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.

This paper presents refined one-dimensional (1D) finite element models develop by an effective nodal kinematics optimization method. The refined models belong to Best Theory Diagrams, which are built by using the Carrera Unified Formulation (CUF), Axiomatic/Asymptotic method and a Genetic Algorithm (GA). The influence of different chromosome types on the refined models and GA performance have been investigated. It is shown that the proposed method can improve the accuracy of regular 1D-CUF finite element models. Furthermore, the results suggest that it is possible to built refined models for compound loads from the ones optimized for individual loads.

This article presents a numerical solution for the static analysis of functionally graded porous deep curved beams with various boundary conditions. The main objective is to develop an accurate reference model for structures with high curvature and arbitrary support conditions, where simplified theories—such as higher-order shear deformation models—exhibit limited accuracy. The strong form of the governing equations is derived from two-dimensional elasticity theory for curved beams and solved using the Differential Quadrature Method, which ensures interlaminar continuity of displacements and stresses as well as boundary condition equations. Numerical validation is performed by comparison against results reported in the literature and those obtained using commercial finite element software. A parametric study is performed to investigate the influence of geometric curvature, material gradation, and porosity on the structural response. The results demonstrate the model’s capability to yield accurate solutions applicable to the design of curved structural components made of functionally graded materials.