Classical, Refined, Zig-Zag, Layer-Wise Models and Best Theory Diagrams for Laminated Structures

This chapter overviews classical and advanced theories for laminated plates and shell structures. Findings from existing historical reviews are used to confirm that the advanced theories can be grouped and referred to as Lekhnitskii multilayered theories, Ambartsumian multilayered theories, and Reissner multilayered theories. The unified formulation proposed by the first author, which is known as CUF (Carrera Unified Formulation), is used to make numerical assessments of various laminated plate/shell theories. The chapter provides details of a recent reliable finite element formulation for laminated shell analysis. It is embedded in the CUF framework, and it leads to the classical, zig-zag, and layer-wise models as particular cases. Numerical mechanisms such as shear and membrane locking are contrasted by developing an appropriate choice of shape functions and mixed assumed shear strain techniques. Furthermore, the Best Theory Diagram (BTD) is introduced as a tool to evaluate the accuracy of any structural model against a reference solution. The BTD is obtained through an axiomatic/asymptotic method (AAM) developed by the authors and using genetic algorithms. BTDs for plate and shell Equivalent Single Layer models (ESL) are presented, and guidelines and recommendations are provided for the proper development of refined structural theories.