Best shear deformation theories based on polynomial expansions for sandwich beams

An up-to-date problem in analysis of composite beams is to analyze higher-order beam theories with a considerable number of displacement variables and evaluate the influence of each term in order to reduce the model computational cost. In this paper the optimization of those higher-order beam theories to find the best theories in terms of accuracy and computational efforts is presented. The analysis is carried out by the so-called N-objective optimization evolutionary technique. The refined beam models are developed in the framework of the Carrera Unified Formulation (CUF). The influence of polynomial shape strain functions over the cross-section of the sandwich beam is investigated. The governing equations are derived from the Principle of Virtual Displacement (PVD), and Navier closed form solutions have been obtained in the case of simply supported beams subjected to bi-sinusoidal transverse pressure. The best or refined theories reported belong to a Best Theory Diagrams (BTDs), in which the optimum number of terms that should be used to achieve a desired accuracy can be read. The results of refined models are compared with the solution of a robust full model of order nineteen in two benchmark beam problems. It is shown that considering polynomial expansions can enhance the refinement of higher order models with less computational effort.