified Formulation (CUF) has been employed to build the refined models. The CUF makes it possible to generate automatically, and in a unified manner, any plate or shell models. Equivalent Single Layer (ESL) and Layer Wise (LW) refined models have been considered. The governing equations for shells have been obtained through the Principle of Virtual Displacements (PVD), and Navier-type closed form solutions have been considered. BTDs have been constructed by considering the influence of several parameters, such as various geometries, material properties, layouts, different displacement/stress components and loadings. The accuracies of some well-known theories have been evaluated and compared with BTD reduced models. The results suggest that, since the BTD depends on the problem characteristics to a great extent, the systematic adoption of the CUF and the AAM can be considered as a powerful tool to evaluate the accuracy of any structural theory against a reference solution for any structural problem.