Multiobjective Best Theory Diagrams for cross-ply composite plates employing polynomial, zig-zag, trigonometric and exponential thickness expansions

Abstract

This paper presents Best Theory Diagrams (BTDs) for plates considering all the displacement and stress components as objectives. The BTD is a diagram in which the minimum number of terms that have to be used to achieve the desired accuracy can be read. Maclaurin, zig-zag, trigonometric and exponential expansions are employed for the static analysis of cross-ply composite plates. The Equivalent Single Layer (ESL) approach is considered, and the Unified Formulation developed by Carrera is used. The governing equations are derived from the Principle of Virtual Displacements (PVD), and Navier-type closed-form solutions are adopted. BTDs are obtained using the Axiomatic/Asymptotic Method (AAM) and genetic algorithms (GA). The results show that the BTD can be used as a tool to assess the accuracy and computational efficiency of any structural models and to draw guidelines to develop structural models. The inclusion of the multiobjective capability extends the BTD validity to the recognition of the role played by each output parameter in the refinement of a structural model.