Selection of appropriate multilayered plate theories by using a genetic like algorithm

This paper evaluates a number of classical and refined two-dimensional theories for the analysis of metallic and composite layered plates. Thin-plate, shear deformation and higher order plate theories are compared for various plate problems related to different mechanical and geometrical boundary conditions (BCs), as well as geometries and staking sequence lay-out. The theories are implemented by referring to a Unified Formulation (UF) proposed by the first author. The UF allows displacement fields with any order N in the thickness plate direction to be introduced and any variables in the N-order displacement field to be discarded. The finite element method is applied to include anisotropy and complex BCs. The accuracy of given theories for each fixed problem is established in terms of displacement and stress fields. The best plate theories, that is the most accurate plate theories with few computational efforts, is then determined by exploring various possibilities and by selecting appropriate unknown variables upon application of genetic algorithms. A best plate curve is established which shows the best plate theories (number of terms and their meanings) in terms of accuracy. It is concluded that a best plate theory changes with changing geometry, lay-out and BCs. The genetic algorithm used allows the least expensive computational model of each given problem to be detected.