Best theory diagram for metallic and laminated composite plates

ABSTRACT

Best theory diagrams (BTDs) are reported in this article for the static analysis of metallic and laminated composite plates. A BTD is a curve that provides the minimum number of unknown variables of a structural theory for a fixed error. The error is related to a given variable with respect to an exact or quasi-exact solution. The theories that belong to the BTD have been obtained by means of the axiomatic/asymptotic technique, and a genetic algorithm has been employed to obtain the BTD. The Carrera Unified Formulation (CUF) has been employed to obtain refined models, since the CUF can generate automatically, and in a unified manner, any type of plate model. Equivalent single layer (ESL) and layer-wise (LW) kinematics are discussed. Closed-form, Navier-type solutions have been employed, and attention has therefore been restricted to simply-supported plates. The influence of various geometries, material properties, and layouts has been considered, and their influence on the BTD has been evaluated. Furthermore, some known theories have been evaluated and compared with the BTD curve. The results suggest that the BTD and the CUF can be considered as tools to evaluate the accuracy of any structural theory against a reference solution in a systematic manner.