On the effects of trigonometric and exponential terms on the best theory diagrams for metallic, multilayered, and functionally graded plates

This paper presents Best Theory Diagrams (BTDs) employing combinations of Maclaurin, trigonometric, and exponential terms to build two-dimensional theories for metallic, multilayered, and functionally graded plates. The BTD is a curve in which the least number of unknown variables to meet a given accuracy requirement is read. The present refined models are Equivalent Single Layer and are implemented by using the Unified Formulation developed by Carrera. The plate theories presented are obtained using the axiomatic/asymptotic method and genetic algorithms. A multiobjective optimization technique is employed to analyze multiple displacements and stresses simultaneously. Closed-form, Navier-type solutions have been obtained in the case of simply supported plates loaded by a bisinusoidal transverse pressure. The influence of trigonometric and exponential terms in the BTDs has been studied for different materials and length-to-thickness ratios. The results show that the addition of such terms can lead to enhanced BTDs in which fewer unknown variables than pure Maclaurin expansions are needed to detect 3D like accuracies.